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Breakdown Probability Model at Freeway-Ramp Merges Based on Driver Behavior

Permanent Link: http://ufdc.ufl.edu/UFE0024857/00001

Material Information

Title: Breakdown Probability Model at Freeway-Ramp Merges Based on Driver Behavior
Physical Description: 1 online resource (177 p.)
Language: english
Creator: Kondyli, Alexandra
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: behavior, breakdown, cooperative, driver, forced, merging, turbulence
Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre: Civil Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: BREAKDOWN PROBABILITY MODEL AT FREEWAY-RAMP MERGES BASED ON DRIVER BEHAVIOR A freeway-ramp merging model that considers vehicle interactions and their contribution to the beginning of congestion was presented. Focus group discussions were conducted to attain knowledge about drivers? thinking process when merging. Three types of merging maneuvers were considered (free, cooperative, and forced), based on the degree of interaction between the freeway and the ramp merging vehicle. Field data collection was undertaken to quantify the effect of individual driver characteristics on their merging decisions and associate those with the breakdown occurrences at the freeway-ramp junctions. The data collection entails observations of participants driving an instrumented vehicle and simultaneous video observations of the freeway during these experiments. Behavioral characteristics of the participants were also evaluated. The collected data were used for calibrating driver behavior models that pertain to ramp vehicles? gap acceptance decisions and freeway vehicles? decisions to decelerate, change lanes or not interact subject to the ramp merging traffic, considering their behavioral attributes. A merging turbulence model was developed that captures the triggers for vehicle decelerations at the merging areas. The merging turbulence model due to vehicle interactions was evaluated through macroscopic observations at near-congested conditions. It was shown that the merging turbulence can be used as an indicator of the breakdown events.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Alexandra Kondyli.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Elefteriadou, Ageliki L.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2010-08-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024857:00001

Permanent Link: http://ufdc.ufl.edu/UFE0024857/00001

Material Information

Title: Breakdown Probability Model at Freeway-Ramp Merges Based on Driver Behavior
Physical Description: 1 online resource (177 p.)
Language: english
Creator: Kondyli, Alexandra
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: behavior, breakdown, cooperative, driver, forced, merging, turbulence
Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre: Civil Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: BREAKDOWN PROBABILITY MODEL AT FREEWAY-RAMP MERGES BASED ON DRIVER BEHAVIOR A freeway-ramp merging model that considers vehicle interactions and their contribution to the beginning of congestion was presented. Focus group discussions were conducted to attain knowledge about drivers? thinking process when merging. Three types of merging maneuvers were considered (free, cooperative, and forced), based on the degree of interaction between the freeway and the ramp merging vehicle. Field data collection was undertaken to quantify the effect of individual driver characteristics on their merging decisions and associate those with the breakdown occurrences at the freeway-ramp junctions. The data collection entails observations of participants driving an instrumented vehicle and simultaneous video observations of the freeway during these experiments. Behavioral characteristics of the participants were also evaluated. The collected data were used for calibrating driver behavior models that pertain to ramp vehicles? gap acceptance decisions and freeway vehicles? decisions to decelerate, change lanes or not interact subject to the ramp merging traffic, considering their behavioral attributes. A merging turbulence model was developed that captures the triggers for vehicle decelerations at the merging areas. The merging turbulence model due to vehicle interactions was evaluated through macroscopic observations at near-congested conditions. It was shown that the merging turbulence can be used as an indicator of the breakdown events.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Alexandra Kondyli.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Elefteriadou, Ageliki L.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2010-08-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024857:00001


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BREAKDOWN PROBABILITY MODEL AT FREEWAY-RAMP MERGES
BASED ON DRIVER BEHAVIOR




















By

ALEXANDRA KONDYLI


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2009





































2009 Alexandra Kondyli







































To my parents












ACKNOWLEDGMENTS

I would like to thank my graduate advisor, Dr. Lily Elefteriadou of the University of

Florida for her insights and guidance throughout this dissertation and her valuable support

throughout all my years of study. I would also like to thank the remaining members of the

committee, Dr. Scott Washburn, Dr. Yafeng Yin, Dr. Siva Srinivasan, and Dr. Orit Shechtman,

for their assistance and their advices.

I would like to thank my friends and fellow students of the University of Florida

Transportation Research Center for their assistance during the data collection effort. Without

them, it would be impossible to complete this effort. Special thanks are addressed to Aaron Elias,

George Chrysikopoulos, Dimitra Michalaka, Seokjoo Lee, Grady Carrick, Kevin Heaslip, Irene

Soria, Daniel Sun, and Cuie Lu. I am also grateful to the staff at the Jacksonville Traffic

Management Center for their assistance and accommodations during the data collection effort.

Above all, I am grateful to my parents, Apostolos and Maria for their love and support.












TABLE OF CONTENTS

page

A C K N O W LED G M EN TS ............................................................................ .............................4

LIST O F TA B LES ...................... .............................................................................................. 8

L IST O F FIG U R E S ....................................................................................... ............................9

A B ST R A C T ................................................................................... ..........................................12

CHAPTER

1 IN TR O D U C TIO N ............................................................................... .............................14

Traffic Operations at Freeway-Ramp Merging Segments...................................................14
Driver Behavior at Freeway-Ramp Merging Segments .........................................17
Objectives of the Dissertation......................................... ............................................ 19

2 LITERATURE REVIEW ..................................................................... ...................... 20

Capacity and the Breakdown Process at Freeway Ramp Merging Segments ......................20
The N nature of Capacity ..................... .. ........ .. .... ... .................................21
Breakdown at Freeway Ramp Merging Segments and Its Causes................................24
Driver Behavior Models for Merging Maneuvers .............................. ......................27
Modeling Acceleration Behavior for MLC ................................. ......................28
Modeling Gap Acceptance for MLC............................................. ......................33
Integrated Models for MLC....................................................................................42
Mandatory Lane Changing Models Used in Simulation Programs......................................49
Merging Under Congested Conditions ........................................................55
Using Instrumented Vehicles to Study Driver Behavior.........................................56
Sum m ary of Literature Review ............................................................ ...................... 60

3 BEHAVIORAL BREAKDOWN PROBABILITY METHODOLOGY.............................63

M erging M odel Structure ..................................................................... ............................63
Free M erge M odel ......................................................................... ............................65
Cooperative M erge M odel....................................... ............................................66
Forced M erge M odel ................................................ ........................................... 68
Breakdown Probability Model Formulation ......................................................................68
Modeling the Behavior of the Freeway Vehicle........... ............. ......................72
Merging Turbulence and the Probability of Breakdown............................................77
Methodological Framework...................... ...................... ...........................77
D ata Types for M odels .................................................................. ......................78
R research Tasks ......................................................................................................... 80
Step 1 Conduct focus group meetings: ......................................................80
Step 2 Conduct field data collection effort: ..........................................80












Step 3 Calibrate the merging models: .................................. ......................81
Step 4 Develop merging turbulence models: ........................... .............. 81
Step 5 Develop breakdown probability model: .........................................81

4 FOCUS GROUP EXPERIMENTS ...................................................... ......................82

Setting U p the Focus Groups................................................................ ......................82
Overview of Focus Group Questions ................................................... ......................84
Focus Group Key Questions................................................................................................85
Question 1 Merging Process Under Free-Flowing Conditions and Selection of
A acceptable G aps ........................ ....... .............................................................85
Question 2 Merging Process Under Decreased Speed (40-60 mi/h)............................87
Question 3 Cooperative Merging and Forced Merging Maneuvers Under
Decreased Speed (40-60 mi/h)....................... .................................87
Question 4 Merging Under Stop-and-Go Traffic.........................................................87
Question 5 Effect of other people on driving behavior...............................................88
Assembly of Focus Group Data........................................ ..........................................88
Overview of the Freeway-Ramp Merging Process.................................... .........................88
Refining Merging Process Under Free-Flowing and Dense Traffic .............................88
Focus Group Results for Gap-Acceptance .................................... ......................89
Focus Group Results for Cooperative and Forced Merging..........................................91
Relationships Between Driver Behavior and Driver Characteristics ...................................95
O their O observations ............................................................................. ............................100
C onclusions..................................................................................... ......................................100

5 FIELD DATA COLLECTION.................................................................................102

In-Vehicle Data Collection .........................................102
Description of Instrumented Vehicle..................................................102
D driving R outes............................................................................... ....................103
Geometry of the Freeway Ramp Junctions ................................. ......................104
Selection of Participants.............................................................. ...................... 106
Data Collection Procedures ......................................................... ......................109
In-Vehicle Data Processing ...................... ......................... 110
Gaps with adjacent vehicles and gap change rates.............................................. 110
Speeds and accelerations...................................................... ...........................
V vehicle positions .................................................................. ............................ 111
Average density and freeway speed.................................................. ............111
Data Collection at the Jacksonville TMC........................................... ....... ...............111
TM C D ata Processing.................................................................. ......................113
Field Experiment Results..........................................................................................116
Overview of the Observed Merging Process........................................................... 116
Distinction of Merging Maneuvers ........................... ......................... 16
D river Behavior Types ................................................................ ...................... 119
Driver Decision-Making Process ................................................ ......................124
Summary and Conclusions ................................................................. ......................124












6 MODEL DEVELOPMENT............................................. .........................................126

Development of the Gap Acceptance Model.................................... ............. 126
Estimation Dataset for Gap Acceptance Model ...........................................126
The Gap Acceptance Model........................... ............................. ......................133
Development of the Deceleration Model....................................................136
Estimation Dataset for Deceleration Model .......................................... ............137
Dataset for initiation of cooperation........................ .... ....................137
Dataset for initiation of forced merging........................................................... 140
Deceleration Model Due to Cooperative Merging .........................................141
Deceleration Model Due to Forced Merging............................ ..................145
The Deceleration Probability Model ........................................... ......................148
The M erging Turbulence M odel................................... ............................................148
The Breakdown Probability Model .................................................... ......................151
Sum m ary and Conclusions ................................................................. ......................153

7 C O N C LU SIO N S ................................................................................ ............................155

R research Sum m ary ....................................................................... ..................................155
Research Conclusions.............................................. 155
Future R research .......................................................................... ....................................158

APPENDIX

A PRESCREENING QUESTIONNAIRES........................................... ......................160

Focus Group Questionnaire ............................................ .......................................... 160
Instrumented Vehicle Questionnaire .................................................. ......................163
Participants Background Survey.................................................. 165

B ROUTES FOR INSTRUMENTED VEHICLE EXPERIMENT .......................................167

A M R oute ...................... .......................................................................................................167
PM R oute ................................................................................................ ............. ...........168

C MEASURING LENGTHS ON DIGITAL IMAGES ..........................................169

LIST O F REFEREN CES...................................................................... .................................171

BIOGRAPHICAL SKETCH ............................................... ............................................ 177












LIST OF TABLES


Table page

2-1 Game matrix between freeway through vehicle and merging vehicle.......................... 39

4-1 Demographic characteristics of focus group participants........................... .......... 83

4-2 Factors affecting cooperative merge decisions for freeway vehicles ........................... 92

4-3 Factors affecting forced merge decisions for ramp merging vehicles .......................... 93

4-4 Factors affecting deceleration and lane-changing decisions of freeway vehicle, when
a ramp vehicle has initiated a forced merge................................................... 94

4-5 Behavioral categories based on focus group scenarios and background survey form...... 99

5-1 Demographic characteristics of instrumented vehicle experiment participants ........... 108

5-2 Merging maneuver categories............................................................ 118

5-3 Driver behavior types based on actual observations and background survey form........ 122

5-4 Demographic characteristics by driver behavior type ........................ ..................... 123

6-1 Statistics of merging position by ramp design.......................................................... 130

6-2 Statistics of ramp vehicle gap acceptance parameters by driver type for free merges ... 130

6-3 Statistics of ramp vehicle gap acceptance parameters by driver type for cooperative
m erges ............................................................................................... ............ ........... 13 1

6-4 Statistics of ramp vehicle gap acceptance parameters by driver type for forced
m erges ............................................................................................... ............ ........... 132

6-5 Parameter estimates for total accepted gap ........................................ 134

6-6 Statistics of dataset for forced merging model ......................................................... 140

6-7 Parameter estimates for MNL model........................................ 142

6-8 Parameter estimates for utility of initiation forced merge.......................................... 146












LIST OF FIGURES


Figure page

1-1 Critical ram p junction variables....................................................... .......................... 15

1-2 Bottleneck location at freeway-ramp merging segments......................... ............ 16

2-1 Lane changing model structure proposed by Ahmed (1999)........................................ 43

2-2 Lane changing model structure proposed by Toledo (2003) .......................................... 45

2-3 Structure of proposed model by Choudhury et al. (2007). ............................................. 47

2-4 Extended model proposed by Choudhury et al. (2007) ....................................... 49

3-1 Conceptual description of merging process.......................................... ........... ..... 63

3-2 The lead, lag, and total gap. .............................................................. ..................... 64

3-3 The free-m erge m odel ....................................................................................................... 66

3-4 The cooperative-m erge m odel. ........................................................ .......................... 66

3-5 The forced-m erge m odel.................................................................. ..................... 68

3-6 Interactions between the mainline vehicle N and the ramp merging vehicle R
resulting to deceleration or lane change of vehicle N...................... ......... ........... 70

3-7 Following vehicle in shoulder lane (F) and interacting mainline (M) and ramp (R)
vehicles. ............................................................................................ ............................ 70

3-8 Deceleration event due to ramp merging maneuver ..................... .......... ........... 71

3-9 Potential freeway vehicle decisions due to a ramp merging maneuver........................ 73

3-10 Nested model for cooperative behavior of mainline vehicle N .................................... 74

3-11 M ethodological plan. ....................................................................... ......................... 80

4-1 Figures discussed during scenario 1 ................................................ ..... ................ 85

5-1 Inside view of the TRC instrumented vehicle............................................ 103

5-2 Geometric characteristics of tapered entrance ramps on 1-95....................................... 105

5-3 Geometric characteristics of parallel entrance ramps on 1-95. ..................................... 105

5-4 Location of available cameras along 1-95........................................ 112












5-5 Camera field of view along 1-95. .......................................................... 113

5-6 Observed breakdown locations and congestion propagation along 1-95 SB direction,
and N B direction. ........................... ....... ............................................................ 114

6-1 The ramp, lag and lead vehicle, their related gaps and positions ................................. 127

6-2 Distribution of ramp vehicle speed ......................................... 128

6-3 Distributions of the lag, lead, and total gap. ........................................ 128

6-4 Relationship between total gap and proportion of acceleration lane used by driver
type and m maneuver type. ................................................................ ..................... 135

6-5 Relationship between total gap and ramp vehicle's acceleration by driver type and
m maneuver type ................................................................................ .......................... 135

6-6 Relationship between total gap and average density by driver type and maneuver
type.................................................................................................... ............. ........... 136

6-7 Distribution of relative speed between the freeway vehicle and the ramp vehicle, and
freeway vehicle speed for initiation of cooperation ............................................ 138

6-8 Distribution of average density, and speed difference between the freeway vehicle
and the average speed on the right lane for initiation of cooperation........................... 139

6-9 Probability of decelerating, changing lanes or no cooperating as a function of the
distance to end of the acceleration lane for conservative and non-conservative drivers.
.................. ...................................... 143

6-10 Probability of decelerating, changing lanes or no cooperating as a function of the
cluster size for conservative and non-conservative drivers. ......................................... 143

6-11 Probability of decelerating, changing lanes or no cooperating as a function of
distance to the ramp vehicle for conservative and non-conservative drivers ............... 144

6-12 Forced merging probability as a function of average density and driver's
aggressiveness.......................................................... ................................................. 147

6-13 Forced merging probability as a function of proportion of acceleration lane used and
driver's aggressiveness. ................................................................. ..................... 147

6-14 Forced merging probability as a function of the ramp vehicle acceleration and
driver's aggressiveness. ................................................................. ..................... 148

6-15 Time-series of speed and number of decelerations on October 9th, 2008..................... 149

6-16 Relationship between total freeway and ramp flow and probability of merging
turbulence. .......................................................... ..................... 151












6-17 Breakdown probability model and merging turbulence...................... ................ 152

C-l Image geometry with horizontal camera axis and measurements on the digital image.. 169












Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

BREAKDOWN PROBABILITY MODEL AT FREEWAY-RAMP MERGES
BASED ON DRIVER BEHAVIOR

By

Alexandra Kondyli

August 2009

Chair: Ageliki Elefteriadou
Major: Civil Engineering

A freeway-ramp merging model that considers vehicle interactions and their contribution

to the beginning of congestion was presented. Focus group discussions were conducted to attain

knowledge about drivers' thinking process when merging. Three types of merging maneuvers

were considered (free, cooperative, and forced), based on the degree of interaction between the

freeway and the ramp merging vehicle. Field data collection was undertaken to quantify the

effect of individual driver characteristics on their merging decisions and associate those with the

breakdown occurrences at the freeway-ramp junctions. The data collection entails observations

of participants driving an instrumented vehicle and simultaneous video observations of the

freeway during these experiments. Behavioral characteristics of the participants were also

evaluated.

The collected data were used for calibrating driver behavior models that pertain to ramp

vehicles' gap acceptance decisions and freeway vehicles' decisions to decelerate, change lanes or

not interact subject to the ramp merging traffic, considering their behavioral attributes. A

merging turbulence model was developed that captures the triggers for vehicle decelerations at

the merging areas. The merging turbulence model due to vehicle interactions was evaluated












through macroscopic observations at near-congested conditions. It was shown that the merging

turbulence can be used as an indicator of the breakdown events.












CHAPTER 1
INTRODUCTION

Traffic Operations at Freeway-Ramp Merging Segments

Freeway-ramp merging segments are important components of the freeway facilities since

they connect the freeway system and the adjacent arterial network, and also they feed traffic into

the freeway. These segments are also the source of dynamic interactions, as they involve the

merging of two traffic streams. Conflicts occur because these segments usually serve as physical

bottlenecks (acceleration lane is dropped after some length), and the two traffic streams are

competing for the same space. The literature has described the dynamic interactions between the

two traffic streams as either cooperative (through vehicles move to the inner lanes, or yield to

create gaps for the merging vehicles) or competitive (merging traffic forcing its way into the

freeway, causing the through vehicles to decelerate). It has also been observed that the composite

behavior of acceleration and gap acceptance of the merging traffic and the cooperative behavior

of the freeway traffic can result in conflicts and even congestion.

In the current version of the Highway Capacity Manual (HCM 2000), the analysis of a

freeway facility is based on segmenting the facility to basic freeway segments, ramps and ramp-

junctions and weaving segments, neglecting possible interdependencies between the different

freeway segments, and the impact of these on capacity (TRB, 2000). The Ramps and Ramp

Junctions methodology (Chapter 25, HCM 2000), defines the ramp influence area to be a 1,500 ft

long segment downstream of the gore (which includes the acceleration lane and the two outmost

lanes of the freeway) and the operations of vehicles within that segment is the focus of the

analysis. An illustration of the ramp influence area as well as other important variables used in

the HCM methodology is provided in Figure 1-1.






















Figure 1-1. Critical ramp junction variables (Source: HCM 2000-Chapter 25).

In addition, the HCM 2000 provides a clear connection between the definition of capacity

and the breakdown occurrence. According to the manual, capacity is defined as "...the

maximum hourly rate at which persons or vehicles reasonably can be expected to traverse a point

or a uniform section of a lane or roadway during a given time period, under prevailing roadway,

traffic and control conditions" (HCM 2000, p. 2-2). Inherent to this definition is the notion that

once capacity is achieved, the freeway facility will break down (transition from free-flowing

conditions to congestion, i.e., level of service F); otherwise there is still the potential of

observing higher maximum flows. This is also associated with the development of queues

upstream of the bottleneck, indicating excess of demand.

In the field, capacity at ramp junctions is typically measured at the bottleneck (as shown in

Figure 1-2), where vehicles are in discharge state. Capacity cannot be measured inside the queue

because the flow there is restricted by the downstream capacity (beyond the front of the queue)

(Elefteriadou et al., 2006). On the other hand, capacity at basic freeway segments cannot be

measured in the field, as the literature has not shown any evidence that these segments can break

down without the presence of a bottleneck or other sources of demand restriction.



















Capacity
SMeasurement


Figure 1-2. Bottleneck location at freeway-ramp merging segments.

In addition to the measurement issues of capacity, the literature has examined various

definitions of capacity. Suggested flow rates from the literature that define capacity are: (1) the

maximum pre-breakdown flow; (2) the average pre-breakdown flow; and (3) the flow rate after

the upstream queue has formed (Elefteriadou et al., 2006). Irrespective of whether capacity is

defined as the maximum or the average pre-breakdown flow or queue discharge flow, the

literature has shown that this is not a fixed number, but rather a random variable (Persaud and

Hurdle, 1988, 1991; Agyemang-Duah and Hall, 1991; Minderhoud et al., 1997; Lorenz and

Elefteriadou, 2001; Brilon, 2005).

Regarding the breakdown events and the beginning of congestion at freeways, research has

shown that breakdown does not always occur at the same demand levels (Elefteriadou et al.,

1995; Okamura et al., 2000). Moreover, the HCM 2000 states that (pp. 25-3) "... the turbulence

due to merging and diverging maneuvers does not affect the capacity of the roadways involved,

although there may be local changes in lane distribution and use", but field observations show

the opposite. The data show that at merging segments, the presence of platoons of ramp vehicles

that want to merge and "squeeze" on the freeway (Elefteriadou et al., 1995; Kerner and Rehborn,

1996, 1997; Yi and Mulinazzi, 2007) may have "invasive influences" on the freeway vehicles,

such as decelerations and lane changes. These observations lead to the conclusion that


Vehicle Queue


Bottleneck












breakdown events at freeway merging segments are associated with the interactions between the

two competing traffic demands, and this might explain the observed variability in capacity.

Driver Behavior at Freeway-Ramp Merging Segments

In the previous section it was shown that driver behavior affects capacity and traffic

operations at freeway-ramp merging segments. Based on Rasmussen's model (1986) driver

behavior can be divided into a hierarchical structure with three levels:

* Strategic level: At this level the driver determines its goals and plans its route. The
decisions made at this level, are affected by driver's familiarity with the transportation
network and by any available real-time information.

* Tactical level: At this level the driver selects certain maneuvers to achieve short-term
objectives (e.g. interactions with other drivers). Here, driver behavior is influenced by
both the most recent action, and the driver's goals at the highest level.

* Operational level: At this level, the driver performs real actions such as steering,
accelerating, and gearing. These actions are skill-based and mostly done automatically,
with little conscious effort.

Several interactions can be observed between the different driving tasks: At the strategic

level, the driver makes decisions related to the path choice and to determine a schedule for the

trip (e.g. in terms of desired arrival time). Tactical decisions are affected by the vehicle's driving

neighborhood and by the strategic concerns. For example, the driver has to be in the correct

lanes in order to follow the path plan. If the trip schedule is not kept or in the presence of traffic

information the driver may decide to reevaluate the path plan and switch paths. The choices of

speed and lane are translated to mechanical actions to control the vehicle. In turn, the outcome

of these actions affects the positioning of the vehicle within its neighborhood.

Travel behavior researchers study drivers' strategic choices (level 1) while the operational

behavior (level 3) is studied in human factors research. Driving behavior models capture tactical

decisions at level 2. The most notable driving behavior models are acceleration and lane

changing models. Other important driving behaviors include negotiation of intersections and












merging areas and response to signals and signs. Two of the most important microscopic models

in traffic engineering, car-following and lane changing, are tactical-level models.

Car-following models describe the vehicle's behavior while following the leading vehicle.

Car-following models assume that the subject vehicle reacts to the leader's actions. Recent

research developed general acceleration models that also capture the behavior of drivers in other

situations; such as in car following and free-flow conditions. Based on these models, drivers that

are not close to their leaders may apply free-flow acceleration to reach their desired speed. Lane

changing models have mostly been developed for micro-simulators. The lane changing process

is normally modeled in two steps: (i) the decision to consider a lane change and (ii) the execution

of the lane change. Lane changes are further classified as either mandatory (MLC) or

discretionary (DLC). MLC are performed when the driver must leave the current lane, such as in

freeway-ramp merging segments. DLC are performed to improve vehicles' driving conditions.

In the vicinity of freeway-ramp junctions, mandatory, but also discretionary lane changes take

place (DLC are performed upstream to avoid conflicts with the ramp merging vehicles). Recent

research categorizes lane changes depending on the degree of interference with the adjacent

vehicles, to free, cooperative and forced lane changes. Lane changes are usually modeled using

gap acceptance models.

Existing driving behavior models have several limitations. An important limitation is that

inter-dependencies between vehicles' behaviors are not addressed, as different behaviors are

modeled separately. Most significantly, the combination of merging and lane changing behavior

on the traffic operations of the freeway is ignored. Similarly, factors that influence drivers'

decisions while performing (or being affected by) merging maneuvers have not been studied

from the drivers' perspective. Lastly, although driver behavior parameters are crucial for the












investigation of breakdown occurrences at freeway-ramp merges and gap acceptance decisions,

these are not explicitly incorporated in current models. The unavailability of driver-related data

may lead to inaccurate models since decisions at the tactical level are very much dependent on

the interactions between individuals.

Objectives of the Dissertation

The objectives of this research can be summarized as follows:

1. To develop a ramp merging model that considers the merging process near congested
conditions, as it is perceived by individual drivers. The scope of this objective includes the
following elements:
* The ramp merging model should address all different types of merging maneuvers, such as
free, cooperative and forced merging.

* The model should capture the vehicle interactions that occur during the merging process.
It should also account for stochasticity of driver behavior in accepting gaps and in making
decisions, for the same driver and across all drivers. An in-depth analysis of the drivers'
perspective is required to collect information about factors that affect their decision process
and their behavioral differences. The model should also consider the geometry of the
merging area as a factor.

* The behavior of the freeway vehicles upstream of the merge point (lane changing activity)
should be addressed in all relevant components of the merging model. Evaluation of the
effect of the lane changing behavior on the distribution of gaps, and therefore the merging
process, will be performed.

* The effect of cooperative and forced merging on the traffic conditions should also be
addressed. The research will quantify the impact of these maneuvers on the probability of
breakdown.

2. To develop an analytical model that can determine the probability of breakdown on the
freeway given the behavior of both mainline and ramp merging vehicles.












CHAPTER 2
LITERATURE REVIEW

The chapter summarizes past research related to the estimation of capacity at freeway ramp

merging segments and the description of the breakdown phenomenon at these locations, either

through observational studies or through modeling of the driver behavior. The first section

describes previous research efforts to model the behavior of the merging vehicle (acceleration,

lane changing, and gap acceptance) and discussion on specific models that have been used in

microsimulation programs follows. The next section presents findings regarding the merging

process under complete congested conditions. Following that, a summary of literature review on

driver behavior-related studies is presented. This chapter concludes with a summary of the

literature findings and their limitations.

Capacity and the Breakdown Process at Freeway Ramp Merging Segments

According to the current version of the Highway Capacity Manual (HCM 2000) the

capacity of a facility is defined as "...the maximum hourly rate at which persons or vehicles

reasonably can be expected to traverse a point or a uniform section of a lane or roadway during a

given time period, under prevailing roadway, traffic and control conditions (HCM 2000, p. 2-2)."

This definition implies that once capacity is achieved, the facility will break down; otherwise

capacity has not been attained (HCM 2000 also notes that capacity is the upper boundary of LOS

E). Thus, the observation of breakdown is closely related to the capacity of a facility.

Several studies that focused on the capacity of freeway segments and the investigation of

the speed/flow/density relationships have observed traffic flow and the breakdown process in the

vicinity of ramp merges that usually serve as freeway bottlenecks. The findings of these studies

vary significantly, and this indicates that (i) capacity is stochastic in nature, (ii) individual

drivers' behavior may trigger the breakdown phenomenon, (iii) vehicles merging onto the












freeway from an on-ramp may create traffic turbulence, which can result in freeway flow

breakdown.

The Nature of Capacity

According to the definition of capacity used by the HCM 2000, each facility type has

different capacity values; however these remain invariable for facilities with similar geometric

and traffic conditions. For example, capacity values are given as 2,250 passenger cars per hour

per lane (pcphpl) for freeways facilities with free-flow speeds of 55 miles per hour (mph), and

2,400 pcphpl when the free-flow speed is 75 mph (under ideal geometric and traffic conditions).

While the current version of the HCM treats capacity as a deterministic value that depends

on the geometric conditions of the facility, there is a significant amount of recent literature based

on field data observations, which contradicts this argument, and proposes that capacity is

stochastic in nature. Researchers have come to acknowledge the stochasticity of capacity,

however this has raised several other questions related to which value of flow rate should be

measured (maximum pre-breakdown flow rate, pre-breakdown flow rate, discharge flow rate),

where and when it should be measured, what time interval should be used, and if it is a random

variable what percentile of the distribution should be used as the descriptive statistic. The

remaining of this section presents proof from the literature that capacity rather stochastic than

deterministic in nature.

Persaud and Hurdle (1991) examined various definitions and measurement issues for

capacity; such as maximum flow, mean flow, and expected maximum flow definitions. Based

on observations of field data at a three-lane freeway site, over three days, they recommended that

the mean queue discharge flow is the most appropriate, partly due to the consistency they

observed in its measurement.












Agyemang-Duah and Hall (1991) collected data over 52 days on peak periods to

investigate the capacity drop issue when a queue forms, and to recommend a numerical value for

capacity. They showed that the distribution of pre-queue flows and queue discharge flows in 15-

minute intervals, with the first one slightly more skewed toward higher flows. They

recommended two capacity values: one for pre-breakdown conditions at 2,300 pcphpl, and one

for post-breakdown conditions at 2,200 pcphpl. They recognized the difficulty in defining and

measuring capacity, given the variability observed.

Wemple et al. (1991) also collected near-capacity data at a freeway site and discussed

various aspects of traffic flow characteristics. High flows (above 2,000 vphpl) based on fifty 15-

min time periods were identified, plotted, and fitted to a normal distribution, with a mean of

2,315 vehicles per hour (vph), and a standard deviation of 66 vph.

Elefteriadou et al. (1995) developed a model for describing the process of breakdown at

ramp merge junctions. Observation of field data showed that, breakdown may occur at flows

lower than the maximum observed, or capacity flows. In addition, it was observed that, at the

same site and for the same combination of ramp and freeway flows, breakdown may or may not

occur. Elefteriadou et al. developed a probabilistic model for describing the process of

breakdown at ramp merges, which gives the probability that breakdown will occur at given ramp

and freeway flows, and it is based on the occurrence of ramp-vehicle clusters.

Minderhoud et al. (1997) also studied the random nature of capacity by considering

stochastic theories for estimating capacity. Similar to Wemple et al. they proposed a normal

distribution to describe the statistical properties of capacity. They were also the first who

proposed to estimate the distribution of capacity using the Product Limit Method based on field

observations. They borrowed the theory from lifetime statistics analysis, assuming that a system












failure (traffic breakdown) occurs when there is traffic spillback from the bottleneck; however,

they used flow observations taken from the upstream location. Thus, in this way they included

congested data points in the analysis, that are inside the queue, and volumes at that location may

be lower than the maximum possible. Brilon and Zurlinden (2003) and Brilon (2005) built upon

this method, although they assumed as events of failure cases of distinct breakdown observed at

the bottleneck and not upstream (also assuming that congestion does not propagate from

downstream). Brilon and Zurlinden (2003) evaluated various mathematical functions and they

concluded that the Weibull distribution provides the best fit to the empirical data.

Sarvi and Kuwahara (1999) performed an evaluation study of the merging capacity in

Tokyo Metropolitan Expressway to determine the impact of geometric design and traffic

characteristics on the capacity of seven merging sections. Based on their research, capacity is

positively related to the taper length, but no correlation with the length of the acceleration lane

was found. This may occur because under congested conditions the drivers try to merge soon

after entering the acceleration lane. Sarvi and Kuwahara also found that the merging capacity

increases slightly with increasing relative grade (ramp grade minus the freeway grade). With

respect to the merging ratio (percentage of merging flow), the evaluation concluded that capacity

increases when the merging ratio increases up to 0.32 and then decreases. Therefore, the

maximum capacity was observed for a 0.33 merging ratio, but it is noted that additional data are

required to identify the maximum capacity.

Okamura et al. (2000) collected data on several freeway sections in Japan over a whole

year where they observed several breakdown events. They considered that freeway capacity is

the average of the breakdown volumes (i.e., traffic volume immediately before the breakdown

event), which varied over a wide range.












Lorenz and Elefteriadou (2001) conducted an analysis of speed and flow data for two

freeway bottlenecks in Toronto, Canada. They suggested incorporating a probability of

breakdown in the definition of freeway capacity, such as: "...the rate of flow (in pcphpl and for a

particular time interval) along a uniform freeway segment corresponding to the expected

probability of breakdown deemed acceptable under prevailing traffic and roadway conditions in

a specified direction." The value of the probability component should correspond to the

maximum breakdown risk deemed acceptable for a particular time period. According to this

definition, on the average, highest flows occur before the breakdown.

Sarvi et al. (2007) performed an analysis of the macroscopic observations on driver

behavior, and showed that capacity (measured after the onset of congestion: i.e., discharge rate)

varies from one bottleneck location to another, and its range is between 1,679 and 2,068 vphpl.

An important finding of this research is that capacity at merge junctions were generally lower

than capacity at other freeway segments.

Breakdown at Freeway Ramp Merging Segments and Its Causes

Buckley and Yagar (1974) observed the breakdown phenomenon at an entrance ramp or

lane drop. According to their observations, at the entrance ramp drivers merge into minimal

gaps in the adjacent lane, and as they move downstream, they tend to increase their spacing to a

more acceptable distance. This occurs when initially drivers decelerate in a car-following mode,

and consequently, if one driver slows down then those upstream will need to decelerate more

rapidly. They suggested that this shock wave moving upstream is seen as the flow breakdown,

which becomes the long-term slow-and-go traffic condition observed upstream of the lane drop.

Elefteriadou et al. (1995) collected data using four video cameras along the ramp merge

area at two bottleneck locations, and they concluded that the breakdown was associated with the

presence of vehicle clusters coming from the on-ramp. Based on their observations, the ramp












vehicle clusters would "force" their way into the freeway and this would result in vehicles

slowing down and eventually the following vehicles would reduce their speed, creating an

overall sudden speed drop.

Similar to Elefteriadou et al. (1995), Yi and Mulinazzi (2007) found that the influences of

ramp vehicles on freeway vehicles (also defined as "invasive-influences") are related to the

presence of persistent platoons on the ramps. More specifically, they found that the number of

evasive events (slow down or change lanes) increases and the standard deviation decreases with

the merging platoon size. The note that these invasive-influences of the ramp vehicles may

cause the freeway vehicles to slow down and even change lanes. For the model development,

they observed the brake-light indications and lane change maneuvers to account for the evasive

behavior of the freeway vehicles that travel on the shoulder lane. They also defined the

following three merge situations depending on the arrival patters:

* Free Merge (FM): random arrival of ramp vehicle that does not interact with the freeway
vehicle,

* Challenged Merge (CM): ramp vehicles conflict with freeway vehicles on the shoulder
lane before merging, and

* Platoon Merge (PM): clusters of ramp vehicles force their way ignoring the priority order,
and trigger invasive-influences to the freeway vehicles.

The significance of the invasive-influence on the shoulder lane traffic was estimated by

considering: (i) the distribution of traffic on that lane; i.e., less traffic on the shoulder lane means

higher invasive-influence, and (ii) the speed decrease of the shoulder lane caused by the

persistent platoons. Lastly, the authors proposed alternative LOS indicators that correspond to

these relationships between the invasive-influence with volume shift and the speed reduction.

Kerner and Rehborn (1996, 1997) defined the breakdown phenomenon as the transition

from free-flow to synchronized flow (average speeds are almost synchronized in different lanes).












Based on data from German highways, the free-flow to synchronized flow transition was

detected from the abrupt changes in the average speed. They stated that in bottlenecks,

breakdown occurs due to local speed decrease and density increase that is observed when on-

ramp vehicles "squeeze" on the highway or due to unexpected speed decrease and lane changing

activity.

Daganzo et al. (1999) presented a model describing traffic behavior, which assumes that

vehicles respond to changes in the speed of the lead vehicle in the same fashion, irrespective of

the past history. They defined the "deceleration disturbance" as occurring when one of the

vehicles in the platoon decelerates and allows a gap to grow in front of it to allow another vehicle

to merge in. This causes the following vehicles in the platoon to decelerate as well. Eventually,

the entire platoon returns back to the original speed, causing a wave to travel within the platoon

and propagate upstream. This results in further instabilities and perturbations, which lead to

higher densities and the development of "jam" states. They also defined "acceleration

disturbance" to occur when a vehicle accelerates and closes the gap in front of it. They

concluded that if the acceleration disturbances are persistent, then the queue disturbances could

propagate forward and reduce the flow through the bottleneck.

Daganzo (2002), assuming two types of drivers (fast-moving and slow-moving), modeled the

freeway breakdown event at a freeway ramp merging segment, as follows: Fast moving vehicles

stay in the passing (left) lane, willing to accept shorter headways, while on-ramp vehicles enter and

stay in the shoulder lane. Further downstream of the merge, fast-moving vehicles that had entered

from the on-ramp leave the shoulder lane and merge into the passing lane; thus they increase the

passing-lane flow (this is defined as the "pumping mechanism" as the drivers are willing to accept

reduced headways and let the on-ramp vehicles merge). In high and uncongested flow, fast-moving












vehicles follow each other in small headways, suggesting that they are "motivated" by their desire

to pass. When the through and/or the merging flow is high, the passing lane becomes saturated

downstream of the merge (because of the merging fast-moving vehicles), and a shockwave will

move further upstream. This also means that the passing-lane speed will decrease near the merge,

causing the fast-moving vehicles to lose their "motivation" to follow closely and change lanes to

equalize speeds; thus the queue on the passing lane eventually spills over to the shoulder lane. An

evaluation study of Daganzo's theoretical model was performed by Banks et al. (2003), where it

was concluded that some of the phenomena described in Daganzo's theory do occur, but not at

all locations, and that the underlying assumptions were oversimplified. More specifically, Banks

et al. verified the increase in time gaps (loss of motivation) but only at one site, but contrary to

Daganzo's model (and other literature), the speed equalization does not take place at all

locations. In addition, they did observe redistribution of flow among lanes, even though the

speeds were not equalized, and distinction between capacity and discharge flow were not

observed downstream from queues (as predicted by Daganzo).

Driver Behavior Models for Merging Maneuvers

Several studies have investigated the maneuvering decisions in order to model driver

behavior. These models are mostly valuable to microscopic simulators but also to safety and

capacity analysis where aggregate traffic flow characteristics can be obtained from modeling

individual drivers' behavior.

Generally, the literature on driver behavior models has studied mainly three significant

topics: acceleration, lane changing and gap acceptance. The acceleration models try to capture

the parameters that affect drivers' acceleration decisions and process, while the drivers are either

in a car-following situation or not. Therefore, these models can be grouped (Toledo, 2003) into

(1) car-following acceleration models (drivers reacting to the behavior of their leaders), and (2)












general acceleration models. This chapter provides an overview of the acceleration models that

were specifically developed to describe the acceleration of vehicles involved in merging

situations (usually, these models are focused on the ramp vehicles and the lag vehicles that

approach the merge area).

Typically, the lane changing models found in the literature contain two steps: the lane

selection process and the lane changing execution process, where gap acceptance formulations

are used for the model development. In addition to that, these models distinguish lane changes

into two categories: (1) discretionary lane changes (DLC) and (2) mandatory lane changes

(MLC). Discretionary lane changes are performed in order for drivers to improve their position

in the traffic stream. Mandatory lane changes are performed when drivers must leave the current

lane, in order to follow a specific route, such as in merging from the acceleration lane on the

freeway, or because of a lane drop or lane closure due to work zone activity.

The literature review included in this section, provides a discussion on all models related to

MLC, since this type of lane changes describes the ramp merging behavior. A description of

specific DLC models that were developed in conjunction with components for MLC is also

available, because this type of lane changes can be observed at the vicinity of ramp junctions, as

the mainline vehicles may choose to avoid any disruption from the merging vehicles. Past

research focused on the development of merging models integrating both gap acceptance and

acceleration decisions is also provided in this section.

Modeling Acceleration Behavior for MLC

Significant amount of research has focused on modeling the acceleration of either the ramp

or the freeway vehicles near the merge area. Kou and Machemehl (1997) presented a

methodology for modeling the acceleration-deceleration behavior of ramp vehicles. Merging

vehicle position data and freeway and ramp volume data from both parallel and taper ramps were












obtained and analyzed (both long and short segments). The volume data cover off-peak and peak

periods; however fully congested conditions were not included.

In short acceleration lanes, most of the traffic (approximately 70 percent) merges at the

section where the acceleration lane width decreases from 12 ft to zero (parallel-type) or at the

section immediately after the gore, where the acceleration lane width drops from 12 ft to 9.5 ft

(taper). At long acceleration lanes it was found that the merging position is not affected by the

flow levels, which does in fact contradict the initial hypothesis that the larger the freeway and

ramp flow rates the longer the distance ramp vehicles travel in the acceleration lane.

No significant relationship was found between ramp vehicles' speed and distance to

complete the maneuver, or between time to complete the maneuver and time lags with the

freeway lead/lag vehicles; however, this may be the result of limited data availability. Finally,

they did conclude that as the speed differential between the ramp vehicle and the freeway lag

vehicle increases, the merging percentage decreases.

The ramp vehicle acceleration-deceleration model was based on the stimulus-response

concept implemented in the car-following models, with respect to the distance lag, D. The

methodology was expanded linearly to incorporate the influence of the freeway vehicles and the

ramp geometric constraints. Solving for the non-linear regression for D = 0, 18.29, and 36.58 m

(0, 60, and 120 ft) yielded that the best calibrated acceleration-deceleration model was for D

=18.29 m (60 ft):

xr.092(d + 18. 29 )[
X,(d + 18.29) = -2.145 + 0.002 '- (d 0135 [Xgd) X(d)
[X,(d) Xfla(d).
Xk1.092(d +18.29) [
-0.020 r 699 [X(d) Xfead(d)] (2.1)
[Xflead(d) Xr(d)
X I 092(d +18.29) [ 1
+ 3.484 1726 (d)]
[L- X,r(d)iL











Where:
Xri(dj): Location of ramp vehicle i when it passes the fiducial mark j,
Xfljgi(dj): Location of corresponding freeway lag vehicle for ramp vehicle i when
vehicle i passed the fiducial mark,
Xfleadi(dj): Location of corresponding freeway lead vehicle for ramp vehicle i when
vehicle i passed the fiducial mark,
X,,(dj): Velocity of ramp vehicle i when it passes the fiducial mark,
X flag(d ): Velocity of the corresponding freeway lead vehicle i when vehicle i when
it passes the fiducial mark j,
X,(dj + D): Acceleration rate of ramp vehicle i at location dj+D,

The relevant R-square value was 0.566. A weakness of the proposed model is that it was

calibrated with a limited amount of field data. In addition, the ramp merging position was found

not to depend on any traffic parameter, which is controversial with common expectations and

requires further examination.

Research conducted along the Tokyo Metropolitan Expressway in Japan (Sarvi et al.,

2002) has focused on modeling ramp vehicle acceleration-deceleration behavior during the

merging process in congested conditions. This methodology also, uses the stimuli-response

equation to model the acceleration-deceleration behavior. In their research they introduce three

stimuli to evaluate the ramp vehicle response. These are the relative speed regarding the freeway

leader, the relative speed regarding the freeway lag vehicle and the spacing regarding the

freeway leader. The hypothesized expression of the ramp vehicle acceleration-deceleration

behavior of a ramp platoon leader entering the freeway is given as:


aR(t + T) = a + a, VR(t+T) [VFlead(t) VR(t)]
[X Flead(t) X R(t)1
Vm + T)
+ a2 ( ) 2 [VR(t) VFlag(t) (2.2)
S[XR(t) XFlag(t)

+ a [ {S(t) f [v(t)]}
S[x ,ead(t) XR(t
Where:
aR(t+T): Acceleration rate of the ramp vehicle at time t+T (m/s2)












XR(t): Location of the ramp vehicle at time t (m)
XFlead(t): Location of the freeway lead vehicle at time t (m)
XFiag(t): Location of the freeway lag vehicle at time t (m)
VR(t): Speed of the ramp vehicle at time t (m/s)
VFlead(t): Speed of the freeway lead vehicle at time t (m/s)
VFiag(t): Speed of the freeway lag vehicle at time t (m/s)
S(t): Spacing between the ramp vehicle and the freeway leader vehicle at time t
(m) (XFlead(t)-XR(t))
f[v(t)]: Desired spacing as a function of speed (m)
T: Time lag or driver reaction time (s)

Although the data collected were not enough to cover all geometric conditions, they were

used to calibrate the acceleration models. Two sets of models were investigated, linear and non-

linear acceleration models, and these were proven to be equally significant.

Sarvi and Kuwahara (2005) have also developed an acceleration-deceleration model for the

lag vehicle that approaches the merge area from the freeway under congested flow. They

investigated the lag vehicle behavior in terms of its relative speed and spacing with its

corresponding ramp and freeway lead vehicles. In their method, they used a non-linear

specification to the stimuli-response equation.

Field data were collected through videotapes and image processing techniques during

congestion periods. Based on the data, the lag vehicle has higher speed than the ramp vehicle in

the beginning of the acceleration lane, but the lag vehicle either decelerates (to accommodate the

merging) or the ramp vehicle accelerates (to force the merging). Next, the vehicle continues to

accelerate to reach the leader vehicle. The leader and ramp vehicles have higher speeds than the

lag vehicle.

The modeling of the lag vehicle is built upon previous work for modeling the ramp vehicle

merging (Sarvi et al., 2002). The main stimuli identified are the relative speed and spacing

between the lag vehicle and its leading and ramp vehicles. The lag vehicle acceleration-

deceleration behavior is given by the following expression:












aa(t + T ao + +T) [VFa (t) V (t)
Flag+ ) 0 1 XFad(t) XF(t1Flag

(t+ A ati at + T)he f y l v a t
S(t) f lag (2.3)


+VR(t): Spd oSt t t [( t )








VF1ead(t)t Speed of the freeway lead vehicle at time t (m/s)
+a4 XR( x ( t) {()2 f[v(t)]}

Where:
AFiag(t+T): Acceleration rate of the freeway lag vehicle at time t+T (m/s)
XR(t): Location of the ramp vehicle at time t (m)
XFlead(t): Location of the freeway lead vehicle at time t (m)
XFS(t): SLocation of the freeway lag vehicle at time t (m)
VR(t): Speed of the ramp vehicle at time t (m/s)
VFlead(t): Speed of the freeway lead vehicle at time t (m/s)
VFlag(t): Speed of the freeway lag vehicle at time t (m/s)
S(t)2: Spacing between the freeway lag vehicle and the freeway leader vehicle at
time t (m) (XFlead(t)-XFlag(t))
S(t)2: Spacing between the freeway lag vehicle and the ramp vehicle at time t
(m) (XR(t)-XFlag(t))
f[v(t)]: Desired spacing as a function of speed (m)
T: Time lag or driver reaction time (s)
ao, a,a2,a3,a4: Parameters
m, l,12,13,14 : Parameters

This acceleration model was calibrated through linear and non-linear regression. Even

though the non-linear model has greater R-sq value than the linear model, this difference was not

significant, thus the linear model is sufficient for replicating the vehicle interactions.

Sarvi et al., (2000) developed a simulation program that was used for calibrating and

validating the ramp vehicle acceleration model (Sarvi et al., 2002) and the lag vehicle

acceleration model (Sarvi and Kuwahara, 2005), in conjunction with field measurements. In

both cases the authors compared the vehicle trajectories from simulation data and the field data

and it was shown that there is agreement between the two trajectories.












Kesting et al. (2007) presented a car-following model that includes the lag vehicle in the

decision-making process and it is focused on modeling the acceleration. Safety constraints are

also considered in the lane changing decision. The utility of a lane changing increases if the gap

with the lead vehicle increases; however, if the speed of the lead vehicle is lower, then the

subject vehicle may decide to stay on the present lane. They proposed a lane changing utility

function that considers the difference in the accelerations (or decelerations) after the lane

changing. For example, higher acceleration on a given lane suggests that this is closer to the

"ideal" acceleration on an empty road; thus, it is more appealing to the driver. Another

important feature of the proposed model is that it considers a "politeness" factor, which denotes

in essence the (dis-)advantage of the lag vehicle (degree of cooperativeness). Moreover, the

model considers a safety threshold which guarantees that after the lane change the deceleration

of the follower will not exceed a given safe limit.

Examination of the lane changing rate through simulation showed that this primarily

depends on the politeness factor. The politeness factor is an important model parameter,

however, the proposed model represents only the last decision of whether to change lanes or not.

Thus, information related to the decisions prior to the final lane-changing step, is not provided.

Lastly, it is suggested that varying the safety threshold changes the "critical" lane change and

this could further affect the breakdown probability.

Modeling Gap Acceptance for MLC

During the past 20 years, research has been involved with the study of gap acceptance

during the merging process. Michaels and Fazio (1989) developed a freeway ramp merging

model based on driver behavior. The concept of the model is that ramp drivers accept a gap

based on an angular velocity. Michaels and Fazio note the continuous process of acceleration

and gap-acceptance, and they distinguish several discrete tasks during the merging maneuver.












These are (1) the ramp curve tracking, (2) the steering transition from the ramp to the

acceleration lane, (3) acceleration, (4) gap search, and (5) steering transition from acceleration

lane to freeway or abort. During the gap search task the angular velocity is defined as the first

order motion vector relative to the ramp driver and it is estimated as:

w =k(V, V,)/l2 (2.4)
Where:
w: Angular velocity (rad/sec)
Vf: Freeway vehicle speed (ft/sec)
Vr: Ramp vehicle speed (ft/sec)
1: Distance separation (ft)
k: Lateral offset (ft)

The angular velocity may have three different values, depending on the relative velocity

and the distance. When the speed of the ramp vehicle is greater than the speed of the freeway

vehicle (angular velocity is negative), this is an opening condition, and the ramp driver can

merge as long as there is sufficient gap from the lead vehicle. When the speed of the ramp driver

is less than the speed of the freeway driver (angular velocity is positive), this is a closing

condition, and the merging decision depends on the angular velocity of the following vehicle, as

long as the ramp vehicle is always behind the lead vehicle over the whole segment of the change

speed lane. The third situation occurs when the relative speed and distance generate angular

velocity below the threshold of 0.004 rad/sec (angular velocity is zero). An important hypothesis

made, is that the merging maneuver can be an iterative process under congested conditions,

where the ramp vehicle accelerates and searches for a gap iteratively, until its speed reaches that

of the freeway.

In their model, they also incorporated the ramp curvature and the gap distribution function

of the freeway traffic. Under heavy traffic conditions it was found that: (1) the median angular

velocity is consistent with the literature, (2) drivers tend to decrease their speed between












successive accelerations as they are in a gap search process and not in_speed control, and (3) the

probability of merging increases with successive trials. Based on the proposed model, the authors

present a procedure for estimating the length of the acceleration lane to provide adequate gaps.

These findings indicate that the length is independent of freeway volume over a range of 1,200 to

2,000 pcphpln and that 650-800 ft is a sufficient lane length to ensure 85% or more merging

opportunities for ramp drivers (for most used ramp design speeds). The proposed model however

does not consider the interactions between the merge vehicles and the freeway vehicles as it

assumes that the merging traffic has no influence on the mainline traffic.

Kita (1993) examined the merging behavior on an on-ramp section in the case where the

merging vehicles are running slower than the through vehicles. The author developed: (1) a gap

acceptance model that describes the merging behavior based on the merging probability and (2) a

method to relate the safety level in a merging section with road and traffic characteristics.

The gap acceptance model (only sections with parallel acceleration lanes and not tapered

were used) was based on a binary logit model of "accept" or "reject" choices of a sequential gap

choice process. This model also considers the influence of the merging lane length on the

driver's decision process. The two alternative choices are formulated as:

1
1 + exp[- (U -U)] (2.5)
P, =I P

Where:
Pi: Probability that a driver chooses the alternative i
Ui: Deterministic part of the drivers utility to the alternative i
i: Alternatives (i = a: accept; i = r: reject)

and,

J
U, U, = 0o + YO>x (2.6)
j1













Where:
Xj: Explanatory variables
Oj: Parameters
(j = 1, ..., J)

Data from a three-lane freeway and one-lane ramp merging section were used for the

model calibration. The data included measurements of speed, gap length, and merging position

of each vehicle (distance from the merging nose to the point where the vehicle performs the

merging maneuver). The first gap is defined as the time difference between the time when the

merging vehicle reaches the merging nose and the follower vehicle reaches the merging nose.

The second gap is defined as the time headway between the first vehicle and the second vehicle

in the through traffic when the first vehicle reaches the same position as the merging vehicle.

Cases where the through vehicle would change lane to avoid a conflict with the merging vehicle

were excluded from the analysis. Additionally, when multiple merging occurred, only the data

of the first merging vehicle were considered.

The explanatory variables selected for the model calibration are the gap length (sec), the

remaining distance of the acceleration lane (m), and the relative velocity of the merging vehicle

to the corresponding through vehicle (m/sec). The resulted goodness-of-fit measure was

considered satisfactory (p2 = 0.785).

Kita also developed models for the distribution of the merging position and the time-to-

collision after merging, depending on the acceleration lane length. A case study to test the effect

of the acceleration lane length on the distribution of time-to-collision was also developed. It was

shown that the probability of a vehicle merging into a dangerous gap with shorter time-to-

collision decreases when the acceleration lane length is longer.












Ahmed et al. (1996) developed a lane changing model which captures the gap acceptance

process using discrete choice models. Lane changes were categorized as mandatory (MLC) and

discretionary (DLC). A driver that needs to perform an MLC may either respond immediately or

delay. This depends on the remaining distance, number of lanes to cross, and traffic density. If

the driver does not respond to an MLC situation (or MLC does not apply), then he/she decides

whether to consider a DLC or not, and its satisfaction with the current lane is evaluated. This

decision depends on speed differences, deceleration, heavy vehicle presence and presence of

ramps. Ahmed et al. developed a desired lane choice model (for both MLC and DLC) when

both the adjacent lanes are candidate lanes. The explanatory factors are the speed differentials,

deceleration, heavy vehicles, ramp presence and need for mandatory response. The last

parameter forces the vehicles to perform an MLC should they be in this situation and they

postpone the response.

The developed model was applied to the case of merging (MLC case). The gap acceptance

model presented by Ahmed et al. (1996) addresses issues of heterogeneity and state dependence.

The heterogeneity in the driver population was captured by introducing a random term in the

critical gap specification, which varies across different components of a gap for the same

individual, across different gaps for the same individual and across individuals. The lane

changing model is assumed to be binary logit. The probability that a lane changing takes place

given a gap is acceptable depends on several explanatory variables such as the time delay (since

the gap searching process began), the remaining distance to the point where the lane change must

be completed, the lag relative speed and a first gap dummy (captures the initial hesitation of the

drivers to merge as soon as they appear at the beginning of the acceleration lane). The model

formulation estimates both the lead and lag gap parameters separately. The lead critical gap was












found to be insensitive to traffic conditions, whereas the lag critical gap was found to be a

function of the relative speed, remaining distance to the point at which the lane changing must be

complete, and whether the gap is the first one considered or not. Ahmed et al. research captures

the structure of the decision process and it also accounts for the stochasticity in driver behavior,

but it does not capture any inter-dependence relation between the subject vehicle and the freeway

vehicles.

Kita (1999) modeled the interactions between the merging vehicle and the through vehicle

on on-ramp merging sections, using game theory. These interactions occur when the freeway

through vehicle on the shoulder lane, changes lane to accommodate the merging maneuver of the

ramp vehicle. Giveway behavior occurs when traffic conflict with a merging vehicle is likely to

happen, and it deals with low-speed merging where the speed of the merging vehicle is lower

than that of the through vehicle. This study supplements a previous study performed by the

author (Kita, 1993) which dealt with the influence of the freeway through vehicles to the

merging behavior of the ramp vehicles. The interaction is modeled as a zero-sum non-

cooperative game, where each driver chooses their best action considering the forecast of the

other drivers, and its validity is tested through field data. Kita (1999) considers only the merging

and the through vehicles as their interaction is the most dominant, but their behavior may affect

the surrounding vehicles as well. It is also assumed that the number of games is one for each of

the through vehicles in conflict and these games are independent. The game can be characterized

as non-cooperative (the drivers cannot exchange any information) with perfect information (both

drivers know the situation that the other driver is facing). By solving for the equilibrium

condition the model derives the merging probabilities of a merging vehicle and the giveway

probabilities of a through vehicle.












Even though the merging vehicle may monitor the traffic conditions in a much wider area,

the model estimates the payoff functions (utility functions) for both merging vehicle and through

vehicle based only on their position and speeds relative to the neighboring vehicles, but it

indirectly accounts for the influence of the adjacent through lane in the equilibrium solution.

The concept behind this model is based on the assumption that the driver selects the action with

the lower risk level, where the risk is the time to collision (TTC). However, this assumption is

oversimplified and unrealistic, as it does not account for other factors such as the presence of the

leader in the through lane that creates unsafe conditions for merging directly.

Kita et al. (2002) presented an improved giveway behavior model based on game theory.

Kita et al. developed a method to estimate the payoff functions of merging and through vehicles

without any information about equilibrium selection (which is rather difficult to estimate), and

then analyzed the merging and giveway behavior by using the estimated method. In their

analysis, the merging-giveway behavior is described by the through vehicle that gives way and

the merge vehicle that merges in front of the through vehicle. In this situation, both vehicles

attempt to take best action by forecasting the other's behavior. This behavior is modeled as a

two-person non-zero-sum non-cooperative game under complete information. The actions of the

merge vehicle are either merging or passing up the specific gap and the actions of the through

vehicle are either to go with giveway or without giveway. The game matrix is defined as:

Table 2-1. Game matrix between freeway through vehicle and merging vehicle (source: Kita et
al., 2002)
Merging vehicle action Through vehicle actions
Go with giveway Go without giveway
Merge (F11,G11) (F12,G12)
Pass up (F21,G21) (F22,G22)












In this method a set of probabilities is assigned to each action. If the probability of the

merge vehicle merging is p and the probability that the through vehicle goes with giveway is q,

then the expected payoffs of the merge driver (EF(p,q)) and the through driver (EG(p,q)) are:

EF(p, q)= p.{q. F11 + (1- q) F12 }+(1 q) .{q. F21 + (1 q). F22
EG(p,q)= p.{qG11+(1-q).G12}+(1-q).{q-G21+(1-q).G22}
EG(p, q) = p j {q G + (I q) G1}+ (1 q) jq G21 + (I q) G221

Thus, the best response of a driver, which is the probability that maximizes their expected

payoff under the probability chosen by another driver, can be obtained from the derivative of the

equations above and by checking if it is positive or negative. The equilibrium condition is the

intersection point between the best responses of the drivers. The intersection point can be found

if both drivers know the payoffs, however the external observer cannot estimate these

deterministically. For this reason, Kita et al. consider that the equilibrium to be utilized is

selected in a probabilistic manner. The probabilities that each type of best response is given are

a function of the payoffs and also of factors that characterize the environment.

They examined three models for the payoff functions: a standard Time-To-Collision (TTC)

model, a log TTC model and a model that considers the influence of leading vehicles. The

estimation results showed that the model's capability of estimating the probabilities of

equilibrium selection are fairly good, and can be used for the analysis of phenomena with strong

interactions. This model however does not consider a minimum safe gap between the vehicles.

Another limitation is that it does not account for the fact that the merging vehicle will slow down

and stop at the end of the acceleration lane if it cannot merge safely. Also, it is assumed that all

vehicles travel at a constant speed, with no provision for slowing down for the through vehicle

when staying in the through lane. Lastly, it is assumed that the merging vehicle does not take

any action to improve its merging position.












Goswami and Bham (2007) studied the gap acceptance behavior using the NGSIM data,

along 1-80 in Emeryville, California. Their focus was to obtain statistical distributions for the

accepted and rejected gaps (and therefore, the critical gaps) in MLC maneuvers. Their

motivation to study the distribution of acceptable gaps derives from the fact that the minimum

acceptable gap does not represent the critical one, but only the gap acceptance behavior of an

aggressive driver.

The data consisted of vehicle trajectories between an on-ramp and an off-ramp, under both

uncongested and congested conditions. They examined the vehicle trajectories and considered

vehicle interactions to occur when their distance is 250 ft or less. The Gamma and Lognormal

distributions were tested for the (lag and lead) accepted gaps, and it was found that in some

occasions the gaps are Gamma-distributed, while in some others they are Lognormal-distributed.

They also used both deterministic (cumulative frequencies, acceptance curve) and stochastic

methods (maximum likelihood, logit, probit) for estimating the critical gaps and conclude that

the results from the logit and probit methods fit best to the data. Analysis of the critical gaps as a

function of the location of lane changes indicates that in uncongested conditions the critical gaps

(from the shoulder to the adjacent lane) are smaller than in congested conditions.

Zhang and Kovvali (2007) used the NGSIM data as well, to develop a gap acceptance

model for the mainline vehicles. They considered the mandatory lane changes (MLC) but only

from the vehicles exiting the freeway from the off-ramp at the study area. They evaluated 24

explanatory variables for the gap acceptance model, among these are: speeds, accelerations,

vehicle types, etc., for the subject vehicle and also the lead and lag freeway vehicles. Two

variables were also introduced, that are MLC-related, and these are the number of lane changes

required to exit from the off-ramp and the distance to the MLC point.












Comparison between accepted gaps in MLC and DLC showed that these are statistically

different (drivers in MLC situations select smaller gaps than in DLC). It was also found that the

gap size decreases with increasing number of MLC, and that there is correlation between the

acceptable time gaps and the distance to the MLC point (reveals drivers' urgency to change

lanes). They also showed a correlation between the vehicle size and the accepted gap between

the subject and the lag vehicles, (i.e., heavier vehicles accept larger gaps). Moreover, relative

speeds were found to have little effect on acceptable gaps in MLC. Examination of the

accelerations showed that the accepted distance gaps are smaller with higher subject vehicle

accelerations, and that relative accelerations do not affect gaps significantly. Regression models

of gap acceptance for both MLC and DLC were developed, however the regression coefficients

are 0.495 and 0.389 respectively, which shows that there are still other unidentified factors that

influence the gap acceptance process.

Integrated Models for MLC

Recent studies have developed models incorporating acceleration decisions to the merging

models. Ahmed (1999) developed a lane changing model and an acceleration model to describe

merging behavior under congested traffic. The structure of the lane changing model is presented

in Figure 2-1. The lane changing process is described in three-steps through discrete choice

framework: a decision to consider a lane changing, choice of a target lane and acceptance of gaps

in the target lane.

































Figure 2-1. Lane changing model structure proposed by Ahmed (1999).

Ahmed (1999) proposed a lane changing model for uncongested conditions and a forced

merging model for congested conditions based on his previous work (Ahmed, 1996). The lane

changing model includes the lane selection model and the gap acceptance model.

Ahmed introduces the term "courtesy yielding" of the lag vehicle and "forced merging" of

the subject vehicle to describe the proposed forced merging model. The merging vehicle

evaluates the traffic environment in the target lane continuously, to decide whether to merge in

front of the lag vehicle. The merging vehicle also communicates with the lag vehicle to check

whether his/her right of way is established. If both of these occur, then the vehicle initiates a

forced merging. If not, then the vehicle continues this process at the next time interval. Using a

binary logit model, the probability of switching from the "start a forced merging state" to the "do

not start a forced merging state" is modeled. Explanatory variables are the lead relative speed

when the lead vehicle is slower, the lag relative speed, the remaining distance to the point that












the merging must be completed, the delay, the sum of lead and lag gaps, and the presence of

heavy vehicles.

An important addition of Ahmed to the acceleration model was to include two

components: the car-following model and the free-flow acceleration model. Ahmed defined a

headway threshold to differentiate between the car-following regime and the free-flow regime.

Another improvement of the acceleration model proposed by Ahmed (1999) was that he relaxed

the assumption that the car-following stimulus is a linear function of the lead vehicle relative

speed and used the density in front of the subject vehicle to capture the impact of traffic

conditions. However, this model does not capture explicitly the impact of the lane changing

decisions on the acceleration decision.

Toledo (2003) developed an integrated driver behavior model that captures lane changing

and acceleration behaviors. The method is based on short term goals and plans. Drivers that

target a lane change but cannot change lanes immediately, choose a short-term plan, and adapt

their acceleration behavior to facilitate the lane changing. The model's structure searches for

interdependencies between the different decisions of lane changing and acceleration. The model

considers four levels of decision-making: target lane (lane choice), gap acceptance (lane

changing), target gap (gap choice) and acceleration.

Toledo introduces three mechanisms that allow capturing interdependencies between the

various decisions. These are causality, unobserved driver/vehicle characteristics and state

dependency. The causality captures the effect of lower level choices on higher level decisions,

because, the lower level choices are modeled conditional on those made at higher levels (e.g. the

acceleration is conditional on the short-term plan). This was done by introducing variables that

capture the expected maximum utility (EMU) of the alternatives at the lower level in the














specification of higher-level choices. A driver/vehicle specific variable was introduced in the

model to capture correlations between observations obtained from a given driver. Finally, the

state dependency mechanism aims in re-evaluating and potentially modifying the short-term

goals and plans due to changes in driving conditions. This also addresses the fact that different

combinations of short-terms and plans may result at the same observed conditions.

The target lane model integrates MLC and DLC into the same utility function for each

target lane, rather than considering separate utility functions (Ahmed, 1999). The conceptual

structure of the model is illustrated in Figure 2-2. Toledo integrated the two lane changing

situations to capture potential trade-offs between mandatory and discretionary considerations.






Target Left Current Righ
Lane


Gap No Change Change No
acceptance Change Left Right Change



Target Gap Gap Gap Gap
Gap L LM



Acceleration A ... Acc Acc Ac Ac .. c


Figure 2-2. Lane changing model structure proposed by Toledo (2003).

The gap acceptance model captures the decision whether to change lanes immediately

using the adjacent gap, conditional on the target lane choice. Explanatory variables for this

model are the subject's speed, the relative speeds with respect to the lead and lag vehicles, the

traffic density and the urgency of the lane changing. If the adjacent gap is rejected the driver

does not change lanes and he is assumed to create a short term plan by choosing a target gap on












the target lane. The driver chooses between the adjacent, the backward and forward gaps. The

explanatory variables affecting the utilities of each gap are the gap size, the gap trend, the

subject's relative speed, and the distance to the point where the lane change must complete.

Three acceleration models were developed: the stay-in-the-lane acceleration, the

acceleration during a lane changing (when the adjacent gap is accepted) and the target gap

acceleration (when the driver does not change lane immediately). Additionally, two driving

regimes are considered, depending on whether the operations are constrained or unconstrained.

The stay-in-the-lane acceleration model is based on the model developed by Ahmed (1999). The

constrained and unconstrained driving regimes assume car following and free-flow behaviors,

respectively. For the lane changing acceleration model it is assumed that the driver determines

the acceleration by evaluating the relations with the target lane leader. For the target gap

acceleration model, the driver constructs and executes a short-term plan which depends on the

target lane and the target gap choices. If unconstrained, the driver targets a desired position with

respect to the target gap, which would allow the lane change to be performed. In this case the

stimulus is the difference between the vehicle's desired and current position.

Although the proposed integrated model incorporates many different features and accounts

for drivers' planning capabilities, behavior-related data were not used for the model validation.

In addition, there is no accountability for lane changing during congested conditions, where

courtesy yielding and even forced maneuvers take place.

Choudhury et al. (2006, 2007) present a lane changing model for merging and weaving

that considers four levels of decision making process: normal gap acceptance, decision to initiate

courtesy merging, decision to initiate forced merging, and gap acceptance for courtesy and

forced merging. The structure of the proposed model is given in Figure 2-3.
































Figure 2-3. Structure of proposed model by Choudhury et al. (2007).

The data collected for this model are part of the Federal Highway Administration (FHWA)

Next Generation Simulation (NGSIM) project. The data include vehicles' trajectories (position,

acceleration and speed) along the Interstate 1-80 in Emeryville, California, during transition to

congestion and congested conditions. Observations of the lead, lag and the subject vehicle were

recorded in a second-by second basis. The distributions of the relative speeds and gaps show

that when a gap is accepted, the subject vehicle is traveling slower than the lead vehicle and

faster than the lag.

For the gap acceptance model, a gap is accepted if it is greater than the critical gap, which

is modeled as a random variable following lognormal distribution.

ln(G )= ig ,,x + aig *u + (2.8)
g e {lead, lag}, i e {normal, courtesy, forced}
Gt : Critical gap g of individual n at time t for merge type i,
Xt : Vector of explanatory variables,
igT : Corresponding vector of parameters that depend on the merge type,












'g : Random term for gap acceptance for merge type i of individual n at time t,
u,: Driver-specific random term,
ai" : Coefficient of the driver-specific random term of gap g, and merge type i.

The model assumes that the driver must accept both lead and lag gaps in order to perform a

lane change. Explanatory variables are the relative speed between the subject and lead/lag

vehicles, the remaining distance to the MLC point and the acceleration of the lag vehicle. If the

gaps are unacceptable the driver evaluates the speed, acceleration, and relative position of the

freeway vehicles and anticipates a gap that will be available in a later time. If these gaps are still

not acceptable, then the subject vehicle will consider initiating a forced merge. Variables that

affect the decision to initiate a forced lane changing are related to the status of the merging driver

(distance to the MLC point, delay (intolerance), and speed), the lag vehicle status (vehicle type,

speed and acceleration), and the traffic conditions (congestion level and tailgating dummy).

Choudhury et al. (2007) recently extended their model by integrating drivers' acceleration

and deceleration actions to facilitate their merging maneuvers. They incorporated three different

acceleration models (Figure 2-4), which are: lane change_acceleration and target gap acceleration

(similar to Toledo, 2003), and initiated courtesy/forced merging acceleration. The lane change

acceleration occurs when the existing gaps are acceptable and it is based on the relative speed

with the leader. The target gap acceleration is performed when the subject vehicle seeks an

improved position with respect to the lead and lag vehicles (can select forward, adjacent or

backward gap). The initiated courtesy/forced merging acceleration seeks to obtain an improved

position while in the subject lane, with respect to the lead and lag vehicles. These acceleration

models are still under development and have not been finalized to this moment.
















Gap f
A aep c i l m e e e e i mc





Artiiipad_ ( ,,











to provide a more realistic representation of traffic operations. Yang and Koutsopoulos (1996)



priority, while the lane changing model distinguished between MLC and DLC lane changes. In
Sam i I n


New Adia t Gap NeE Adjacenit G!


Figure 2-4. Extended model proposed by Choudhury et al. (2007).

Mandatory Lane Changing Models Used in Simulation Programs

Lane changing rules and models have been extensively used in microsimulation programs

to provide a more realistic representation of traffic operations. Yang and Koutsopoulos (1996)

presented the Microscopic Traffic SIMulator (MITSIM) where they implemented a rule-based

lane changing model. They presented a merging model, separately from the lane changing

model. The merging model is classified into: (i) priority-based merging and (ii) merging without

priority, while the lane changing model distinguished between MLC and DLC lane changes. In

contrast to other models, merging from on-ramps is modeled through the merging model and not

through the MLC model. More specifically, the priority-based merging includes merging from

on-ramps or dropped lanes to the freeway, and from minor to major streets, and the merging

without priority includes merging downstream of toll plazas. They define that MLC occurs

when vehicles have to change lanes to (i) connect to the next link on their path, (ii) bypass a lane












blockage, (iii) avoid entrance to a restricted use lane, and (iv) respond to LUS or VMS. DLC

occurs when a driver wants to increase speed, or overtake a heavy vehicle, or to avoid the lane

connected to an on ramp.

For the priority-based merging model, the merging vehicle checks whether there is an

upcoming vehicle and executes the maneuver only if the projected headway gap is acceptable. If

the headway gap is not acceptable, the vehicle either calculates the acceleration rate (by treating

the freeway vehicle as leader) or stops at the end of the acceleration lane, depending on which

case is the critical one.

In addition, the merging model incorporates a courtesy yielding parameter in case the

vehicle decides to decelerate to create space for another vehicle to merge. This is done by

assigning a probability of courtesy yielding to the drivers, and applying the deceleration rate

calculated from the car-following model; however not enough details are provided about this

process.

The lane changing algorithm in MITSIM (based on Gipps model) is implemented in three

steps: (i) check the necessity of lane change and define its type (mandatory or discretionary), (ii)

select desired lane, (iii) execute lane changing if gaps are acceptable. For DLC, the decision to

change lane is based on traffic conditions on both current lane and adjacent lanes. The model

introduces an impatience factor and a speed indifference factor, to determine whether the speed

is low enough and the speeds at the adjacent lanes are high enough for considering a lane

changing. A lane change is executed only if both the lead and lag gaps are acceptable. The

critical gaps used in MITSIM are assumed to follow the lognormal distribution.

Hidas (2002) presented a lane changing and merging algorithm implemented in the

simulator named Simulation of Intelligent TRAnsport Systems (SITRAS). Key aspects of these












algorithms are the forced and cooperative lane changing modules, which are significant for

modeling congested traffic conditions. The necessity of a lane change is evaluated in each

simulation interval, and depending on the situation (turning movement, incident, end-of-lane,

transit lane, speed advantage, queue advantage), it can either be essential, desirable, or

unnecessary. Next, the feasibility of the lane change is examined, depending on the gap

availability at the target lane. A lane change is considered feasible if (i) the

deceleration/acceleration needed for the subject vehicle is acceptable, and (ii) the deceleration

required by the potential follower is acceptable. An aggressiveness parameter is incorporated to

the deceleration calculation, to differentiate between driver types.

When an MLC is warranted, the lane selection process is terminated. Hidas incorporated

the driver courtesy in the case of forced lane changes. This concept deals with the reduction in

acceleration required for the potential new follower to allow the subject vehicle to move to the

target lane. Other important elements presented by Hidas (2002) with respect to the merging

model, are:

* acceptance of shorter critical gaps than those that derive from the car-following model,

* implementation of acceleration in order for the subject vehicle to better position during the
lane change,

* implementation of lane changing behavior for the right-lane freeway vehicles approaching
the ramp merge, if ramp vehicles are present, in order to avoid any friction,

* application of lower deceleration when ramp vehicles try to merge into the freeway using
very short gaps, instead of using large deceleration that could potentially disturb the
freeway flow, and,

* application of the driver courtesy function only to congested traffic conditions.

In 2005, Hidas presented an updated version of SITRAS (renamed to ARTEMiS), for

simulating lane changing and merging models under congested conditions. The objective of the

lane changing model in ARTEMiS is to determine under which conditions a vehicle is allowed to












move into the target lane, and consider the issue that the drivers are willing to tolerate much

shorter gaps when they can anticipate the actions of other drivers, and do not use the maximum

but a moderate deceleration.

Data collected in the field showed that in congestion, lane changes occur at short gaps and

that the accepted gaps are more closely related to the relative speed between the leader and the

follower than to the absolute speed of the follower vehicle. It was also shown that when the

leader is faster than the follower, the minimum accepted gap was constant, but if the leader is

slower than the follower, the minimum accepted gap increases with the speed difference.

Analysis of gap acceptance led to the classification of lane changing maneuvers as free,

forced and cooperative. Free lane changing occurs when there is no significant change in the

relative gap between the leader and follower, which means that there is no interference between

the subject and the follower vehicle. Generally, in a free lane change there is no interaction

between the vehicles. Forced lane changes are associated with apparent change in the gaps

before and after the merge point, i.e., the gap between the leader and the follower was either

constant or narrowing before the merge and it widens after the merging vehicle enters. Thus, the

subject vehicle forces the follower to decelerate. In essence, the subject vehicle plays an active

role by initiating the merge, and the follower reacts to that action. In cooperative lane changes

the gap between the leader and the follower is increasing before the entry point and it decreases

afterwards, which indicates that the follower decelerates to allow the vehicle to merge. In

cooperative lane changes, at first, the subject vehicle indicates its willingness to move to the

target lane, then the follower acknowledges the situation and cooperates by slowing down, and

eventually, the subject vehicle realizes that the follower gives way and when the gap is long

enough, it merges.












Wang et al. (2005) present a model of freeway merging behavior that considers the

acceleration and gap acceptance behavior. The authors introduce two plausible

behaviors/reactions of the freeway traffic approaching the merge: cooperative lane changing (to

allow vehicles to merge) and courtesy yielding (decelerate to create gaps). The following series

of sub-models are introduced to capture the merging behavior and to develop the simulation

model:

* Cooperation model: It captures the cooperative yielding behavior and the cooperative lane
changing, that essentially facilitates the merging process by creating gaps for the ramp
vehicles.

* Acceleration model: It captures the acceleration-deceleration decisions of the merging
vehicle. It is influenced by the target gap on the freeway, the leading vehicle on the
acceleration lane and the remaining distance to the end of the acceleration lane. They
modeled the ramp vehicle's acceleration to reach the speed of the leading vehicle, as well
as the deceleration of the vehicle based on the relative speed and gap with the leader. If
the speed of the merging vehicle is very close to the speeds of the follower or the leader
(small relative speeds), another acceleration model is employed which aims in creating
larger lead or lag gaps. A parameter for the driver aggressiveness is also introduced. The
model incorporates a maximum acceptable deceleration as an urgency, to prevent the
merging vehicle from running into the vehicle in front or the end of the acceleration lane.

* Gap selection model: It is based on the speed of the merging vehicle and its position
relative to the freeway leader and follower. The target gap is assumed to be the adjacent
gap, unless different situations occur, such as a fast moving vehicle that overtakes the
leader on the acceleration lane and takes the previous gap as its target gap, or a slow
moving vehicle that chooses to take the following gap.

* Gap acceptance model: It is based on the game theory idea proposed by Kita et al. (2002)
where the merging vehicle makes a decision considering the forecast of the other vehicles'
actions and its own actions. The model calculates the acceptable lead and lag gaps as a
function of the speed, merging driver's reaction time and maximum decelerations of the
merging, the leader, and the follower vehicles, depending on their projected reactions to
the merging process.

* Merge model: It captures the presence of an acceptable gap and the merging process.
However, if the vehicle is reaching towards the end of the acceleration lane and an
acceptable gap is not found then a merge failure is registered.

The model was tested through simulation and a sensitivity analysis was performed to

evaluate how the parameters affect the merging process. The model was found to be sensitive to












the length of the acceleration lane and the average freeway flow. For long acceleration lanes and

low speed on the freeway, the merging failures were fewer and there is a greater chance that a

following gap will be chosen. The optimal acceleration lane length for smooth merging

(accepting the adjacent gaps) was found to be approximately 100 meters (330 ft.). With longer

acceleration lanes vehicles tend to take the following gaps and not the adjacent gaps. It was also

found that the accepted lead and lag gaps decrease with increasing flows but these do not vary

with increasing merging flows. The authors tested a range of values for the gap acceptance factor

and the driver's reaction time and compared the derived outputs with field data from the

literature; however, a direct calibration of the proposed model parameters was not performed.

CORSIM (Halati et al. 1997) distinguishes three types of lane changing: (i) mandatory, (ii)

discretionary and (iii) anticipatory lane changes. Mandatory lane changes are considered in the

following situations: (i) merging traffic entering on the freeway, (ii) lane changing for diverging

traffic to exit the freeway, (iii) leaving a blocked lane due to an incident, (iv) vacating a dropped

lane. In CORSIM, a lane change is performed if both lead and lag gaps are acceptable. The gap

acceptance process involves a risk factor. More specifically, the model compares the acceptable

level of risk (acceptable deceleration) for avoiding collision, between the potential follower and

the merging vehicle. The acceptable risk factor depends on lane changing type, driver type, and

urgency of lane changing.

In addition, vehicles initiate the merging as soon as they enter the acceleration lane.

Merging vehicles' acceleration is determined by considering that it car-follows a stopped

'dummy' vehicle at the end of the acceleration lane and this is compared with the deceleration

required to stop at that location. The minimum of the two decelerations is applied. CORSIM












also models the anticipatory lane changes of the freeway vehicles that give up the shoulder lane

to avoid potential conflict and speed reduction caused by the merging traffic.

VISSIM applies a psychophysical model that presents critical gaps as thresholds depending

on the relative speeds of the subject vehicle and the assumed leader and follower. Lane changing

vehicles may accept progressively higher deceleration rates as an urgency to complete the

merging maneuver. At the same time, the merging vehicles may cause the through vehicles to

accept higher deceleration rates as the merging vehicle approaches the end of the acceleration

lane. During lane changes the subject vehicle may accelerate to facilitate its maneuver, and there

is provision for cooperation between the vehicles.

Merging Under Congested Conditions

Various researchers have contributed to the investigation and modeling of merging

behavior during congested traffic conditions. Sarvi et al. (2002) performed research for

modeling ramp vehicle acceleration-deceleration behavior during the merging process in

congested conditions. Based on the field data collected at two ramp junctions along the Tokyo

Metropolitan Expressway, Sarvi et al. observed that the merging behavior under congested

conditions occurs on a one-by-one basis regardless of the length of the available gap (also

referred to as zip merging or zipper effect). The authors do not make use of the gap acceptance

methodology because previous research (Sarvi and Kuwahara, 1999) found that during heavy

congestion, unstable or stop-and-go traffic flow appears to take place, and the gap searching and

acceptance maneuvers do not occur. This zip merging behavior has been characterized also as

turn-taking merging by Cassidy and Ahn (2005), who showed that the merging occurs in an

almost one-by-one basis, and this ratio remains constant at each site, irrespective of the merge

outflow. Furthermore, Sarvi et al. (2007) performed an analysis of macroscopic observations on

driver behavior, and they showed that under congested conditions, the ratio of ramp flow over












the total flow does not affect the capacity of the merging segment. They further observe that the

opposite occurs during merging under free flowing conditions, where the distribution of these

two volumes is related to the easiness of the merging operation: i.e., all else held constant, fewer

ramp vehicles suggests easier merging. Lastly, after examining the lane distribution they

conclude that the shoulder lane is being under-utilized, i.e., the shoulder lane volume was

approximately 1/3 of the median lane, and the ramp shoulder lane volume was half of the volume

on the ramp median lane.

Using Instrumented Vehicles to Study Driver Behavior

Various studies have been conducted with the participation of subjects and the use of

instrumented vehicles to study closely a variety of driver behavior-related issues. Researchers in

psychology have deployed instrumented vehicles to study physiological responses of drivers and

how these relate to the driver-vehicle-environment system (Helander, 1978). Measurement of

the electrodermal response (EDR) and heart rate (HR) in the occurrence of various external

factors showed that a vehicle merging in front of the subject vehicle may induce great difficulty

in the driving task. Lane changing activity may have similar psychological implications.

Recently, Chang et al. (2001) showed that driver's load in acceleration lane before merging is

higher than the freeway section and that it was maintained after the completion of the merging

maneuver.

Other researchers in the field of robotics and control theory have collected behavioral data

using instrumented vehicles, aiming in modeling and predicting driver's maneuvers that can

potentially be used in automated driver assistance systems and ITS applications (Salvucci et al.

2007; Hegeman et al. 2005; Oliver and Pentland, 2000; Pentland and Liu, 1999). In the same

context, Shimizu and Yamada (2000) studied the effectiveness of the AHS (Advanced and

cruise-assist Highway System) in merging behavior under non-congested conditions, using an












instrumented vehicle. Their results indicated that the system could result in smoother merging

behaviors, given that the driver recognizes the traffic flow on the mainline in advance.

Traffic safety and driver performance is another research field where instrumented vehicles

have been used. Such example is the 100-car naturalistic study performed by Virginia Tech's

Transportation Institute, where the purpose was to collect pre-crash naturalistic driving data.

Additional research performed by the 100-car naturalistic study (Hanowski et al. 2006), focused

on the interactions between light and heavy vehicles. In their study, video cameras and other

equipment were installed to one hundred light vehicles and the analysis entailed recording of

each light vehicle-heavy vehicle interaction event. Sayer et al. (2007) performed a naturalistic

driving study using 36 drivers in order to examine their engaging in secondary behaviors

(conversation, grooming, cell phone use, eating/drinking, etc.) and to explore the effect of these

behaviors on the driving performance. Horrey et al. (2007) have gone beyond exploring the

effect of secondary behaviors on drivers' responses and they examined to which degree drivers

are aware of these distraction effects (namely, the cell phone use).

Classen et al. (2007) used an instrumented vehicle and surveys to evaluate the safety

effects of geometric improvements at intersections, on the driving ability of older drivers.

Analysis of the data indicated that at the improved intersections the average speed was increased

and also drivers made fewer errors compared to the unimproved intersections. Further

comparisons between younger and older drivers indicated that older drivers make more mistakes

than the younger ones, however, all drivers benefit from the geometric improvements.

In addition, a significant amount of research has been involved with the examination of

microscopic traffic characteristics. Brackstone et al. (1999) performed a study using an

instrumented vehicle for developing and calibrating models of driver behavior. The vehicle was












equipped with various sensors such as: optical speedometer, microwave radar which measures

distances to the adjacent vehicles, and two video cameras (one rear-facing and one front-facing)

with audio recording system. Information from all sensors was stored at a PC for further

analysis. Seven subjects were used where each was instructed to follow another test vehicle.

Analysis of the data showed that the front and rear gaps, and the time to collision (TTC) are

important factors that affect lane changing decisions. Brackstone et al. also found two thresholds

for TTC: one of 45 seconds above which a gap is almost always accepted and a second at about

20 seconds, below which a gap is almost always rejected. The authors hypothesize that there

might be an intermediate threshold for which the decision for a lane change would mostly

depend on lane and local flow and density, among other parameters. Lastly, in-vehicle

interviews with a limited number of subjects were performed to investigate their perception of

relative speed (denoting as "closing", "constant" or "opening").

Brackstone (2003) used an instrumented vehicle to collected data for a car-following study.

He applied the same instrumented vehicle in this research which is relevant to the classification

of drivers' attributes. Brackstone examined correlations between different indicators of driver

personality/ experience and found that at low speeds, drivers with high externality (measures

drivers feelings regarding locus of control and responsibility) will have high following distances,

while drivers who score high on the sensation scale would have lower following distances. They

did not conclude to anything similar at high speeds.

Recently, Wu et al. (2007) examined the effect of ramp metering on the driving

performance of merging vehicles, using the instrumented vehicle described in Brackstone et al.

(1999). More specifically, they examined whether ramp metering can reduce the stress of the

merging vehicles and whether it can smooth traffic downstream of the merge junction. In












addition to the vehicle sensors, loop detector data were available on the freeway (upstream of the

merge junction) and on the on-ramp. All data (in-vehicle, loop and video data) were used for the

investigation of gap acceptance, speed at merge and merge location during the merge process.

The subjects were instructed to follow both a merging route and a through route. Wu et al.

performed three investigations: (i) the behavior of the through traffic, (ii) the behavior of the

merging vehicles at the merge point, and (iii) the behavior of the freeway through vehicles

upstream of the merge. The research finding showed that ramp metering has insignificant effect

on the behavior of the through traffic (mean speed, acceleration, and time headway). It was also

found that ramp metering resulted in increased lane changing activity and higher headways from

the outside lane to the middle lane, which indicates a flow reduction upstream of the merge.

Speeds and headways on the middle and median lanes were not found to be statistically different.

Lastly, the effect of ramp metering on the merging traffic included increase of acceptable gaps,

and reduction in merging speeds, which indicates easier merging conditions for merge traffic.

There are other studies as well that collected data using instrumented vehicles to establish

microscopic driver behavior relationships. Cody et al. (2007) used instrumented vehicles to

examine the gap acceptance decision making during left-turn maneuvers from an intersection.

Ma and Andreasson (2007) also used an instrumented to collect car-following data on Swedish

roads. The authors also developed a fuzzy clustering algorithm to distinguish between the

different car-following regimes.

Henning et al. (2007) examined several behavioral and environmental indicators that

predict drivers' intent to change lanes. Data collected from an instrumented vehicle include

speed, acceleration/deceleration, yaw rate and inclination, eye movement, steering wheel

position, pedal use and turn signal use, distance to the car in front and GPS positioning. Cameras












were also set to record 5 different views around the vehicle. The indicators considered for the

lane change maneuver are the first glance to the left mirror, the turn signal and the actual lane

crossing, all three of which were found in the data collected.

In concluding, instrumented vehicles have been widely implemented for data collection in

transportation-related studies. By combining data from vehicle sensors (gear, acceleration,

throttle, etc) in-vehicle cameras either facing the driver or the roadside environment or both, and

loop detectors, researchers have gathered useful information for understanding and modeling

driver behavior at the operational and also tactical level.

Although the use of instrumented vehicles can provide useful information about driver

behavior, the experiments should be designed with care, and the results should be analyzed with

caution, as research has shown that human behavior may change even if very subtle indication

exists of being watched. Not only is this true, but it has been also shown that the behavior

becomes more altruistic as people, and even some animals are being observed (Milinski and

Rockenbach, 2007). This derives from the fact that by observing (or rather "snooping on") other

people, we actually work out how to behave in the future. Consequently, people (and also

animals) try to deceive the observers in order to secure future gains (e.g., positive reputation).

The authors further comment that:

Watchful eyes induce altruistic behavior and an 'arms race' of signals between observers
and the observed.

Summary of Literature Review

According to the literature, capacity associated with breakdowns at freeway ramp merging

segments is a stochastic variable, because the breakdown events can occur over a wide range of

traffic conditions. It has been also shown that these breakdown events are the result of conflicts

that occur during the merging process, when traffic moves towards congested conditions. For












example, Elefteriadou et al. (1995) and Yi and Mulinazzi (2007) discuss vehicle platoons;

Kerner and Rehborn (1996, 1997) mention of vehicles "squeezing" on the highway. Further

observations in the vicinity of ramp merges note that the consequence of these interactions

between the on-ramp and the freeway vehicles may be for several vehicles to decelerate and

cause other vehicles to reduce their speed as well, leading towards the occurrence of breakdown.

Merging behavior during complete congestion (queues on the freeway and the on-ramps)

appears to follow the "zipper effect" or is described by taking turns (Cassidy and Ahn, 2005).

This behavior could potentially be easy to model, given that the queue lengths are known.

The merging process has been studied to a significant degree in the literature, and the

developed models are typically applied in microscopic simulators to provide a more realistic

representation of traffic operations. Most of the MLC models are based on gap acceptance rules.

Recent refinements of the models include the addition of the cooperative behavior of the freeway

through vehicles (cooperative merging), and also the competition between freeway and ramp

vehicles (forced merging). Recent research has also incorporated acceleration-deceleration

decisions of the merging vehicle, to provide a more complete outlook of the merging process.

Important parameters identified to affect drivers' choices of acceptable gaps during the merging

process pertain to traffic conditions, geometric attributes, relative speeds, and also individual

driver characteristics (impatience factor, aggressiveness).

The merging process on freeway-ramp merging segments has been studied in a significant

extent during the past twenty years, however many limitations are identified to date. For

instance, decisions that occur during the merging process have been established by various

researchers, but these have not been evaluated by actual drivers. As such, the effect of individual

drivers' characteristics on the decision-making process is still unknown. Generally, driver












behavior has been considered an important factor in the literature, but this has not been examined

closely. This also means that there are no data showing if the merging process differs by driver's

aggressiveness, e.g., if an aggressive driver makes different acceleration and gap acceptance

decisions differently than a timid driver.

In addition, current research has included the effect of traffic conditions on the merging

decisions, but has not studied the opposite; the impact of individual drivers' merging maneuvers

on the overall traffic stability. This type of research could provide some answers concerning the

breakdown events and the resulting capacity at freeway ramp merges. Thus, how the behavioral

characteristics of drivers can trigger instabilities affect at a given freeway-ramp junction can give

insights regarding the occurrence of a breakdown.














CHAPTER 3
BEHAVIORAL BREAKDOWN PROBABILITY METHODOLOGY

This chapter presents the methodological framework for the development of the

breakdown probability model at freeway merges considering driver behavioral characteristics.

First, the structure of the merging process with the respective decision-making steps is presented.

Following that, the breakdown probability model is formulated, which accounts for the effect of

driver interactions and merging maneuvers on the freeway operations.


Merging Model Structure

This section presents the proposed structure of the merging process. The conceptual

framework of the merging process is illustrated in Figure 3-1.


Gap Acceptance Determine
Critical Gap




Free Merge Gap > Critical Gap Gap< Critical Gap


Mainline vehicle is Mainlin v 7ce
Initiate Cooperative changing lanes ce gice io s
Merge NOT cooperating


Gap > Gap <
Initiate Forced anticipated gap anticipated gap
Merge


Perform Perform Perform Perform Perform Next
e Mg Fe M Cooperative Forced Forced Gap
Free Merge Free Merge Morge m Gap
Merge Merge Merge


Figure 3-1. Conceptual description of merging process.

The conceptual merging process combines ideas from previous models in the literature


(Toledo, 2003; Choudhury, 2007), with the data collected through this thesis. The model presents

4 levels of decision-making: gap acceptance, decision for free merge maneuver, decision to

initiate cooperative merge, and decision to initiate forced merge maneuver.













As it is shown in Figure 3-1, the merging model is based on gap acceptance. The critical

gaps depend on driver's aggressiveness, the traffic conditions and the geometry of each site. The

critical gaps are typically the minimum acceptable gaps.

The gap acceptance model checks which gap is acceptable for merging. Each gap is

defined by the lead and lag gaps in the shoulder lane, as depicted in Figure 3-2.

Direction of flow

Total gap
Lag vehicle Lead vehicle
Vehicle
Lag gap lLength Lead gap



Ramp vehicle

Acceleration lane


Figure 3-2. The lead, lag, and total gap.

The available lead, lag and total gaps are compared to the ramp driver's critical (i.e.,

minimum acceptable) gaps, and these are accepted if they are greater than the critical gaps. The

critical gaps are assumed to follow a lognormal distribution to ensure their non-negativity.

In(Gead,i= X lead,i lead,i
ln(GR R P (3.1)
In(Gk"g'") = XR lag,i plag,
ln(Gl R) R *

Or equivalently,

n(G total) X total ,* total,i (3.2)
ln(G ) R (3.2)
i e {free, cooperative, forced}

Where, X"'adI, Xla and X '"to are vectors of explanatory variables affecting the lead, lag

and total critical gaps under the different types of merging maneuvers, respectively. Ple"d,,

flag,i and Pf'o"1t' are the corresponding vectors of parameters. The gap acceptance model assumes












that both the lead gap and the lag gap or the total gap must be acceptable in order for the ramp

vehicle to merge, under any merging maneuver. The probability of accepting a gap and

performing any of the possible merging maneuvers is given by:

PR (m) = PR ((accept lead gap)') PR ((accept lag gap)') =
PR (Glead,i > Glead,cr ,i) PR ( agi > ag,cr,i)

or (3.3)
PR (m) = PR (accept total gap)'
i e {free, cooperative, forced}

Assuming that critical gaps follow a lognormal distribution, the conditional probability that

the lead gaps and the lag gaps are acceptable is given respectively by:

PR (G'ta' > G1R nc) PR [n(GR 'tl) > ln(GRto~Cr

[ ln(Gtta') a (X'otal ptotal, ) (3.4)
L total ,i

Where (['] is the cumulative standard normal distribution.

If the gap is rejected, then the ramp vehicle needs to re-examine the situation, by

evaluating the mainline lag vehicle's reaction. If the mainline vehicle initiates cooperation

(decelerate or change lanes), the ramp vehicle may decide to accept the gap and merge. If the

mainline vehicle is not willing to yield or its deceleration is not enough, the ramp vehicle may

decide to initiate a forced merge.

The following sections present the basic elements of the three preliminary merging models

in more detail.

Free Merge Model

This section presents the detailed free merge process. The structure of the proposed free

merge model is illustrated in Figure 3-3.

















Gap Acceptance


Free Merge u ap > untical ap



Mainline vehicle is
Changing lanes




Perform Perform
Free Merge Free Merge



Figure 3-3. The free-merge model.


If the gap is larger than the critical gap, or if the freeway vehicle yields by changing lanes,


then the ramp vehicle initiates a free merge. The critical gap is the minimum acceptable gap


under free gap acceptance conditions. The critical gap is the critical total gap between the


potential freeway lead and lag vehicles, as shown in Figure 3-2.


Cooperative Merge Model


Gap Acceptance Determine


Initiate Cooperative
Merge


Perform
Free Merge


Figure 3-4. The cooperative-merge model.


r l ,,, h,,, i 1,, :1 .
4... 4~ll~~












During this decision level, both ramp and mainline lag vehicles need to evaluate the

situation ahead. Frequently, a mainline vehicle that is approaching the on-ramp will evaluate

whether it should change lanes or decelerate to make room for the ramp vehicle, or continue its

course. If the freeway vehicle changes lanes, then the ramp vehicle will merge under free-merge

conditions. However, if the freeway vehicle decelerates, then the ramp vehicle will evaluate the

situation and depending on its perception of the mainline vehicle's actions, it will react by

accepting the freeway vehicle's cooperation and merge.

The decision to accept the gap formed after the cooperation depends on whether the

mainline vehicle is willing to decelerate or not. The freeway vehicle's willingness to decelerate

(Hidas, 2005) may depend on several factors such as the driving experience, the freeway

vehicle's degree of aggressiveness, the mental state of the driver (being in a hurry, disconcerted

about other things, etc), the urgency of the maneuver as this is perceived by the freeway vehicle,

and the downstream traffic conditions.

Given that the mainline vehicle slows down, the potential gap size increases; thus, the

ramp vehicle evaluates whether the current gap is (or will be) acceptable for cooperative

merging. If the mainline vehicle does not slow down, the ramp vehicle will decide whether to

perform forced merge or to search for next gap. At this step, it is considered that the acceptable

gap for cooperative merging is a random variable, with a mean value less than the critical gap.














Forced Merge Model


Gap Acceptance Determine
Critical Gap




Gap < Critical Gap



Mainline vehicle is Mainline vehicle is Manl icle is
changing lanes decelerating NOT cooperating


Initiate Forced
Merge Gap> Gap<
anticipated gap/ anticipated gap




rform Perform Perform Perform Next
eerg Cooperative Forced G Forced Gap
Merge Merge Merge

Figure 3-5. The forced-merge model.

The ramp driver will initiate a forced merge maneuver in two situations: (i) the courtesy

that the mainline vehicle is providing (by slowing down) is not enough for the development of an

acceptable gap for cooperative merge and the ramp vehicle decides to force its way so that the

follower will decelerate more, and (ii) no action of cooperation is perceived, however, the ramp

vehicle will attempt to force its way, waiting for the follower to comply. Alternatively, the ramp

vehicle may decide to evaluate the next gap and return to the initial state.

Breakdown Probability Model Formulation

This section presents the structure of the breakdown probability model. As it was

previously stated, the goal of this model is to bridge the gap between individual drivers'

behaviors and traffic characteristics, and to provide an explanation of how the drivers' choices

and actions related to merging can trigger the breakdown phenomenon at ramp junctions.












In this research it is assumed that all vehicles attempting to merge can create a certain

degree of traffic instability in the freeway traffic stream. The magnitude of the turbulence

depends on the maneuver type that the ramp vehicle will perform. This magnitude also depends

on the degree of interaction between the ramp vehicles and the freeway through vehicles. As it

was shown in the conceptual description of the merging process (Figure 3-1), there are three

types of merging maneuvers: free, cooperative and forced. In terms of explaining vehicle

interactions, these maneuvers can be defined as:

* Free merges: No obvious interaction exists between the merging vehicle and the mainline
vehicle. The free merge maneuver does not affect the driving behavior of the mainline
vehicle, and vice versa.

* Cooperative merges: The mainline vehicle yields to the ramp merging vehicle by either
slowing down or changing lanes, to create an acceptable gap.

* Forced merges: There is a clear conflict between the merging vehicle and the mainline
vehicle. The merging vehicle initiates this interaction and the mainline vehicle reacts by
slowing down or changing lanes.

Based on these definitions of merging maneuver types, it is clear that the free merging

maneuver does not create any disruption to the freeway traffic stream. However, the cooperative

or forced merging maneuvers can create instabilities due to vehicle interactions which may lead

to a series of vehicles slowing down to accommodate the merges and eventually, to a sprawling

speed reduction (i.e., breakdown) at the location of the merge. The models developed in this

thesis account for all three merging maneuver types.

Typically, the likelihood of cooperative or forced merging maneuvers increases as traffic

operations move towards congested conditions, because vehicle conflicts become more frequent.

Figure 3-6 shows the reaction of the mainline vehicle N, in response to the merging maneuver of

the ramp vehicle R. At time t = 0 the mainline vehicle N at the shoulder lane identifies the

intention of the ramp vehicle R to merge into the freeway. In anticipation of that fact, at time t =













ti, the mainline vehicle M may be involved in a cooperative or a forced merge maneuver with

vehicle R. vehicle. The resulting action of the vehicle N would be either to decelerate, or to

change lanes. It is also possible that the mainline vehicle N will not yield to the ramp vehicle R,

and continue with the same speed or even accelerate to avoid any interaction.

Time Time
t = 0 t= t1 Travel direction



I -
IN
_i _


IN "- N-


I





Figure 3-6. Interactions between the mainline vehicle N and the ramp merging vehicle R
resulting to deceleration or lane change of vehicle N.

It is also useful to know how the behavior of the upstream vehicles is affected by the

merging maneuver downstream.

Travel direction

---- --- ---- --- ---- ---
Lane2
-1 -- -- --
Lane1 :i iiiiiii~i--> M_- t- | |







Figure 3-7. Following vehicle in shoulder lane (F) and interacting mainline (M) and ramp (R)
vehicles.

For example, assume that a cooperative or a forced maneuver takes place and the mainline

vehicle N decelerates to X mph (Figure 3-7). The vehicle upstream of N (vehicle F) may react to

the situation ahead by decelerating as well. At this point it is clear that the merging maneuver

was the cause of the speed drop for both vehicles N and F, which eventually can lead to braking













for several of the through vehicles. However, depending on spacing between vehicles F and N, it

is possible that the following vehicle F does not respond at all to the situation downstream

(continues with constant speed) or moves to the inside lane depending on the gap availability.

Thus, vehicle decelerations as a result of the cooperative and forced merging maneuvers at a

ramp junction, may affect not only the interacting vehicles but the following vehicles as well.

Depending on the extent of this impact, it is possible that this interaction might trigger a chain

reaction of braking and lane changing activity near the merge, which may eventually result in a

breakdown.

To describe the aggregate effect of the merging vehicle's maneuvers on the traffic stream

over a certain period of time, a new term is introduced, called merging turbulence: Merging

turbulence is defined to occur when there is a series of cooperative or merging maneuvers,

capable of affecting the speed choice of either the freeway vehicles (vehicle N or F). Thus,

merging turbulence represents the frequency of ramp merging maneuvers that cause the freeway

vehicles to decelerate, over a specific period of time (e.g., one minute). An illustration of

turbulence is shown in Figure 3-8.

Travel direction
Time





Travel direction

Time
t= tl
i ....................Cooperative or
-- ^o I--e-- ^ -.-:forced maneuver




Figure 3-8. Deceleration event due to ramp merging maneuver.












At time t = 0, Figure 3-8 shows vehicle R entering the on-ramp. At that time, vehicles N

and F are faced with three options: to continue driving with same speed, to move to the inside

lane, or to decelerate. At time t = tl vehicle N decides to decelerate, and potentially forces the

following vehicle F to decelerate as well. If the probability that any freeway driver N decelerates

due to a cooperative or forced merging maneuver is Pn(DEC), then the probability of merging

turbulence can be expressed as:

1 N
P(MergingTurbulence) = P (Dec) (3.5)
RampFlowRate n=,

The following two subsections discuss the proposed models for modeling the behavior of

vehicle N, to predict their contribution in the development of turbulence due to merging

maneuvers, and the relationship between the merging turbulence model and the probability of

breakdown.

Modeling the Behavior of the Freeway Vehicle

The probability of merging turbulence depends on the decision-making process of the

freeway vehicles as they are approaching the merge area. During the ramp merging event,

vehicle N has three alternatives: (i) to decelerate (and remain in the current lane), (ii) to change

lanes, and (iii) to continue with the same speed in the current lane. The first two alternatives are

associated with the cooperative or forced merge maneuvers. The third alternative suggests that

the freeway vehicle does not yield (no cooperation is provided) or the ramp vehicle does not

initiate a forced merge. In this case, the ramp vehicle will have to merge after vehicle M, and

possibly interact with vehicle F. Figure 3-9 describes the potential interactions between the ramp

vehicle and the freeway vehicle and the resulting decisions of the freeway vehicle. Whether the

deceleration or lane changing occurs as a result of a cooperative merge or a forced merge













depends on who initiates the interaction (as described in the definitions of merging types

presented in the previous section).

Vehicle N


Initiates Does not initiate
S cooperation. T cooperation


Vehicle R
vehicle d f Vehicle R does not
Ss (n i t t initiates forced ent are mta ecie, i
initiate forced merge
nerge


Lane neous Lanerefore, the probability that the freeway vehicle will
de rae Deceleratibon Deceleration No action
Change Change

Figure 3-9. Potential freeway vehicle decisions due to a ramp merging maneuver.

As illustrated in Figure 3-9, the behavior of the freeway vehicle can be modeled

considering two components. The first component describes the event that the freeway vehicle

will decelerate by initiating a cooperative merge, indicating the transition from the normal state

(no interaction) to the cooperative state. The second component captures the event that a freeway

vehicle will decelerate as response to a forced merge by the ramp vehicle, given that no

cooperation was provided earlier. This assumes the transition of the freeway vehicle from the

normal state (no interaction) to the forced state. These two events are mutually exclusive, i.e.,

they cannot occur simultaneously. Therefore, the probability that the freeway vehicle will

decelerate can be described by the following expression:

Pn(DECt) = Pn(DEC, St,n= coop/st-1,n= normal)
+ Pn(DEC, st,n = forced/st-1,n = normal) (3.6)

Where st is the state of the freeway vehicle n at time t, which can be normal (no

interaction), cooperative, or forced. Both components of this model are developed in a discrete

choice framework. The exact structure of both discrete choice models is dictated by the freeway













vehicle's decision-making process. A discussion on the modeling specifications of both

components follows.

Freeway vehicle behavior under cooperative merging: Assuming that the freeway

driver decision-making process is a two-step process, nested structures of the model were

evaluated initially. An example of a nested structure related to the cooperative merges is given in

Figure 3-10.


Cause Potential
cooperative merge


Effect Vehicle N





Level 1 Nest 1 Nest 2
Cooperate Do not cooperate



Maintain
Level 2 Decelerate speed and
lanes
travel lane


Figure 3-10. Nested model for cooperative behavior of mainline vehicle N.

According to this structure, at the first level the driver evaluates the situation and makes

the decision whether to cooperate or not. If the driver is willing to cooperate, then they evaluate

which form of cooperation to provide (level 2). This structure was found to be supported by the

data; however, no significant explanatory variables were identified. Other nested structures were

evaluated as well, but these were not supported by the data.

Therefore, the driver behavior under cooperation is modeled as a Multinomial Logit

(MNL) model where the freeway vehicle has three choices: to decelerate, to change lanes, to do












nothing. If gaps are not available, then lane changing is not an option, thus the freeway vehicles'

choices are to decelerate or not yield to the ramp vehicle.

Freeway vehicle behavior under forced merging: If the freeway vehicle does not show

cooperation towards the ramp vehicle, then the ramp vehicle may attempt to force its way into

the freeway (Figure 3-9). In this case, the role of the freeway vehicle is reactive. They can either

decelerate or move to the inside lane, provided that there is a gap available. The freeway

vehicle's decision is also modeled as a Multinomial Logit (MNL) model.

For the development of both behavioral models under cooperative, forced or normal state,

the utility functions (U) of the choices for the freeway vehicle N have the property that an

alternative is chosen if its utility is greater than the utility of all other alternatives in the

individual's choice set. These functions are:

U = V + (3.7)
i e {decelerate, change lanes, no action}
s e {cooperative, forced, normal}

In Equation 3.7 Vs represent the observable deterministicc) portion of the utilities of

driver n to decelerate, change lanes and do nothing under either state. The terms cS, are the error

terms associated with the three utilities. The error terms are assumed to be Gumbel distributed

and also identically and independently distributed across the alternatives and across the

individuals.

The deterministic components of the utilities for all three choices are:

VL,n = X L,n PL, (3.8)
V = X 63ction,n 39)
NoAction,n NoAction,n NoActon,n (3.9)
DEC,n = DXEC,n DEC,n (3.10)












Where X XL and XNoAcionn are the vectors of explanatory variables that affect the

utilities to change lane, decelerate and do nothing. &PL, P EC,n and PoAct.onn are the

corresponding vectors of the parameters.

Generally, the explanatory variables are related to: (1) alternative-specific attributes, (2)

characteristics of the drivers, and (3) interactions between the attributes of the alternatives and

the characteristics of the drivers. The function that describes the decision of vehicle N to

decelerate, change lanes or do nothing has the following form:

V = ao +p*x +r*z +*(XZ) (3.11)
s e [cooperative, forced, normal}

In Equation 3.11, ao are the alternative-specific constant parameters, Xn is the vector of

explanatory variables related to the traffic conditions and the environment of the subject vehicle,

p are the parameters associated with explanatory variables Xn, Zn is the vector of variables

related to the characteristics of the driver, y are parameters associated with explanatory variables

Z, 6 are parameters associated with the interaction terms between the explanatory variables, X,

and driver characteristics variables, Z.

The final expressions for the probabilities of all three alternatives are:


Pn (DEC, s = j/s,, = normal) exp(V-EC, (3.12)
exp(VDEC,n) + exp(VcL,n) + exp(Vlo Action,n)
exp(VC, )
P,(CL, s = j/s,, = normal) = exp(VC). C" (3.13)
exp(VE + e(Vn) + exp(V o-Action,n)

P1 (No Action, s, = j/st, = normal) = exp(o-Acion,n (3.14)
exp(VyjECn)+ exp(Vn, ) + exp(Vo-Action,n)












Merging Turbulence and the Probability of Breakdown

The merging turbulence model accounts for the effect of the merging maneuvers on the

occurrence of the freeway flow breakdown. The merging turbulence model should be compared

with a breakdown probability model to evaluate their relationship.

To account for the stochastic nature of the breakdown, the method for developing the

breakdown probability model is based on the lifetime data analysis, and particularly the Kaplan-

Meier estimation method, as this was introduced by Brilon (2005). For the development of this

model, historic speed-flow data at the breakdown location are required. The distribution function

of the breakdown volume F(q) is:


F(q) = 1- k- ; i {B} (3.15)
i:q, q ki
In Equation 3.15 q is the total freeway volume (veh/h), qi is the total freeway volume

(veh/h) during the breakdown interval i, (i.e., breakdown flow), ki is the number of intervals with

a total freeway volume of q > qi and {B} is the set of breakdown intervals (1-minute

observations).

The breakdown interval is typically identified as the interval when the average speed at

that location drops below a specific threshold (e.g., 10 mi/h lower than the posted speed limit).

Methodological Framework

This section presents the data that are required for the development of the driver-behavior

models and the macroscopic models of merging turbulence and breakdown probability, as these

were described in the previous sections of this chapter. The chapter concludes with a step-by-

step summary of the methodology pertained in this thesis.












Data Types for Models

The development of the microscopic driver behavior models require data related to the

drivers' thinking process, the interactions with the adjacent vehicles and the traffic conditions on

the freeway.

The drivers' thinking process is required to investigate when they start (or fail) to interact

and cooperate with their adjacent drivers, what actions they are performing to accomplish their

decision (decelerate, change lanes or do nothing), how they perceive the adjacent vehicles and if

they see any cooperation (or not) from the adjacent vehicles. In additions, drivers' characteristics

are also important to examine how their decisions vary across traffic conditions and across

different drivers. To obtain driver behavior-related information, actual input from different

drivers is required. This could be through conversations with drivers in the format of focus group

sessions, as well as actual driving observations, where driver actions and reactions are observed

from the inside.

Data that describe the relationship between the subject vehicle and the adjacent vehicles in

the traffic stream are also required to produce the variables used in the models. This type of data

include the gaps and gap change rates between the ramp vehicle and the freeway lead/lag, their

relative speeds and accelerations, the positions of the freeway lag when the ramp vehicle enters

the acceleration lane, the percent of acceleration lane used, the position of the freeway lag and

lead vehicles during the merging maneuver. Other types of information, such as the type of the

interacting vehicles are also required. These data can easily be obtained through video

observations, however this should be at the individual vehicles level. Video observations taken

from inside the vehicle can provide the quantitative data that are related to drivers' actions and

triggers.












Data related to the prevailing traffic conditions are required to quantify their effect on the

choices of the interacting vehicles. These data include measurements of densities and average

speeds during the merging maneuver, as well as the availability of gaps in the adjacent lanes. The

number of ramp vehicles at the time of the merge is also considered as this may affect both the

decisions of the freeway lag and the ramp vehicle. Data taken from cameras (e.g., traffic

monitoring cameras) that cover the entire merge areas are required to obtain the macroscopic

information.

For the development of the turbulence model video data at the merge junction before the

occurrence of the breakdown are required to distinguish between the different sources of vehicle

interactions (due to merging, lane changing or due to speed reduction downstream), and to

quantify the effect of those interactions to the freeway vehicles. These effects include

decelerating or lane changing activity for each lane. In addition, information about the ramp

volume and the freeway volume are required to provide correlation between the turbulence

model and the breakdown occurrence. To verify the breakdown occurrence speed time-series

plots need to be constructed from the detector sensors close to the merge area. Historic detector

data for the breakdown locations are also required to construct the breakdown probability model

as this was described in the previous section.

In summary, various sources of data are required to observed driver behavior and its

relation to the development of the breakdown. Focus group discussions, as well as simultaneous

data collection using an instrumented vehicle and traffic monitoring cameras are appropriate

sources for identifying how merging decisions affect traffic operations and the breakdown

occurrences on freeway merges.














Research Tasks

The step-by step procedure performed in this thesis is summarized in this section. An

illustration of the entailed tasks is shown in Figure 3-11.

| STEP I Focus Group
Surveys

Model Merging
Process

| STEP 2 In-Vehicle
Studies Microscopic/
Macroscopic
Observe Merging Traffic Data
Process


I STEP3 I Gap Acceptance
and Driver
Behavior Models


I STEP 4 | Merging Turbulence Model

I STEP 5 Breakdown Probability Model


Figure 3-11. Methodological plan.

Step 1 Conduct focus group meetings: In the first step, focus group surveys were

conducted to attain knowledge about how drivers perform merging maneuvers and what are their

concerns. During this step, all important factors indicated from the drivers were used to finalize

the merging process and to formulate the merging models that are calibrated as part of Step 3. A

detailed description of this data collection effort and results is provided in Chapter 4 of this

thesis, while the questionnaires used during the focus group discussions is provided in Appendix

A.

Step 2 Conduct field data collection effort: In this step, drivers were asked to

participate in in-vehicle driver behavior studies. Typically, drivers' intention and process of

thinking related to the merging task cannot be captured by observing field operations, because

only the result of their actions is captured this way. Drivers' thinking process can only be












obtained through questionnaires, where they can explicitly describe their intention about a

maneuver.

These studies aim at obtaining such driver behavior data from participants during their

driving task (merging on the freeway and driving on the mainline). Additional field data (flow,

speed, density) were collected concurrently with the in-vehicle data at the study ramp merging

sections. The combination of in-vehicle and traffic data is used to infer vehicle interactions in

two ways: how the driver merging decisions influence and are influenced by the prevailing

traffic conditions. The field data collection was performed at near-to-congestion conditions to

capture the impact of these interactions on the freeway operations. Information relevant to the

in-vehicle and field data collection and results is presented in detail in Chapter 5.

Step 3 Calibrate the merging models: This step includes the calibration of the gap

acceptance and the driver behavior models. All data collected in the field, from both the in-

vehicle study and the external traffic data were used for the model calibration. The gap

acceptance model considers the different types of merging maneuvers and evaluates the impact

of driver behavior attributes on those maneuvers. The driver behavior models capture freeway

drivers' decisions to decelerate, change lanes or not interact with the ramp merging traffic.

Step 4 Develop merging turbulence models: During this step, the contribution of

individual drivers' action on the freeway traffic stability is evaluated. The external traffic data

were used to quantify the effect of individual vehicle deceleration decisions and associate those

with the beginning of congestion.

Step 5 Develop breakdown probability model: This step includes the proposed

application of the turbulence model to develop a breakdown probability model.












CHAPTER 4
FOCUS GROUP EXPERIMENTS

The first part of the data collection plan undertaken for this research is presented in this

chapter. The focus of this research is to look at merging behavior and vehicle interactions from

the drivers' perspective, and to investigate the effect of individual behavioral characteristics on

drivers' decisions. Focus groups were used as a first step to understand the drivers' thinking

process when merging. The forms as well as the methodology used for the focus group meetings

were pre-approved by the Institutional Review Board (IRB) of the University of Florida.

This chapter describes the formulation of the focus groups and presents the questions

discussed during these sessions. Important focus group findings and conclusions from the

discussions are also presented.

Setting Up the Focus Groups

The focus group study was advertised through local organizations in Gainesville, FL, and

candidates completed a pre-screening questionnaire. The pre-screening questionnaires assembled

information on gender, age-group, ethnicity, years of driving experience, occupation, frequency

of driving and time of day, and vehicle type. The information was used to select a diverse set of

participants for focus group participation. Seventeen participants were invited to join three 2-

hour focus groups, and an attempt was made to select drivers with different demographics, in

terms of their gender, age-group and race. The demographics of all participants are presented in

Table 4-1.









Table 4-1. Demographic characteristics of focus group participants
ID Gender Age Race Experience Occupation Driving Hours per Peak/ Vehicle
group frequency week non-peak ownership
Focus Group 1
1_03 Female 25-35 Caucasian >=10 years Teacher Everyday >14 hrs Peak Sedan/Coupe
1_05 Male 25-35 Caucasian >=10 years Teacher Usually <4hrs Peak Pickup/SUV
1_09 Male 45-55 Caucasian >=10 years Community Sometimes 4-8 hrs Non-peak Sedan/Coupe
design
1_22 Male 25-35 Caucasian >=10 years Student Everyday 4-8 hrs Peak Sedan/Coupe
1_01 Female 25-35 Caucasian >=10 years Student Everyday 4-8 hrs Peak Sedan/Coupe
1_15 Female 25-35 Caucasian >=10 years Legal assistant Everyday 4-8 hrs Peak Sedan/Coupe
Focus Group 2
2_13 Female 55-65 Caucasian >=10 years Accountant Everyday 8-14 hrs BOTH Sedan/Coupe
2_12 Female 35-45 Caucasian >=10 years Massage Everyday 8-14 hrs Peak Pickup/SUV
therapist
2_16 Female 18-25 Afr/American 3-9 years Student Sometimes >14 hrs Non-peak Sedan/Coupe
2_07 Male 18-25 Caucasian 3-9 years Attorney Everyday 4-8 hrs Peak Sedan/Coupe
2_25 Female 35-45 Caucasian >=10 years Student Everyday 8-14 hrs Peak Sedan/Coupe
Focus Group 3
3_26 Male 35-45 Caucasian >=10 years US Navy Everyday 4-8 hrs Peak pickup/SUV
3_04 Male 18-25 Caucasian 3-9 years Student Everyday >14 hrs Peak Sedan/Coupe
3_06 Male 18-25 Afr/American 3-9 years Student Sometimes 4-8 hrs Peak Sedan/Coupe
3_14 Male 35-45 Caucasian >=10 years Manager Everyday 4-8 hrs BOTH Sedan/Coupe
Truck
3_27 Female 55-65 Caucasian >10 yrs Retired Usually 4-8 hrs Non-peak Sedan/Coupe
economist
3_28 Female 25-35 Hispanic >10 yrs Real-estate Everyday 4-8 hrs Peak Sedan/Coupe












Prior to each session, the participants completed a background survey form, which

contained seven multiple-choice questions related to their driving habits. These questions

solicited the subjects' desired freeway speed (assuming good visibility and weather conditions

and a 70-mi/h speed limit), lane-changing habits, how aggressive they consider themselves, how

aggressive their friends/family consider them, when and where they typically merge onto the

freeway, how they react if a vehicle merges onto the freeway while they are driving on the right-

most lane, and whether they plan their trips allowing for additional time to mitigate possible

delays.

Overview of Focus Group Questions

Typically, focus group discussions contain five categories of questions, all of which have

their specific purpose and function (Krueger and Cassey, 2000): opening, introductory,

transition, key, and ending. The opening question is designed to get people talking and make

them feel comfortable. They were asked if they enjoy driving and if they spend a lot of time

driving. The next question is the introductory question which helps people relate to the topic.

Here, the participants were asked "What is the first thing that comes to mind when you hear the

phrase 'Merge into the freeway'?". The transition question moves the conversation to the key

questions. The transition question used was phrased as follows: "Do you believe the way you

merge is different from other drivers? Why or why not?". The key questions are the ones that

typically drive the study. The key questions are open-ended situation-based scenarios, and the

central idea is to obtain the thinking process and potential actions in a merging maneuver. These

scenarios are discussed in detail in the following section. The ending question ensures that all

important topics have been covered. A handout containing all key questions and ending question

was given to the participants to fill out throughout the session.













Focus Group Key Questions

The goal of the key questions is to obtain the participants' thinking process and potential

actions in various scenarios, either as the merging vehicle or the freeway vehicle. Scenarios

under different amounts of congestion were discussed. The effect of other factors (e.g., ramp

geometry, vehicle type, driver's urgency) on driver behavior was also discussed. Participants

were asked to report (up to five) factors that affect their decisions and assign an importance level

("very important", "somewhat important", and "not as important but may consider") to each

factor. These three levels were transcribed into the following importance values for analysis

purposes: "very important" value = 3, "somewhat important" value = 2, and "not as important"

value = 1. The following five scenarios were discussed

Question 1 Merging Process Under Free-Flowing Conditions and Selection of Acceptable
Gaps

Participants were shown Figure 4-1A and B and were asked to provide their actions and

thinking process assuming they are the merging vehicle just entering an on-ramp, while the

freeway vehicles are traveling at their desired speeds. Both cases of parallel and taper ramps

were discussed.

S Direction of travel

MPEED




RAMP
SMerging Parallel type
vehicle A

Figure 4-1. Figures discussed during scenario 1 A) Merging process under parallel type on-
ramp. B) Merging process under tapered type on-ramp. C) Lagged position of
merging vehicle with respect to freeway vehicle. D) Parallel position of merging
vehicle with respect to freeway vehicle.












































I / / venicie ID

Figure 4-1. Continued.

Participants were asked to list and discuss their actions and thought process when merging

into the freeway, given the presence of freeway vehicles (vehicles 1, 2, and 3) at the locations

shown in Figure 4-1C and D. The participants discussed their preferable gaps in each case, as

well as the factors affecting their preference. The effect of vehicles 1, 2, or 3 being trucks in the

gap decision was also discussed.












Question 2 Merging Process Under Decreased Speed (40-60 mi/h)

For this question the participants were asked first to assume that they are the merging

vehicle reaching the acceleration lane, where traffic is denser and vehicles' speeds are low (40-

60 mi/h). They were also asked to report their thinking process in merging under those

conditions, and how this would change if there was another vehicle present on the acceleration

lane (moving towards the end of the lane). Then, they would list their actions assuming they are

the freeway vehicle on the right lane reaching the merging section and observing at least one

vehicle on the ramp trying to merge.

Question 3 Cooperative Merging and Forced Merging Maneuvers Under Decreased
Speed (40-60 mi/h)

This question investigated the likelihood of initiating a cooperative merge (as the freeway

vehicle), and a forced merge (as the merging vehicle), as well as factors (up to five) that affect

each decision. In both cases participants had to select between the "very likely", "somewhat

likely", and "not so likely" responses. Participants were asked to rank their stated factors as

"very important", "somewhat important", and "not as important but may consider". The

definitions of cooperative and forced merges used in this question derive from the literature

(Hidas, 2005), but modified to consider specifically the freeway vehicle actions after the merge:

* Cooperative merge: the gap between the freeway leader and follower is increasing before
the merge, indicating that the follower decelerates or changes lanes to allow the ramp
vehicle to enter.

* Forced merge: the gap between the leader and follower is either constant or narrowing
(follower maintains speed or accelerates) before the initiation of the merge, and starts to
increase as the ramp vehicle enters, indicating that the ramp vehicle has "forced" the
follower to either decelerate or change lanes.

Question 4 Merging Under Stop-and-Go Traffic

Participants were asked to assume that the freeway is congested (stop-and-go traffic). The

discussion concerned participants' actions when starting a forced merge (as the ramp vehicle),












and when giving way to a ramp vehicle that initiated a forced merge (as the freeway follower).

They were also requested to express the likelihood of performing these maneuvers ("very likely",

"somewhat likely", and "not so likely").

Question 5 Effect of other people on driving behavior

This last question obtained information related to the effect of other people's presence in

the vehicle, in driving performance.

Assembly of Focus Group Data

The data from the focus groups contained: (i) voice recordings of the 2-hour sessions, (ii)

documentation of the participants' background survey form, and (iii) documentation of

participants' responses on distributed handouts during the session. Before analyzing the data, the

voice recordings for each focus group were transcribed, and matched with the responses obtained

from the handouts.

Overview of the Freeway-Ramp Merging Process

This section presents the focus group findings related to participants stated actions and

thinking process while merging.

Refining Merging Process Under Free-Flowing and Dense Traffic

Based on participants' responses, a series of steps was developed for merging under both

free-flowing and dense traffic conditions. The process was found to be similar for all

participants. These steps are summarized below:

* Step 1: As drivers arrive on the on-ramp, most of them first think about merging when they
have a clear view of the freeway traffic (this depends on the ramp design). Others when
they are half way on the on-ramp, or when they have accelerated to a speed of 50-55 mi/h.

* Step 2: Most of the drivers become aware of their surroundings. They check: (i) their side
to assess the speed and flow of traffic on the right lane (possibly the left lanes too), (ii)
their front to evaluate the length of the acceleration lane and the time left for merging, and
(iii) their rear to acknowledge potential followers.












* Step 3- free-flowing conditions: All drivers start to accelerate when arriving at the
beginning of the acceleration lane. The acceleration and speed adjustment may be related
to targeting a specific gap that was visible from the on-ramp, which could be used for
merging. If there is no vehicle in front, all drivers want to reach a speed close to the
freeway speed or the speed limit, as the optimal speed for merging. Some drivers indicate
they target a specific gap at this stage.

* Step 3- dense conditions: Several drivers indicated they would accelerate as soon as
entering the acceleration lane to match or even drive 5 mi/h faster than the freeway traffic.
Due to the denser traffic (speeds are lower), there is less variability in speeds, therefore the
vehicle can adjust its speed immediately, and there is no need for fast acceleration.

* Step 4 free-flowing conditions: This step includes the gap acceptance and merging
process. If a gap has not been targeted through the acceleration process, the drivers select a
gap and may adjust their speed to fit the gap. Tasks such as actuating the turn signal and
checking of the mirrors or blind spots follow. Most of the participants (16 out of 17)
indicated they would accept a minimum gap of 2 3 vehicle lengths, while only one
participant indicated they would accept a gap of about 5 vehicle lengths.

* Step 4 dense conditions: The gap acceptance and merging process is similar. Additional
considerations: if the acceleration lane is long enough, they might consider going faster
than the rest of traffic and decelerate if necessary, to allow more opportunities to get in
(one participant). On the other hand, another participant stated that if speed was low (about
40 mi/h) she might consider letting 1-2 vehicles pass before merging, to assess the traffic
conditions downstream (e.g., presence of stopped vehicles). All participants agreed that the
acceptable gap size in this case ranges from 1.5 to 2 car lengths.

* Step 5: After merging, several drivers may consider moving to the inside lane, especially if
the right-most lane is slow.

Focus Group Results for Gap-Acceptance

When participants were asked to compare their merging process (Figure 4-1A and B),

several suggested that, in taper ramps they would be more cautious and anxious to merge.

Fourteen also indicated they would accelerate sooner and faster than in the parallel type on-ramp,

and that they would be more aggressive in selecting a gap. However, two participants suggested

being less aggressive, and less worried about their acceleration, but more worried about finding a

gap to merge with lower speed. Both these participants drive manual cars, and indicated so

independently, as they were in different focus groups.












When participants were asked to select a preferred gap (Figure 4-1C and D) their answer

differed as a function of several parameters. In Figure 4-1C, almost all participants (16 out of 17)

chose the gap between vehicles 1 and 2, while one chose the gap after vehicle 1. Participants'

decision to choose the gap between vehicles 1 and 2 depends on:

* Speed of vehicle 1
* Speed/deceleration of vehicle 2
* Presence of vehicles behind vehicle 1
* Whether vehicle 1 changes lanes
Six participants that initially chose the gap between vehicles 1-2 might consider merging in front

of vehicle 2. This depends on:

* Speed of vehicle 1
* Speed/deceleration of vehicle 2
* Change rate of gap between 1 and 2
* Whether vehicle 2 is a truck
Alternatively, the decision (of 12 participants) to merge after vehicle 1 depends on:

* Speed of vehicle 1
* Whether vehicle 1 is a truck
* Presence of vehicles behind vehicle 1
* Whether vehicle 2 is a truck
* Relative speed between merging vehicle and vehicle 2
* Acceleration capabilities of merging vehicle
* Freeway speed
Almost all participants (16 out of 17) would merge between vehicles 1 and 2 or after 1, while

only a few (6 out of 17) would merge between 2 and 3. This selection changes if the merging

vehicle is approximately at the same lateral position with vehicle 2 (Figure 4-1D). In this case,

drivers would prefer to merge between vehicles 2 and 3 (12 out of 17), depending on:

* Relative speed between merging vehicle and vehicle 2
* Speed/deceleration of vehicle 2
* Acceleration capabilities of the merging vehicle
* Change rate of gap between 2 and 3
* Whether vehicle 2 is a truck
Comparison of the two figures showed that the majority of the participants (14 out of 17) would

merge between vehicles 1-2 or 2-3 (Figure 4-1D) given that previously they selected gaps after 1












and 1-2, respectively (Figure 4-1C). The remaining three would select the same gaps in both

cases.

In summary, it was observed that under the same situation, drivers would likely react

differently, and that each driver considers different factors for making their decision. Some

drivers are more likely to choose a specific gap, while others may choose any of the three gaps,

depending on the traffic conditions.

Focus Group Results for Cooperative and Forced Merging

A significant portion of the focus group discussion aimed in understanding the drivers'

thought process while being either on the freeway approaching a merging section, or the on-

ramp. The purpose of this discussion was to identify factors that affect:

* Cooperation of the freeway vehicle towards the ramp vehicle by decelerating or changing
lanes.

* Whether the ramp vehicle forces its way onto the freeway.

* Whether the freeway vehicle yields to a ramp vehicle by decelerating or changing lanes
when the later initiates a forced merge.

Throughout the discussion, several factors that affect drivers' decisions were identified and

grouped into the following categories:

* Environmental Factors: These include the roadway, weather and lighting conditions.

* Freeway Vehicle Factors: These are associated only with the freeway vehicle/driver.

* Ramp Vehicle Factors: These are associated only with the ramp vehicle/driver.

* Interaction Factors: These pertain to the relation between the subject vehicle and another
vehicle of the immediate environment (e.g., relative speed).

* Traffic Factors: These are associated with the general traffic conditions of the merging
segment (e.g., average speeds, gap availability).

Table 4-2 presents all factors reported to affect vehicle decisions to cooperate towards a

merging maneuver, their frequency, and average importance. The average importance is a












measure of both frequency and importance value and it is calculated as the frequency-weighted

average of importance.

Table 4-2. Factors affecting cooperative merge decisions for freeway vehicles
Factors for cooperative merging Frequency Avg. importance
(max=3)
Weather 2 2.5
Lighting conditions 1 2.0
Speed of vehicle 1 3 3.0
Emotional status 1 3.0
Route selection 1 3.0
Headway between vehicle 1 and upstream vehicle 5 2.2
Speed of upstream vehicle 2 2.5
Vehicle 1 ramp vehicle relative speed 1 3.0
Speed of vehicle 2 1 2.0
Speed/acceleration capabilities 9 2.7
Vehicle size/type 6 2.5
Distance traveled/position on acceleration lane 4 2.8
Competency Erratic behavior 2 2.5
Traffic awareness (eye-contact) 2 2.5
Previous unsuccessful merges 1 3.0
Attempt to start a forced merge 1 3.0
Gap availability on left lane 8 2.8
Speed in all/left lanes 5 2.8
Traffic congestion 2 2.0
Coop. behavior of other freeway vehicles 1 3.0
Lane-changing activity 1 2.0

In the cooperative merge case, the participants are assumed to be the freeway vehicle

(vehicle 1, Figure 4-1C). The three most important factors highlighted in this table are:

* Speed/acceleration capabilities of the ramp vehicle: If the participants perceive that the
ramp vehicle has achieved a reasonable merging speed, they are willing to yield. This
perception depends on the make/type of the vehicle, but also the driver (primarily age).

* Gap availability on left lane: Participants are very likely to give way to the ramp vehicle, if
they can move to the inside lane. This is consistent with the responses to Question 2, which
investigated participants' actions when approaching the merge area from the freeway (right
lane).

* Size/type of the merging vehicle: Participants that consider this factor are reluctant to
cooperate with trucks, especially if these are open-bedded or if they are stopped at the end
of the acceleration lane. One participant indicated willingness to decelerate for a
motorcycle.












Table 4-3 presents the stated factors that affect drivers' decisions to initiate a forced merge

maneuver. In the forced merge case, the participants are assumed to be the ramp vehicle. The

three most important factors highlighted in Table 4-3 are:

* Average speed on the freeway: ramp vehicles are more likely to force their way in if
freeway speeds are low and traffic is dense.

* Amount of congestion and gap availability on the right lane: These two factors are grouped
together because they are correlated. The more congested the freeway, the less available
gaps exist, and drivers are more willing to perform a forced merge.

Table 4-3. Factors affecting forced merge decisions for ramp merging vehicles
Factors for forced merging Frequency Avg. importance
(max=3)
Roadway conditions 3 2.3
Weather 2 3.0
Speed of vehicle 2 3 2.7
Vehicle size-type 5 3.0
Relative speed between vehicle 2 and ramp vehicle 2 3.0
Coop. behavior of vehicle 2 1 2.0
Speed/acceleration 6 2.7
Emotional status 1 3.0
Position on acceleration lane 1 3.0
Speed in all/right lanes 9 2.6
Gap availability on right lane 7 3.0
Traffic congestion 7 2.9
Number of following vehicles on ramp 2 2.0
Number of leading vehicles on ramp 1 3.0
Gap availability farther upstream 1 2.0

Table 4-4 presents the factors that affect drivers' decisions to yield to a ramp vehicle that

forces its way in, by either decelerating or changing lanes. Participants were asked to assume

they are freeway vehicle 1 of Figure 4-1C. Table 4-4 includes all factors reported by the

participants. The three most important factors for the decision to decelerate or change lanes are

shown in italics.












Table 4-4. Factors affecting deceleration and lane-changing decisions of freeway vehicle, when
a ramp vehicle has initiated a forced merge
Factors for deceleration Frequency Avg. importance (max=3)
Roadway conditions 1 3.0
Weather 1 2.0
Headway between vehicles 1 and 2 5 2.8
Speed of vehicle 1 4 2.8
Relative speed between vehicle 2 and ramp 1 3.0


vehicle
Headway between vehicles 2 and 3
Speed/ acceleration/ deceleration capabilities
Vehicle size/type
Position on acceleration lane
Gap availability on left lane
Speed/relative speed in all/left lanes
Traffic congestion
Factors for lane-changing
Roadway conditions
Speed
Route selection
Trip urgency
Headway between vehicles 1 and 2
Relative speed between vehicle 2 and ramp
vehicle
Speed/acceleration
Vehicle size/type
Gap availability on left lane
Speed/relative speed in all/left lanes
Traffic congestion


1
5
3
1
12
8
2
Frequency
1
2
2
1
5
1


2.0
3.0
2.3
3.0
2.9
2.4
2.5
Avg.
3.0
3.0
2.5
2.0
2.8
3.0


importance (max=3)


The most important factors shown in Table 4-4 are:

* Gap availability in the left lane: If there are gaps in the inside lane they will change lanes,
otherwise they will decelerate.

* Freeway speed (or relative speed between lanes): If the speed of the left lane is less than
the speed of the right-most lane, then there is not much incentive for the freeway vehicle to
change lanes, thus, it will remain to the right lane and decelerate. However, if the speed in
the inside lanes is higher, they would be more willing to change lanes. This factor is
related to the amount of deceleration that the freeway vehicle is willing to accept. The












freeway vehicle is not willing to decelerate significantly, thus, if the merging vehicle
forces them to, they will likely move to the left lane.

* Speed/acceleration capabilities of the ramp vehicle: Similar to the cooperative merge, the
freeway vehicle is more likely to change lanes if it perceives that the ramp vehicle cannot
accelerate to the merging speed, or will not match the freeway speed quickly once it has
merged onto the freeway.

Relationships Between Driver Behavior and Driver Characteristics

Driver behavior is related to the individual's characteristics, vehicle capabilities, the

traffic/geometric environment, and also the task performed. This section identifies differences in

driver behavior, categorizes the stated behaviors as aggressive, average and conservative, and

evaluates whether drivers are consistent in degree of aggressiveness under various scenarios.

Based on focus group analysis aggressive behavior can be described by "selfishness" and

consideration of factors that affect mostly the subject vehicle. An average behavior can be

defined as considering both the subject vehicle status and the other vehicles. A conservative

behavior is assumed to occur when the subject vehicle will only act as a response to the other

vehicles' actions. For the purposes of evaluating driving behaviors vs. driver characteristics, the

focus group scenarios of cooperative and forced merging maneuvers under both dense and stop-

and-go traffic conditions were considered.

An attempt was made to categorize different behaviors in the case where the participants

are on the ramp, under dense traffic conditions. Participants were asked to discuss how likely

they are to initiate a forced merge. These responses, along with the discussion on how

competitive and considerate of other vehicles they are, were grouped. The following categories

are distinguished:

* Aggressive behavior: participants would not hesitate to cut somebody off if they only had
one chance. They have a sense of pressure and eagerness to get in, and not run out of
space. They assume that others will let them in. These participants consider mostly factors
associated with their own individual status when making the decision to merge.












* Average behavior: participants will consider a forced merge, but their decision also
depends on the prevailing traffic (available gaps, speeds) and their perception of the
freeway vehicles. Their decision to merge depends equally on their own status and the
surrounding traffic conditions.

* Conservative behavior: they are less likely or not likely at all to attempt a forced merge
under any situation. These participants will probably wait for a large gap to merge without
causing any disruption on freeway vehicles.

Participants' responses were also grouped for the scenario of the cooperative merge under

dense traffic conditions. Even though both options of deceleration and lane-changing were given,

all of the participants responded that lane-changing is their first choice. In fact, some participants

reported they would be moving to the inside lane "out of habit". Thus, the distinction of the

different behaviors was based on the event that lane-changing is not a feasible option (no

available gaps on the left lane). Given that, behavior was categorized as follows:

* Aggressive behavior: participants are not very likely to start a cooperative merge by
decelerating. They will at least maintain their speed so the ramp vehicle merges behind
them. Also, they are not likely to initiate a cooperative merge if the ramp vehicle is stopped
at the acceleration lane. They might decelerate only if the merging vehicle is approaching
the end of the lane but still moving, and traffic permits.

* Average behavior: these drivers are willing to decelerate and create gaps for the ramp
vehicle to merge; however, they are not willing to decelerate significantly. These drivers
appear to be more cautious about stopped vehicles at the end of the ramp, because they
believe these could make poor judgments at merging.

* Conservative behavior: these drivers will firstly consider decelerating, than changing lanes.
This behavior was not represented in the focus group.

Similar analysis was performed for the remaining scenarios that deal with congested

conditions. The first case deals with ramp vehicles' willingness to wait on the on-ramp for a

larger gap instead of forcing their way in. Driver behavior was categorized as follows:

* Aggressive behavior: Participants feel that forcing their way in is their only option, thus
there is a high probability that they will force their way into the freeway. They also feel
that the freeway vehicles are more willing to give way, because everybody is in the same
position, sharing the same motivation. They will mostly consider themselves when making
the decision to merge.












* Average behavior: Participants prefer making eye-contact with the freeway vehicle and
wait for them to signal, or a gap to form. Their thinking process involves the surrounding
freeway vehicles as well. They feel that this situation yields for cooperation rather than
forcing their way in.

* Conservative behavior: Conservative drivers are not likely to perform forced merge, as
they would wait for a substantive gap to form; older drivers might fall in this category.
However, no such behavior was identified from the focus group, as the sample did not
include older drivers.

Lastly, the case that involves freeway vehicles' willingness to give way to a ramp merging

vehicle under congested conditions showed a small differentiation among participants'

responses. The following categories are drawn from this case:

* Aggressive behavior: Drivers are not willing to let any vehicle in. All participants reported
that they do not react in this manner, however, they have seen such behaviors from others.

* Average behavior: Drivers are not willing to let more than one vehicle in.

* Conservative behavior: Drivers may let one or two vehicles in. High probability of giving
way to the merging vehicles.

Table 4-5 summarizes the results related to behavioral categories of the participants for

each question (columns 1 to 4). This table also presents participants' responses from the

background survey. As shown in columns 1 to 4, the same participant might exhibit different

degrees of aggressiveness depending on the situation. For example, under dense traffic, a ramp

driver that hesitates to perform a forced merge (conservative behavior column 2), might

become aggressive under congested traffic (aggressive behavior column 3). Likewise, in dense

traffic, the same driver may be equally or more aggressive when they are on the freeway than

when they are the merging vehicle. This may be explained by the fact that ramp vehicles do not

have the right-of-way or speed advantage compared to the freeway vehicles, thus, they seem to

feel less entitled to receive priority. Freeway vehicles are more likely to change lanes than

decelerate to accommodate a merging vehicle. Another significant result is that congested

conditions yield less variability in driver behavior. Under these conditions, ramp vehicles will












either force their way in, or they will wait for the freeway vehicle to yield, and freeway vehicles

become more accommodating and are willing to let at least one vehicle to merge in front of

them.

Cross-tabulation between gender and behavioral categories shows that, in dense traffic

conditions, men appear to be more aggressive than women (Table 4-5). Also, there are

inconsistencies regarding drivers' stated aggressiveness between the focus group results and the

background surveys. For example, drivers that indicated they consider themselves as 'somewhat

aggressive' in the background survey did not show any indication of aggressiveness based on

their responses during discussion.










Table 4-5. Behavioral categories based on focus group scenarios and background survey form
Behavioral categories Background survey responses Pre-screening
ID Dense traffic Congested traffic Speed Lane change Driver Driver type Age
Start Start Start Yield (mi/h) frequency type by friends Gender group
coop. (1) forced (2) forced (3) forced (4) (5) (6) (7) (8) (9) (10)
1 03 Av C Av C 70-75 Sometimes V.C. V.C. Female 25-35


Av Av Ag C 70-75
Ag Av Ag C 65-70
Av Ag Av C 75-80
Av Av Av C 75-80
Av Av Ag C 65-70
Av C Ag Av 75-80
Av Av Av C 75-80
Ag C Ag C >80
Ag Ag Ag Av 75-80
Av Av Ag Av 70-75
Av C Av C 70-75
Av Av Ag C >80
Ag Ag Ag C 75-80
Av Av Av C 65-70
Av C Av C 65-70
Av C Av C 75-80
C: Conservative, Av: Average, Agr: Aggressive
V.C.: Very conservative, S.C.: Somewhat conservative, S.A.:


Sometimes
Very often
Very often
Sometimes
Very often
Sometimes
Very often
Very often
Sometimes
Very often
Seldom
Sometimes
Very often
Sometimes
Very often
Very often


S.C.
S.A.
S.A.
S.A.
S.A.
S.A.
S.A.
S.A.
S.A.
S.C.
S.C.
S.A.
S.A.
S.A.
S.C.
S.A.


S.C.
S.C.
S.C.
S.A.
S.A.
S.A.
S.A.
S.A.
V.A.
V.C.
V.C.
S.C.
S.A.
S.A.
S.A.
S.A.


Male 25-35
Male 45-55
Male 25-35
Female 25-35
Female 25-35
Female 55-65
Female 35-45
Female 18-25
Male 18-25
Female 35-45
Male 35-45
Male 18-25
Male 18-25
Male 35-45
Female 55-65
Female 25-35


Somewhat aggressive, V.A.: Very Aggressive


1.
1
1
1_
1_
2-
2
2
2
2
o 3
3:
3
3-
3-
3












Other Observations


Five participants indicated that urgency might cause them to accept smaller gaps. The

remaining responded that urgency would affect their speed selection and lane-changing activity

on the freeway, but not the way they merge. With respect to the trip purpose, many participants

responded that for casual driving, they drive more relaxed compared to commuting.

The last question entailed differences in driving alone vs. having passengers. Many

participants stated that they are more cautious when they have passengers, because they feel

responsible for them. Conversely, they drive faster when they drive alone. However, if they are

involved in a conversation they are less focused and more distracted.

Conclusions

Several important conclusions were drawn from the focus group study:

* Participants' responses were uniform with respect to the steps involved in merging, both
for non-congested and congested conditions.

* Ramp design appears to affect drivers' merging process. Most of the participants indicated
they would speed up and be more aggressive on taper ramps, compared to parallel design.

* Regarding gap acceptance, the participants would likely react differently, depending on
which factors each one considers. Some drivers (14 out of 17) indicated that they might
choose any gap (adjacent, upstream, or downstream), depending on the traffic conditions,
while others (3 out of 17) would be less flexible. This searching and targeting of the
surrounding gaps has also been described in Toledo (2003). Variables that affect gap
acceptance have also been identified.

* Discussion on vehicle interactions showed that, if participants are on the freeway, their
preference is to change lanes and avoid decelerating. If this cannot be accomplished, they
will cooperate, depending on the speed/acceleration of the ramp vehicle, and its size/type.
If the ramp vehicle attempts to force its way in, they will consider their distance to the
upstream vehicle and the relative speed with the adjacent lane to decide whether to
decelerate of change lanes. Ramp vehicle's decision to initiate a forced merge depends
mostly on traffic-related factors, such as freeway speed, congestion and gap availability.

* Although the discussions captured a significant variability among participants', it is likely
that their reported actions are different than their actual actions, depending on the values of
each individual. For example, someone who values aggressiveness might respond as if
he/she is aggressive.












* The stated driver actions were analyzed to identify differences in driver behavior. The
criterion of "selfishness" was used to develop three behavioral categories: aggressive,
average and conservative. Given this definition, the degree of aggressiveness of each driver
varies as a function of their task and the traffic conditions.

* In congested conditions, driver behavior displays less variability; therefore, it may be more
predictable. This is consistent with findings (Persaud and Hurdle, 1991; Cassidy and
Bertini, 1999) indicating that the mean queue discharge flow displays smaller variability
than other capacity-related measures, and remains consistent from day to day.

The following recommendations are offered:

* The merging process solicited by focus group participants should be considered in
developing or refining existing analytical or simulation models for freeway operations.
Similarly, the factors stated as contributing in gap selection should be considered when
developing or revising gap acceptance models.

* Differences in attitudes and driver behavior between non-congested and congested
conditions should be explicitly incorporated in traffic operational models.












CHAPTER 5
FIELD DATA COLLECTION

This chapter presents the second part of the data collection effort for this research. The

focus of the field data collection is to quantify the effect of individual driver characteristics on

their merging decisions and associate those with the breakdown occurrences at the freeway-ramp

junctions. The data collection undertaken for this task entails observations of participants driving

an instrumented vehicle and simultaneous video observations of the freeway during these

experiments. All survey instruments as well as the methodology used for the field experiments

were pre-approved by the Institutional Review Board (IRB) of the University of Florida. This

chapter describes the formulation of the instrumented vehicle experiments and the simultaneous

collection of traffic data, and presents findings and results related to the field observations of the

merging process.

In-Vehicle Data Collection

The following section provides information on the organization and the setup of the

instrumented vehicle experiment. The section also provides a description of the methods used for

the data collection as well as the selection of the participants. Procedures used to process the in-

vehicle data are also discussed.

Description of Instrumented Vehicle

The instrumented vehicle used in this study is a Honda Pilot SUV, owned by the

University of Florida Transportation Research Center (TRC). The vehicle is equipped with a

Honeywell Mobile Digital Recorder (HTDR400) system. The vehicle has an inbuilt GPS where

all information about vehicle position and speed data is displayed and recorded on the

HTDR400. In addition to the GPS unit, the vehicle includes four wide coverage digital cameras

(DCs) that capture video clips facing the front, the back and the two sides of the vehicle. The












video data, as well as audio data during the driving task, are recorded on the HTDR400, and

stored at a local hard drive that is located at the trunk of the vehicle. An additional camera

facing the driver was installed on the dashboard, to capture facial reactions of the driver during

the experiments. An internal view of the instrumented vehicle is shown in Figure 5-1. The data

collected directly through the instrumented vehicle include:

* Instrumented vehicle geographical position, speed, throttle, and left-right turn signal
activation.

* Video clips of the vehicles in front, behind and adjacent to the instrumented vehicle.

* Audio recordings during the driving task.

A laptop was connected to the system which allows for reviewing the display of all four

cameras, through the HTRD BusView software. All video clips were downloaded from the hard

drive to the laptop shown in Figure 5-1 for further analysis.
















Figure 5-1. Inside view of the TRC instrumented vehicle.

Driving Routes

The exact routes that the participants followed for both AM and PM peak periods are

illustrated in Appendix B. Each participant would conduct two loops during the AM routes and

three during the PM routes.












These routes were developed after selecting the appropriate freeway-ramp junctions that

meet the following criteria:

* The ramp junctions experience mild to heavy traffic during AM and/or PM peak periods.

* The total travel time for the routes does not exceed the expected duration of the in-vehicle
experiment, which is approximately one hour, including the required stop for discussion
with the participants.

* The routes are not too complex so that the participants would not be confused during their
driving.

* Cameras from the Jacksonville Traffic Operations Center should be available at these ramp
junctions. The cameras' field of view should meet the respective criteria for the concurrent
field data collection, as presented in the following section.

* These locations should be free from construction work, as this may affect the driving task
of the participants, as well as the data quality obtained from the detectors.

The final routes consist of four consecutive ramp junctions along 1-95. The locations of

those junctions are at: (i) 1-95 NB @ Phillips Hwy, (ii) 1-95 NB @ Baymeadows, (iii) 1-95 NB @

WB J.T. Butler, (iv) 1-95 SB @ Bowden, and (v) 1-95 SB @ J.T. Butler EB. The participants

would also drive through the J.T. Butler junction both in the SB and NB direction.

Geometry of the Freeway Ramp Junctions

The selected ramp junctions have different designs, concerning the acceleration lane type

and the overall length. Two ramps are tapered and the remaining four are parallel type. All

distances are measured from the gore area until the end of the solid white line, the end of the

dashed line and the end of the acceleration lane. The dimensions of the two tapered ramps at J.T.

Butler SB and NB approaches are illustrated in Figure 5-2.















Direction of flow -


N--

End of solid End of End of
white line dashed line accel. lane

44 4


Direction of flow -- -


End of solid
white line
"-"


-End-of
accel. ~ ne


Butler SB-EB approach


Figure 5-2. Geometric characteristics of tapered entrance ramps on 1-95 at A) J.T. Butler NB-
WB approach, and B) J.T. Butler SB-EB approach.

Figure 5-3 shows the dimensions of the three parallel ramps. The total length of the


acceleration lane ranged from 900 ft to 1,530 ft. All locations have three lanes, except the

junction at Phillips Highway NB which has four lanes.


Direction of flow -


End of solid
white line
""""


End of
dashed line
v^


End of
accel lane
[


Phillips NB


Figure 5-3. Geometric characteristics of parallel entrance ramps on 1-95 at A) Phillips NB, B)
Baymeadows NB, and C) Bowden SB.


Gore

-I


End of
dashed line














Direction of flow


N


End of solid End of End of
Gore white line dashed line --accel.lane_ _





-330 ft-----180 ft-------490 ft

1000 ft
Baymeadows NB B

Direction of flow __N


End of solid End of End of
Gore white line dashed line accel. lane


------------- --45-f------ X ---- 7 t --- 't --- 4 t ---


415 ft -, 570 ft- 545ft

1530 ft
Bowden SB

Figure 5-3. Continued.

Selection of Participants

The instrumented vehicle experiment was advertised through the internet and local

organizations in Jacksonville, FL, and candidates were provided a description of the driving

routes and a pre-screening questionnaire. The questionnaires assembled information on gender,

age-group, ethnicity, years of driving experience, occupation, frequency of driving and time of

day, and vehicle type, similar to those used for the focus group experiment. The information was

used to select a diverse set of participants. Although the targeted number of participants was

sixty, many candidates would fail to appear at the meeting location without earlier notification,

resulting in misspent of time and resources at the expense of the experiment. Therefore, only

thirty-one participants eventually completed the experiment. The demographics of the

participants are presented in Table 5-1.












Similar to the focus group experiment, the participants completed a background survey

form, which contained seven multiple-choice questions related to their driving habits. These

questions solicited the subjects' desired freeway speed (assuming good visibility and weather

conditions and a 70-mi/h speed limit), lane-changing habits, how aggressive they consider

themselves, how aggressive their friends/family consider them, when and where they typically

merge onto the freeway, how they react if a vehicle merges onto the freeway while they are

driving on the right-most lane, and whether they plan their trips allowing for additional time to

mitigate possible delays.










Table 5-1. Demographic characteristics of instrumented vehicle experiment participants
ID Gender Age Race Experience Occupation Driving Hours per Peak/ Vehicle
group frequency week non-peak ownership


Male
Male
Male
Male
Male
Male
Female
Female

Male
Female
Male
Male
Male
Male
Female
Female
Male
Male
Male
Male
Female
Female
Female
Female
Female
Female
Male
Male
Male
Male
Female


55-65
25-35
18-25
25-35
25-35
25-35
25-35
18-25

25-35
45-55
25-35
45-55
45-55
55-65
45-55
25-35
18-25
45-55
25-35
35-45
18-25
45-55
45-55
35-45
45-55
25-35
35-45
18-25
35-45
45-55
55-65


Caucasian
Caucasian
Caucasian
Caucasian
Caucasian
Caucasian
Afr/ American
Asian-
Caucasian
Caucasian
Caucasian
Caucasian
Caucasian
Caucasian
Caucasian
Caucasian
Caucasian
Asian
Caucasian
Caucasian
Afr/ American
Caucasian
Caucasian
Afr/ American
Caucasian
Caucasian
Caucasian
Afr/ American
Caucasian
Asian
Caucasian
Caucasian


>=10 years
>=10 years
3-9 years
>=10 years
>=10 years
>=10 years
>=10 years
3-9 years

>=10 years
>=10 years
>=10 years
>=10 years
>=10 years
>=10 years
>=10 years
>=10 years
1-3 years
>=10 years
>=10 years
>=10 years
1-3 years
>=10 years
>=10 years
>=10 years
>=10 years
>=10 years
>=10 years
3-9 years
1-3 years
>=10 years
>=10 years


4-8 hrs
8-14 hrs
<4 hrs
4-8 hrs
8-14 hrs
<4 hrs
4-8 hrs
4-8 hrs


Retired Military
Clerk
Full Time Student
Professional driver
Full Time Student
Safety Ranger
Full Time Student
Customer Service

Property Manager
Office Manager
University Staff
Military
Qual. Assurance
Pilot
Housewife
Admin. Assistant
Full Time Student
Police Officer
PC Refresh Manager
Cook
Full Time Student
Internet Business
Secretary
Officer
Admin. Assistant
Housewife
Sales
Full Time Student
Drafter
Professional Driver
Sales & Marketing


Everyday
Everyday
Everyday
Everyday
Everyday
Everyday
Everyday
Usually

Everyday
Everyday
Never
Usually
Everyday
Sometimes
Everyday
Everyday
Never
Everyday
Everyday
Everyday
Everyday
Usually
Everyday
Everyday
Everyday
Everyday
Everyday
Everyday
Everyday
Everyday
Usually


Peak
Peak
Peak
Peak
Peak
Peak
Peak
Peak

Peak
Peak
Non-peak
Peak
Peak
Non-peak
Non-peak
Peak
Non-peak
Peak
Peak
Non-peak
Peak
Peak
Peak
Peak
Peak
Peak
Peak
Peak
Non-peak
Peak
Peak


8-14 hrs
<4 hrs
<4 hrs
4-8 hrs
8-14 hrs
4-8 hrs
4-8 hrs
4-8 hrs
<4 hrs
8-14 hrs
8-14 hrs
8-14 hrs
4-8 hrs
8-14 hrs
8-14 hrs
>14 hrs
<4 hrs
4-8 hrs
8-14 hrs
8-14 hrs
<4 hrs
>14 hrs
8-14 hrs


Pickup/SUV
Sedan/Coupe
Sedan/Coupe
Pickup/SUV
Pickup/SUV
Sedan/Coupe
Pickup/SUV
Sedan/Coupe

Sedan/Coupe
Sedan/Coupe
Sedan/Coupe
Pickup/SUV
Sedan/Coupe
Sedan/Coupe
Pickup/SUV
Pickup/SUV
Sedan/Coupe
Sedan/Coupe
Sedan/Coupe
Sedan/Coupe
Sedan/Coupe
Sedan/Coupe
Sedan/Coupe
Sedan/Coupe
Pickup/SUV
Pickup/SUV
Sedan/Coupe
Sedan/Coupe
Pickup/SUV
Sedan/Coupe
Sedan/Coupe


72
73
76
23
27
32
0 37
51
59
60
61
67
68
74
17
18
19
50
56
58
66
70
75












Data Collection Procedures

Participants of the instrumented vehicle experiment were requested to drive the vehicle

along the pre-selected routes on the Jacksonville area, with the presence of the investigator and

an assistant. The participants were driving on 1-95 in the northbound and southbound directions,

during near-congested and congested conditions in AM and PM peak periods. Two experiments

would run during the morning peak period (7:00-8:00 AM and 8:15-9:15 AM) and three during

the evening peak period (3:00-4:00 PM, 4:15-5:15 PM and 5:30-6:30 PM). To examine driver

behavior at merging segments, participants were asked to enter the freeway from specific on-

ramps and also stay on the mainline, passing through other ramp merging sections multiple

times. In this way, both behaviors of the "ramp-merging vehicle" and the "through vehicle" for

the same driver were captured.

In such behavioral studies it is essential to have feedback from the participants, to record

and understand what their stimuli and possible intentions or reactions are, during the driving

task. However, it is not advantageous to ask the participant questions during their driving,

because this will not only distract them from the driving task, but it may also create a feeling of

"being observed", which will contribute to a change in their behavior and thus, result in biased

conclusions. To reduce that bias, the investigator and the assistant were sitting at the back seat

of the instrumented vehicle, so that the participant would not feel that he/she is being observed.

In addition, participants were asked to drive as they normally would, and they were given no

guidance with respect to their lane selection. Also, all questions and discussion regarding the

driving of the participants were done after each route is completed, where the vehicle were

stopped for five to ten minutes. The completion time of all routes was approximately one hour.

During the driving task the participants were asked to inform the investigator whenever

they have an intention to merge or change lanes, and to identify the desired gap with respect to












the freeway vehicles, if such issue would emerge. Participants were also asked to report

perceived actions of cooperation from the other vehicles primarily during the merging maneuver.

After the completion of each route, participants were asked to explain their thinking process that

pertains to specific actions that occurred during the experiment, if this was not reported while

driving.

In-Vehicle Data Processing

This section describes the methods used for the estimation of the model parameters. The

video data collected from the instrumented vehicle mounted cameras were used to estimate

parameters related to relative distances and speeds. Still images were extracted from both front

and rear videos at a 0.5 sec time resolution. When participants were merging into the freeway,

the image extraction would start as soon as the vehicle entered the acceleration lane until it had

completed the merge. When participants were driving on the freeway, the extraction would start

at least 2-3 seconds before they indicated their intention to react to the merge vehicle. Along

with the extracted frames, the instrumented vehicle speed and longitude/latitude data were

recovered from the GPS. The following subsections present the processing techniques of the

collected data.

Gaps with adjacent vehicles and gap change rates

The gaps between the subject vehicle and its adjacent vehicles were estimated for each

consecutive frame. Appendix C describes the method applied for measuring distances from still

images. In addition, the gap change rates were estimated every 0.5 seconds, throughout the

trajectory of the vehicles. The gap change rates represent a measure of the relative speeds and

accelerations of the two vehicles. These were evaluated every o.5 seconds, throughout the entire

observed trajectory of the vehicles.












Speeds and accelerations

The speeds of either the lag, lead or ramp vehicles are estimated through consecutive

frames using the equations of motion. Average speeds and accelerations are estimated every

second. The speeds of the subject vehicle are obtained directly from the GPS, whereas the

accelerations are calculated as the speeds change rate, and evaluated at a one-second resolution.

Vehicle positions

Through the GPS information the exact position of the subject vehicle is obtained. This

position is referenced relative to fixed points in the vicinity of the ramp junction. Usually, the

end of the solid white line of each acceleration lane was used as the reference point.

Average density and freeway speed

Density was calculated from snapshots of the merge area, taken from the TMC cameras, at

the time the instrumented vehicle would enter or drive through. Density was measured as the

total number of freeway vehicles within a segment that ranged from 500 to 1400 ft long

depending on the site. The density measures were transformed to equivalent vehicles per mile

and then averaged across the travel lanes. The average freeway speed of the right-most lane was

obtained from the 1-minute RTMS data, at the time that the instrumented vehicle was at the

subject ramp junction.

Data Collection at the Jacksonville TMC

Concurrently with the instrumented vehicle experiment, traffic-related data were collected.

More specifically, with the collaboration of the Jacksonville Traffic Operations Center, the

selected traffic monitoring cameras become available during the experiment. The Traffic

Operations Center also provided two video feeds to record the video data. An assistant located at

the Traffic Operations Center would switch interchangeably the connection between the cameras

and the communication channels, to capture the instrumented vehicle at each freeway-ramp












merge location it was going through. In addition, traffic-related data collected from the remote

traffic microwave sensors (RTMSs) were also available through the Steward Data Warehouse.

The data that are available through the Steward Data Warehouse are per lane freeway volume,

speed, and occupancy.

As shown in Figure 5-4 there are several cameras placed along 1-95 used by the

Jacksonville Traffic Operations Center for traffic monitoring. Since the cameras were used for

both the selection of the routes for the in-vehicle experiment, and the concurrent field data

collection, the following selection criteria were developed:

* Clear view of the incoming traffic from the freeway and the ramps should be available.

* Locations should be free of construction work, because at those locations the RTMSs are
not calibrated, and that would impact the validity of the data.






iI j



,Rd AV
V iR








Figure 5-4. Location of available cameras along 1-95.

Figure 5-5 provides video snap-shots of four of the five merging segments used in this

study. The TMC cameras face both northbound and southbound travel directions.






















A B










C D
Figure 5-5. Camera field of view along 1-95 A) Phillips Hwy (facing NB), B) Baymeadows
(facing NB), C) Bowden (facing SB) and D) J.T. Butler (facing SB).

It should be noted that, in the event of an incident, the assistant could not have access to

the cameras, as these are also operated by the Highway Patrol officers. Such instances did occur

during the data collection periods, and therefore, the respective videos were not recorded. Also,

due to extended congestion resulting from these incidents, the routes were adjusted to complete

the experiment on time. In both cases participants would use the 1-95 SB entrance from J.T.

Butler WB approach, which is a loop ramp. Of course, video recordings from this ramp were not

available, since the TMC cameras were not adjusted for that location.

TMC Data Processing

The merge junctions that experience breakdown events due to merging operations were

evaluated using the RTMSs data. Speed time-series plots at all detector stations along the

freeway segment were constructed, for all days of the data collection. Visual observations of the














time-series revealed the breakdown locations and times during the AM and the PM peak periods.

The breakdown events that were observed during the data collection days occurred at NB

junction of 1-95 with J.T. Butler Boulevard. Other breakdowns were also observed at the SB off-

ramp at J.T. Butler; however this was due to the off-ramp queue spilling back on the freeway.

Non-recurrent congestion due to an incident was observed at the SB junction of 1-95 with J.T.

Butler. Also, congestion starting from the 1-95 NB junction with J.T. Butler would propagate

further upstream at the junction with Baymeadows, and even reaching the junction with Phillips

Highway NB. At the southbound direction, congestion would start sometimes at the on-ramp

from J.T. Butler EB approach, and sometimes at the SB exit at J.T. Butler. Breakdowns from

those locations would typically propagate congestion further upstream up to the junction with

Bowden Road.


4 -- Extent of congestion
travel direction




rl 0 H


-^
?


Ctd
5-s
oC


travel direction
go--


| |" arS I?"
- | n- l- ll I-
Cs m
r? W re ? Is
Ft; i a 53 iM


oW
| """""""^



*-^ i-

am *o
3S


Figure 5-6. Observed breakdown locations and congestion propagation along 1-95 A) SB
direction, and B) NB direction.


Extent of congestion












Next, the time-series were compared with the times of the TMC video recordings at each

location. Depending on the prevailing traffic conditions, observations were grouped into the

following five traffic states:

* Non congested period (173 observations),
* Before breakdown on-ramp events at NB or SB J.T.Butler (6 observations),
* Before breakdown off-ramp events at SB J.T.Butler (1 observation),
* Before congestion starts at the remaining locations (10 observations),
* Within congested period for all locations (10 observations).
The video recordings before the breakdown events provide information about the merging

maneuvers and the lane changing activity that contributed to the occurrence of the breakdown.

These recordings were used to develop the merging turbulence model, by counting at each

minute the number of interacting merging maneuvers (cooperative or forced) and the number of

lane changes that caused vehicles to decelerate. Additional causes of decelerations were

observed and recorded as well. Sometimes, decelerations on the right lane due to merging would

cause drivers on the middle lane to decelerate. Also, decelerations past the merge area and inside

the bottleneck were observed, which indicated vehicles' effort to discharge. Usually, these

decelerations became more frequent, forcing the incoming traffic on the freeway to decelerate as

well, thus, creating a wave of decelerations moving upstream. After that, it was clear that

merging was not the reason for decelerating people would still decelerate even if there was no

vehicle on the on-ramp. During those intervals, the merging process of the ramp vehicles would

become more difficult, and they would start to form queues on the on-ramp. Examination of the

speeds during that minute would reveal that the speed decrease (i.e., speed-flow breakdown) has

initiated.












Field Experiment Results

Overview of the Observed Merging Process

As part of the field experiment, the participants were asked to put into words their thoughts

as they were driving on the on-ramp and approaching the merge. Generally, the field observed

merging process is quite similar with that identified during the focus group discussions. The

following steps summarize the observed merging process:

* Step 1: Participants start accelerating on the on-ramp and first think about merging when
they have a clear view of the freeway traffic.

* Step 2: Participants evaluate the speed and the flow of traffic on the freeway, to assess how
much they should adjust their own speed. They also account for the presence of other on-
ramp vehicles ahead. If traffic is free-flowing, participants leave a large gap to use later for
acceleration. If the freeway is congested, they do not leave a large gap.

* Step 3: Participants accelerate to a speed close to the freeway speed as they reach the
acceleration lane. They also start looking at potential gaps.

* Step 4: This step includes the gap acceptance and merging process. In free-flowing
conditions participants adjust their speed if necessary to fit a gap. Tasks such as actuating
the turn signal and checking of the mirrors or blind spots follow. In congested conditions,
drivers anticipate cooperation from the freeway vehicles.

* Step 5: After merging, most of the participants move to the middle lane unless they need to
exit at the next junction.

Distinction of Merging Maneuvers

As it was also discussed in Chapter 4, the merging maneuvers are categorized to free,

cooperative and forced merges, depending on the degree and the type of observed interaction

between the ramp vehicle and the freeway lag vehicle. Generally, a free merge does not involve

any interaction between the two vehicles. In a cooperative merge the freeway vehicle decides to

yield to the ramp vehicle by either decelerating or changing lanes. In a forced merge, it is the

ramp vehicle that initiates the maneuver and the freeway vehicle reacts to that by either

decelerating or changing lanes.












The distinction of the merging maneuvers when the participants were driving on the

freeway was done considering their narratives as they were approaching the merge area. When

the participants were the merging vehicle, there was no "inside" information about the freeway

drivers' intended actions. In these cases, the distinction of the maneuvers was done using the

TMC video data and observing the break lights of the freeway vehicle or its trajectory.

However, when drivers decide to provide cooperation (e.g., decelerate) towards the

merging vehicle, they will do so well in advance. As such, their deceleration is not always

captured by the TMC cameras, due to limitations of the cameras' field of view. In this case, the

distinction of the maneuver was done by measuring the gap and its change rate with the lag using

the rear in-vehicle camera. If the lag gap was relatively constant as soon as the ramp vehicle

enters the on-ramp and starts to increase, it suggests that the two vehicles had similar speeds but

the lag vehicle decelerated to increase the gap. If the gap was decreasing, but with a decreasing

rate, this suggests that the lag vehicle speed was higher than the ramp vehicle speed, and as soon

as it decided to yield the gap was decreasing at a lesser rate. As such, at the time the ramp

vehicle is merging, the gap will remain relatively constant; indicating that no further speed

adjustment is required (equalized speeds). In forced merging the gap remains constant or it is

narrowing as the ramp vehicle is traveling on the on-ramp, but it starts to increase or to decrease

with a diminishing rate as soon as the ramp vehicle initiates the merge. After the maneuver is

complete, the gap may continue to increase indicating that the lag needs to prolong the

deceleration to further adjust its speed.

In summary, the definitions of the three types of merging maneuvers considering vehicle

interactions are:

* Free merge: there is no apparent interaction between the ramp vehicle and the freeway lead
or lag.












* Cooperative merge: the lag decelerates or changes lanes to allow the ramp vehicle to enter.
If the lag decides to cooperate by decelerating, the gap between the lag and the ramp
vehicle will be increasing or decreasing with a diminishing rate as soon as the ramp vehicle
enters the on-ramp and it remains relatively constant as the ramp vehicle is merging.

* Forced merge: the ramp vehicle initiates the merging maneuver and the lag responds by
either decelerating or changing lanes. In this case the gap between the lead and lag is either
constant or narrowing (lag maintains speed or accelerates) before the initiation of the
merge, and starts to increase or decrease with a diminishing rate as the ramp vehicle enters.
After the merge the gap continues to increase.

The total number of merging maneuvers that the participants performed as the ramp

vehicle was 273 and 109 as the through vehicle. These maneuvers refer to non-congested

conditions. Table 5-2 summarizes the types of merging maneuvers that the participants

encountered as both the ramp merging and the freeway through vehicle at each merge junction. It

also provides the percent of decelerations or lane changes performed due to vehicle interactions.

Table 5-2. Merging maneuver categories
Ramp Junction Free Cooperative Forced
Ramp merging vehicle
Baymeadows NB 59 22 5
Bowden SB 43 34 6
JTButler NB 9 6 2
JTButler SB 56 7 3
Phillips NB 13 4 4
Total 180 73 20
% decelerations -70% 100%
% lane changes 30% 0%
Freeway through vehicle
Baymeadows SB 19 0 0
JTButler NB 50 28 0
JTButler SB 18 2 0
Total 87 30 0
% decelerations -30.4%
% lane changes 69.6%

Table 5-2 shows that the participants performed all types of merging maneuvers, the

majority of which were free maneuvers. When participants received cooperation, usually it was

through deceleration rather than lane changing. However, it is possible that cooperative lane












changing maneuvers were not captured, neither from the TMC cameras nor from the in-vehicle

cameras, given that these maneuvers typically occur further upstream of the merge area. In this

case, these would be categorized as free merging maneuvers. When the participants performed

forced merging maneuvers, the reaction of the freeway vehicles was to decelerate in all cases.

Table 5-2 also shows that there were observations where participants provided cooperation

towards ramp vehicles. Usually, participants would move to the inside lane to accommodate the

ramp vehicles, and less frequently they would decelerate. This finding is also consistent with the

results from the focus group discussions, presented in Chapter 4. Lastly, the participants did not

incur any forced merging maneuver.

Driver Behavior Types

The data obtained through the in-vehicle experiment allow for investigating differences

and similarities between the drivers and examining how the variability in driver behavior affects

traffic operations during merging. This section describes the identification of driver behavior for

each participant involved in the experiment. Three types of driver behavior were considered:

aggressive, average and conservative behavior. For this task, the actual observed driver behavior

was evaluated considering both qualitative assessment based on the focus group analysis, and

quantitative factors based on the field observations.

The qualitative assessment applies the criterion of "selfishness" for each participant

throughout the entire duration of their driving task. Drivers that exhibit high degree of

selfishness and consider primarily their own status on the road are regarded as aggressive. For

example, aggressive drivers are unwilling to yield to ramp vehicles, and they dislike being cut

off; however they are very likely to impose to other vehicles by forcing them to decelerate.

Drivers that act primarily as a response to the other vehicles' actions are considered to be

conservative. Conservative drivers show increased hesitation when merging and they are very












likely to yield to a ramp merging vehicle. Drivers that consider both their own status but also the

effect of their actions to the other vehicles are categorized as average. Average drivers are

equally likely to show cooperation towards a ramp vehicle depending on the traffic conditions.

These drivers also do not exhibit any characteristics that could describe them as either aggressive

or conservative.

The quantitative assessment was based on two criteria (AAA, 2009): (i) number of

discretionary lane changes and (ii) observed speeds when driving under free-flowing and not car-

following conditions. Given the design of the experiment (i.e., frequent exits from the freeway),

participants had generally limited opportunities for performing discretionary lane changes and

for driving at the inside (faster) lanes. As such, participants that performed up to two lane

changes and/or followed a speed up to 5 mi/h the speed limit were considered to be conservative.

Participants that performed up to five lane changes and/or drove at a speed up to 10 mi/h over the

speed limit were considered to be average. Participants that performed at least six lane changes

and/or drove at high speeds up to 15 mi/h over the speed limit (or 10 mi/h over the limit under

raining conditions) were grouped as aggressive.

The driver behavior types are intended to investigate primarily vehicle interrelations and

traffic operations, and this is addressed in both quantitative and qualitative criteria. Therefore,

the definition of aggressive behavior presented here does not include characteristics such as

increased risk to collision or drivers' noncompliance, which are typically used to examine the

effects of driver behavior on traffic safety.

In summary, the characteristics of the three behavioral types based on both the quantitative

and the qualitative assessment are:

* Aggressive behavior: participants do not hesitate to cut somebody off when merging. They
have a sense of pressure and eagerness to get in, and not run out of space. Participants












perform at least six discretionary lane changes and/or drive at speeds up to 15 mi/h over
the speed limit (or up to 10 mi/h in raining conditions).

* Average behavior: participants' driving behavior depends equally on their own status and
the surrounding traffic conditions. They perform up to five discretionary lane changes
and/or drive up to 10 mi/h over the speed limit.

* Conservative behavior: participants will not perform a forced merge and they will wait for
a large gap to merge without disrupting the traffic. They might decelerate significantly to
allow a vehicle to merge. They also perform up to two discretionary lane changes and/or
their speed is up to 5 mi/h over the speed limit.

Table 5-3 summarizes the results of the driver behavior analysis for all participants. This

table also includes their background survey responses on their degree of aggressiveness as this is

perceived by themselves and by their friends or family, their stated driving speed and lane

changing activity.










Table 5-3. Driver behavior types based on actual observations and background survey form


ID
10
47
49
52
63
65
69
71
72
73
76
23
27
32
37
51
59
60
61
67
68
74
17
18
19
50
56
58
66
70
75


Background Survey Responses


Field Observations
DLC Driving speed
7 77 mi/h
5 71 mi/h
16 72 mi/h
6 68 mi/h (Rain)
12 78 mi/h
9 79 mi/h
16 67 mi/h (Rain)
7 75 mi/h
7 78 mi/h
6 77 mi/h
6 79 mi/h
4 68 mi/h
5 68 mi/h
4 71 mi/h
4 71 mi/h
4 75 mi/h
5 68 mi/h
4 71 mi/h
5 74 mi/h
4 73 mi/h
4 70 mi/h
4 72 mi/h
0 60 mi/h
2 70 mi/h
2 65 mi/h
2 71 mi/h
2 67 mi/h
2 71 mi/h
0 68 mi/h
2 69 mi/h
1 70 mi/h


Driver type






















Anervaive
Anervaive
Anervaive
Conservative
Conservative
AConservative
AConservative
Av'eras ge c
Averia e
Averia e
A '__le is e
A' cnise, \
A,,2eri v e





Average




















Conservative


Lane changing
Very often
Very often
Very often
Very often
Sometimes
Very often
Sometimes
Sometimes
Very often
Very often
Very often
Very often
Sometimes
Sometimes
Sometimes
Very often
Sometimes
Very often
Very often
Sometimes
Very often
Sometimes
Sometimes
Sometimes
Sometimes
Very often
Sometimes
Sometimes
Sometimes
Very often
Sometimes


Driving speed
75 to 80 mi/h
70 to 75 mi/h
70 to 75 mi/h
70 to 75 mi/h
70 to 75 mi/h
75 to 80 mi/h
70 to 75 mi/h
70 to 75 mi/h
70 to 75 mi/h
>80 mi/h
75 to 80 mi/h
70 to 75 mi/h
75 to 80 mi/h
75 to 80 mi/h
70 to 75 mi/h
75 to 80 mi/h
70 to 75 mi/h
70 to 75 mi/h
75 to 80 mi/h
75 to 80 mi/h
70 to 75 mi/h
70 to 75 mi/h
< 65 mi/h
70 to 75 mi/h
70 to 75 mi/h
70 to 75 mi/h
70 to 75 mi/h
70 to 75 mi/h
70 to 75 mi/h
70 to 75 mi/h
70 to 75 mi/h


Aggressiveness
Somewhat ,ir"l'.,i' c
Somewhat ,.lc'._'is c'
Somewhat a,.lc'.',i c'
Somewhat a,.lc'.',i c'
Somewhat conservative
Somewhat i :.i'._l',i c
Somewhat conservative
Somewhat conservative
Somewhat ,i.i'._l',i c
Somewhat ,.'lc',is c
Somewhat ,.'lc',is c
Somewhat conservative
Somewhat i :.i'._l',i c
Somewhat a,._lc'._'i, c'
Somewhat %.lc'.',i c'
Somewhat conservative
Somewhat %.:i'._l'',i c
Somewhat a,._lc'._'i, c'
Somewhat a,._lc'._'i, c'
Somewhat conservative
Somewhat conservative
Somewhat conservative
Very conservative
Somewhat conservative
Somewhat conservative
Very conservative
Somewhat conservative
Somewhat conservative
Somewhat conservative
Somewhat ili"c'%,is c'
Somewhat conservative


Aggressiveness by others
Somewhat aggressive
Somewhat conservative
Somewhat aggressive
Somewhat ,iic',,i\ c
Very conservative
Somewhat aggressive
Very conservative
Somewhat aggressive
Somewhat aggressive
Very ,i,,ii%: c
Somewhat conservative
Very conservative
Somewhat aggressive
Somewhat conservative
Somewhat aggressive
Somewhat aggressive
Very ,iar,,is i e
Somewhat aggressive
Somewhat aggressive
Somewhat aggressive
Somewhat aggressive
Somewhat conservative
Very conservative
Somewhat conservative
Somewhat conservative
Somewhat conservative
Somewhat aggressive
Somewhat conservative
Somewhat conservative
Very wc,,io e'i
Somewhat conservative












In summary, the field observations of driver behavior come in agreement with the

quantitative criteria applied for the driver type distinction. The resulting categorization of drivers

also provided a uniform allocation of all three types. However, there were differences between

the field observed driver types and those stated at the background survey forms by the

participants. For instance, some participants that regard themselves as conservative were found

to be rather aggressive (e.g., participant #63, Table 5-3), whereas others that consider themselves

aggressive, showed the exact opposite behavior (e.g., participant #70, Table 5-3). This

inconsistency may be due to the fact that when asked about their perceived aggressiveness (or

their friends/family perceived aggressiveness), people will respond by comparing themselves

with their peers, thus their responses will not necessarily be objective.

Although the sample is not large enough to perform quantitative analysis on the driver type

profiles, several qualitative conclusions can be drawn, by comparing this sample's demographics

with the assigned driver type (Table 5-4).

Table 5-4. Demographic characteristics by driver behavior type
Driver Type Male Female Average age group Age group range
Aggressive 8 (73%) 3 (27%) 25-35 18-65
Average 7 (64%) 4 (36%) 35-45 18-65
Conservative 4 (44%) 5 (56%) 35-45 18-65
All 19 (61%) 12(39%) 35-45 18-65

The average age group for the entire sample falls between 35 and 45 years old. The

aggressive drivers are on the 25-35 years old group, whereas average and conservative drivers

are on the older group (35-45). Also, the majority of men fall into the aggressive and average

driver types, and women are more often found on the conservative driver type category.












Driver Decision-Making Process


The extraction of drivers' thinking process through the in-vehicle experiments is quite

challenging, since drivers do not explicitly state their rationale behind their course of actions.

However, some conclusions were drawn regarding their cooperation towards the merging

vehicles. Based on the in-vehicle observations, drivers' decision-making is not necessarily a two-

level process, where they decide first whether to provide cooperation or not, and then select the

preferred action of cooperation. It was found that they would evaluate the situation considering

all three alternatives (or two alternatives if lane changing was not an option) at the same level.

Summary and Conclusions

In this chapter the field data collection effort was discussed. The data obtained in this study

contain concurrent observations of the behavior of thirty-one participants at ramp merge areas

(both as the ramp and the freeway vehicle) and macroscopic observations of the traffic stream.

Procedures for processing the raw data for further analysis are also presented in this chapter.

The following conclusions are offered based on the field observations:

* The steps involved in the observed merging process are found to be quite similar with that
identified during the focus group discussions (Chapter 4), for both congested and non-
congested conditions.

* When participants were on the freeway they were involved only in free and cooperative
merging maneuvers, and not in forced merges. Participants would show cooperation
through lane changing more often than through decelerating. This indicates drivers'
preference to change lanes if a gap is available. This finding is consistent with the relevant
discussion from the focus groups.

* When the participants were the merging vehicle the majority of observed merging
maneuvers were free. Cooperative and forced maneuvers were observed as well. When
drivers' received cooperation from the freeway vehicles, usually this was through
deceleration rather than lane changing. However, it is possible that cooperative lane
changes were not captured by the cameras since these would occur considerably upstream
of the merge area. In this case they would be observed and characterized as free
maneuvers.












* The participants' behavior was categorized as aggressive, average and conservative.
Participants were categorized based on the criterion of "selfishness" as this was introduced
in Chapter 4, and quantitative information about their speed and discretionary lane
changing activity. Both assessments are consistent and come in agreement.

* There were few differences between the resulting driver type categorization and the
participants' perceived aggressiveness. This inconsistency is most likely because
participants responses may not be objective as will respond by comparing themselves with
their peers.

* The resulting behavioral categorization showed that aggressive drivers belong to younger
average age group category, compared to the other two types. Also, men were most likely
to be aggressive than women.

* The field of view of the TMC cameras was very important for this study, as they dictate
whether the locations of interest (e.g., bottlenecks) can be considered for data collection.
However, there is a trade-off between the cameras field of view and the required zoom of
the merge area to identify potential vehicle interactions and reactions. If more cameras
were available, it would be possible to use multiple and capture the field of view with
acceptable resolution upstream, at the merge and downstream of the merge area.

* The participation of actual drivers was probably the most challenging task of the data
collection. This was primarily because several times drivers would fail to appear for the
experiments, without any prior notification. In addition to that, obtaining drivers' thinking
process was also challenging since drivers do not explicitly state their rationale behind
their course of actions.












CHAPTER 6
MODEL DEVELOPMENT

This chapter presents the data analysis and estimation results that pertain to the models that

describe ramp vehicles' gap acceptance decisions, through vehicles' deceleration decisions, and

the probability of turbulence and breakdown using the field data. The first section explains the

data used to model the ramp vehicle's gap acceptance decisions and presents the estimation

specifications of the total accepted gap. The following section presents the model developed to

describe the freeway vehicle's behavior at the ramp merge areas, along with a discussion on the

data used to develop this model. The macroscopic model that quantifies the observed turbulence

due to the merging maneuvers and associates this turbulence with the breakdown probability is

discussed in the next section. This chapter concludes with a discussion of the developed models.

Development of the Gap Acceptance Model

Estimation Dataset for Gap Acceptance Model

The estimated parameters used for the merging gap acceptance model are presented in this

section. Descriptive statistics of the estimated parameters are given for the entire dataset and also

as a function of the merging maneuver type (free, cooperative, or forced) and the driver behavior

type (aggressive, average and conservative).

Out of the 273 total observations of merging maneuvers, several free merges did not

involve any freeway lag or lead vehicle therefore these were removed from the dataset. Also, the

cooperative maneuvers that resulted in the lag vehicle changing lanes were excluded since these

do not provide information about the gap acceptance behavior of the ramp vehicle (i.e., the final

selected gaps were free gaps). Lastly, merging maneuvers that occurred under complete

congested conditions were not considered as well since gap acceptance under those conditions is












different. The final estimation dataset includes 142 merging observations across the five

freeway-ramp junctions.

An illustration of the gaps related to the ramp vehicle and the lead and lag vehicles is

provided in Figure 6-1. This figure also shows the positions of the three vehicles with respect to

the white solid line and the entire length of the acceleration lane (parallel type), measured from

the gore.


Direction of flow


Total gap
Lag vehicle Lead vehicle

Lag gap Lead gap







Acceleration lane


Figure 6-1. The ramp, lag and lead vehicle, their related gaps and positions.

The ramp vehicle merging speed ranged from 34.0 to 65.7 mi/h with an average of 55.1

mi/h, and its acceleration ranged from 0.0 to 5.9 ft/s2 with an average acceleration of 1.1 ft/ s2.

The relative speeds with respect to the lag and lead vehicles were calculated as the speeds of

these vehicles less the speed of the ramp merging vehicle. The average relative speed with the

lag vehicle was found to be -0.2 mi/h, varying from -11.2 mi/h to 18.3 mi/h. The average relative

speed with the lead vehicle was 2.6 mi/h, varying from -4.5 mi/h to 16.8 mi/h. Histogram of the

ramp vehicle speed is presented in Figure 6-2.
















30-

25

20

15

10

5-


35 40 45 50 55 60 65
Ramp Vehicle Speed (mi/h)


Figure 6-2. Distribution of ramp vehicle speed.


Traffic conditions such as the average density and the speed in the right-most lane affect


the gap acceptance behavior of the ramp vehicle. The per-lane average density during the


merging maneuvers was 30.8 veh/h/ln and it ranged from 10.9 to 52.8 veh/h/ln. The mean


freeway speed of the right-most lane was 59.1 mi/h, ranging from 43.0 mi/h to 71.0 mi/h.


The gaps with the lag vehicle range from 34.9 ft to 134.8 ft with an average of 75.5 ft. The gaps


with the lead vehicle range from 25.2 ft to 140.1 ft, with an average gap of 74.8 ft. Lastly, the


total gaps (measured when both lead and lag gaps were available) range from 84.3 ft to 222.9 ft,


with an average total gap of 150.3 ft. The distribution of the gaps is shown in Figure 6-3.


14-

12

10



6-

4

2

0
40 60 80 100 120
Lag Gap (ft)



Figure 6-3. Distributions of A) lag gap, B) lead gap, and C) total gap.


















18
16
14
12
i 10
8-1

6
4
2
0
40 60 80 100 120 140
Lead Gap (ft)
B



25-


20


15


10





80 100 120 140 160 180 200 220
Total Gap (ft)
C
Figure 6-3. Continued.


The analysis results of the merging position and acceleration lane usage by ramp design is


shown Table 6-1. It was found that, compared to parallel type on-ramps drivers used more length


on the tapered on-ramps before merging. On parallel on-ramps the acceleration lane usage


averaged to 40.1 percent, however, there were few observations where the participants made


almost full use of the lane (maximum usage was 83.3 percent). Also, there were few merging


maneuvers on parallel on-ramps that were completed prior to the end of the solid white line


(minimum position denoted as -50 ft on Table 6-1).












Table 6-1. Statistics of merging position by ramp design
Parameter Ramp design Mean St.dev. Minimum Median Maximum
Position rel. to solid Parallel 127.6 116.6 -50.0 99.8 480.0
white line (ft) Taper 132.5 72.6 28.5 137.1 246.9
Acceleration lane Parallel 40.1% 12.5% 23.9% 37.6% 83.3%
used (%) Taper 65.8% 6.0% 57.3% 66.2% 75.2%

On average, the merging position considering both types of ramp design was found to be

129.0 ft downstream of the end of the solid white line, and the acceleration lane usage measured

from the gore area to the end of the lane (Figure 6-1) averaged to 48.2 percent.

The parameters related to the ramp vehicle were also grouped based on driver behavior and

merging maneuver type. Table 6-2 presents the ramp vehicle speeds, accelerations, gaps, and

merging positions associated with the free merging maneuvers. The average density under free

merging was 26.6 veh/h/ln and the average speed on the right-most lane was 60.4 mi/h.

Table 6-2. Statistics of ramp vehicle gap acceptance parameters by driver type for free merges
Parameter Driver type Mean St.dev. Minimum Median Maximum
Ramp vehicle speed Aggressive 58.2 5.6 52.0 58.0 65.7
(mi/h) Average 61.8 2.6 59.0 62.0 64.0
Conservative 48.5 9.2 42.0 48.5 55.0
Ramp vehicle Aggressive 1.4 1.9 0.0 0.0 4.9
acceleration (ft/s2) Average 0.4 0.7 0.0 0.0 1.5
Conservative 0.0 0.0 0.0 0.0 0.0
Lag vehicle gap (ft) Aggressive 92.9 26.1 49.1 95.5 134.8
Average 66.0 22.0 47.9 59.6 97.0
Conservative 95.1 34.6 70.7 95.1 119.6
Lead vehicle gap (ft) Aggressive 75.0 32.9 25.2 66.6 140.1
Average 102.5 32.0 72.6 98.6 139.9
Conservative 70.7 17.5 58.4 70.7 83.1
Total gap (ft) Aggressive 168.0 41.5 91.6 178.6 222.9
Average 168.5 25.1 132.7 176.7 187.8
Conservative 165.9 17.2 153.7 165.9 178.0
Position rel. to solid Aggressive 119.8 64.7 28.5 104.5 246.9
white line (ft) Average 139.9 53.1 66.3 153.5 186.0
Conservative 163.0 279.0 -34.0 163.0 360.0
Acceleration lane Aggressive 51.0% 16.0% 30.6% 46.3% 75.2%
used (%) Average 59.2% 18.5% 31.5% 67.5% 70.2%
Conservative 37.8% 18.2% 24.9% 37.8% 50.7%












Table 6-2 shows that the average speeds and accelerations of the merging vehicle under

free merging do not vary significantly by driver type. Also, with respect to the accepted gaps, the

data do not reveal any trend based on driver type. This is expected since in free merges the gap

selection should be random and independent of drivers' interactions. Regarding the merging

position the data show that drivers make use of at most 59.2 percent of the acceleration lane,

which possibly indicates that they have reached an acceptable speed and acceleration for

merging freely.

The summary statistics of the ramp vehicle-related parameters in cooperative merging

maneuvers are presented in Table 6-3. The average density under this type of merging

maneuvers was 32.4 veh/h/ln and the average speed on the right-most lane was 56.2 mi/h.

Table 6-3. Statistics of ramp vehicle gap acceptance parameters by driver type for cooperative
merges
Parameter Driver type Mean St.dev. Minimum Median Maximum
Ramp vehicle speed Aggressive 48.8 12.0 34.0 50.2 61.0
(mi/h) Average 53.3 5.9 49.0 51.0 60.0
Conservative 49.0 8.5 41.0 47.0 53.0
Ramp vehicle Aggressive 1.8 2.1 0.0 1.5 4.2
acceleration (ft/s2) Average 0.2 0.3 0.0 0.0 0.5
Conservative 0.0 0.0 0.0 0.0 0.0
Lag vehicle gap (ft) Aggressive 47.6 17.1 34.9 41.6 72.5
Average 68.4 27.4 44.6 62.4 98.3
Conservative 83.8 30.4 62.3 83.8 105.4
Lead vehicle gap (ft) Aggressive 67.1 36.6 39.1 56.4 116.6
Average 92.1 47.8 43.1 94.7 138.6
Conservative 66.8 17.9 54.1 66.8 79.5
Total gap (ft) Aggressive 114.7 27.5 84.6 111.5 151.4
Average 160.5 35.1 139.2 141.4 201.0
Conservative 150.7 12.5 141.8 150.7 159.5
Position rel. to solid Aggressive 204.1 188.8 75.0 130.6 480.0
white line (ft) Average 176.7 76.2 95.0 189.3 245.9
Conservative 73.4 50.3 37.8 73.4 109.0
Acceleration lane Aggressive 48.2% 23.5% 33.0% 38.3% 83.3%
used (%) Average 43.5% 12.6% 33.3% 39.5% 57.6%
Conservative 46.7% 24.2% 29.6% 46.7% 63.9%












Table 6-3 shows the variation of average speed and acceleration by driver type. Aggressive

drivers appear to have the lowest average merging speeds, however, the observed variability in

their speeds was high (12 mi/h). The data also show a distinct trend of the accepted gaps by

driver type. Gaps (primarily the lag and total) decrease as the degree of aggressiveness increases.

Also, with respect to the merging position, vehicles make use of less than 50 percent of the

acceleration lane when accepting a gap after the freeway vehicle's cooperation.

The summary statistics of the ramp vehicle-related parameters in forced merging

maneuvers is presented in Table 6-4. The average density for the observed forced merges was

36.5 veh/h/ln, and the average speed on the right-most lane was 59.1 mi/h.

Table 6-4. Statistics of ramp vehicle gap acceptance parameters by driver type for forced merges
Parameter Driver Type Mean St.Dev. Minimum Median Maximum
Ramp vehicle speed Aggressive 56.1 4.9 49.0 57.8 60.0
(mi/h) Average 52.0 2.0 50.0 52.0 54.0
Ramp vehicle Aggressive 2.8 1.8 1.0 1.7 5.9
acceleration (ft/s2) Average 2.0 0.8 1.5 1.5 2.9
Lag vehicle gap (ft) Aggressive 55.7 18.9 37.2 52.3 81.3
Average 64.4 21.0 41.5 68.7 82.9
Lead vehicle gap (ft) Aggressive 49.9 29.6 31.9 36.8 94.1
Average 71.0 34.4 31.4 87.8 93.8
Total gap (ft) Aggressive 105.6 22.5 84.3 103.4 131.3
Average 135.4 21.1 114.4 135.3 156.6
Position rel. to solid Aggressive 46.2 91.3 -50.0 32.5 170.0
white line (ft) Average 133.0 91.2 29.1 170.0 200.0
Acceleration lane Aggressive 39.0% 13.8% 23.9% 37.4% 57.3%
used (%) Average 45.7% 8.6% 35.9% 48.9% 52.2%

None of the conservative drivers was observed to perform a forced merge, and this is

expected considering the characteristics of this driver type, as it was also discussed in Chapter 5.

The findings indicate that aggressive drivers merge with higher speeds than average

drivers. Also, the speeds and accelerations of both types of drivers are higher than those recorded

under cooperative merging (Table 6-3). Aggressive drivers also accept smaller gaps than average












drivers (lead, lag and total). Lastly, both aggressive and average drivers have initiated the merge

after covering 39.0 and 45.7 percent of the acceleration lane, respectively.

The Gap Acceptance Model

The gap acceptance model is based on field observations of the total accepted gaps (Figure

6-1). For the model development, the total accepted gaps were assumed to follow a lognormal

distribution to ensure their non-negativity. Regression was performed considering all types of

merging maneuvers. The general form of the total gap is:

ln(Gap) = a+ )T X (6.1)

Or, equivalently,

Gap = exp(a+ 3TX) (6.2)

Where, a is a constant, X is vector of explanatory variables affecting the total gap under the

different types of merging maneuvers, fT is the corresponding vector of parameters.

As it was shown in Table 6-2 through Table 6-4, the accepted gaps vary as a function of

the driver type. Although drivers were categorized to three driver types (aggressive, average and

conservative), only two types were eventually used in the regression model, namely, the

aggressive and the non-aggressive drivers (i.e., average and conservative drivers). This was

primarily because the differences between the average and the conservative drivers were

minimal.

The total gap is a function of the maneuver type (free, cooperative or forced), the

proportion of the acceleration lane used by the ramp vehicle and its acceleration, the average per-

lane density, and whether the ramp driver is aggressive. The results of the regression model for

the total accepted gaps when merging is shown in Table 6-5.












Table 6-5. Parameter estimates for total accepted gap
Parameter Parameter value t-statistic
Constant 5.343 33.46
Free Merge 0.141 1.86
Aggressive driver*forced merge -0.324 -2.80
Aggressive driver*cooperative merge -0.262 -2.46
Proportion acceleration lane used -0.445 -2.43
Average density (veh/mi/ln) -0.005 -1.66
Ramp vehicle acceleration (ft/s2) 0.032 1.84

All selected explanatory variables are significant at the 90% confidence level. The R2 of

Equation 6.3 is 65.5 percent which indicates the percent of variance in the average total gaps

explained by the selected explanatory variables.

As expected, gaps under free merging are larger than under cooperative or forced merging.

Also, the model does not distinguish differences between the driver types in gap acceptance

decisions under free merges.

However, gap acceptance under cooperative or forced merging does depend on the driver

type. The model suggests that aggressive drivers merge at smaller gaps than non-aggressive

drivers, when performing cooperative of forced merging maneuvers. Also, the gaps under forced

merging are smaller than under cooperative merging for aggressive drivers. For non-aggressive

drivers, the differences in gap acceptance between forced and cooperative merging maneuvers

were not significant. Therefore, the model captures differences in gap acceptance between free

and constrained (cooperative or forced) merging maneuvers.

The model suggests that the total accepted gap decreases as the vehicle is approaching the

end of the acceleration lane. This trend indicates that the urgency to merge increases for all

drivers as they approach the end of the lane, and they are willing to accept smaller gaps. The

trend between the total gap and the proportion of acceleration lane used, by driver type and
















merging maneuver, is shown in Figure 6-4. Average values of density and ramp vehicle


acceleration were assumed for this graph.


-- ~ ~- -----------
-


0.2 0.4 0.6 0.8
Proportion of Acceleration Lane Used
All Drivers-Free -Aggressive-Coop
- NonAggressive-Coop/Forced Aggressive-Forced


Figure 6-4. Relationship between total gap and proportion of acceleration lane used by driver
type and maneuver type.


The total gaps increase with increase in the ramp vehicles' acceleration, indicating that the


ramp vehicle has accelerated closer to the freeway speed. The relationship between the vehicle's


acceleration depending on their behavior as well as the maneuver type is shown in Figure 6-5.


0 1 2 3 4 5 6 7 8
Ramp Vehicle Acceleration (ft/s2)
All Drivers-Free -Aggressive-Coop
NonAggressive-Coop/Forced Aggressive-Forced

Figure 6-5. Relationship between total gap and ramp vehicle's acceleration by driver type and
maneuver type.


- - - -



--------- .














The model suggests that the total gap decreases when the average density increases. This is

because in dense traffic conditions smaller gaps are available for all drivers to accept. Figure 6-6

shows the relationship between the average density and the total gap depending on the maneuver

type and driver's aggressiveness. Average values for the proportion of acceleration lane used and

the ramp vehicle's acceleration were applied to develop this relationship.


250
230

210
190
~ 170
150
130 --- -- -- -- -- -- -- -- -- -- -- -- -- ---- -





110
90
10 20 30 40 50 60
Average Density (veh/h/In)
All Drivers-Free -Aggressive-Coop
NonAggressive-Coop/Forced Aggressive-Forced


Figure 6-6. Relationship between total gap and average density by driver type and maneuver
type.

Development of the Deceleration Model

The probability that any freeway vehicle decelerates when facing a cooperative or forced

merging situation is captured by the deceleration probability model. This model has two

components. The first component describes the event that a freeway vehicle will decelerate by

providing cooperation, indicating the transition from the normal state (no interaction) to the

cooperative state. The second component captures the event that a freeway vehicle will

decelerate as a response to a forced merge by the ramp vehicle, given that no cooperation was

provided earlier. This assumes the transition of the freeway vehicle from the normal state (no

interaction) to the forced state. These two events are mutually exclusive, i.e., they cannot occur












simultaneously. Therefore, the deceleration probability model can be described by the following

expression:

Pn(DECt) = Pn(DEC, n,t = coop/st-,n = normal)
+ Pn(DEC, Sn,t = forced/st-,n = normal) (6.3)
Where St,n is the state of the freeway vehicle n at time t, which can be normal (no

interaction), cooperative, or forced.

This section describes the dataset and presents the model formulation for both components.

Estimation Dataset for Deceleration Model

This section describes the datasets used to develop the initiation of cooperation model and

the forced merging model.

Dataset for initiation of cooperation

Observations of the participants while they were driving on the freeway passing through a

merge junction were used to model their reactions (deceleration, lane changing or do nothing)

towards the merging ramp vehicles. The estimation dataset for this model includes observations

both before, and at the time the participant starts to yield to the ramp vehicle. Typically,

participants' actions would be observed as soon as they could see the (potentially interacting)

ramp vehicle entering the acceleration lane, and until they had expressed their decision to

decelerate, change lanes, or driver uninterrupted, by clearly stating so.

The sample includes twenty-three observations where the freeway vehicle cooperated by

either decelerating or changing lanes (Table 5.2), and thirty-one observations where no

cooperation was provided. 13 percent of these observations were decelerations, 29.6 percent

were lane changes and for the remaining 57.4 percent the drivers did not cooperate.

The ramp vehicle speed ranged from 38 to 67.4 mi/h with an average of 54.4 mi/h, and the

freeway vehicle speed ranged from 52 mi/h to 75 mi/h, with an average speed of 64 mi/h. The

relative speed between the freeway vehicle and the ramp vehicle is calculated as the speed of the













freeway vehicle less the speed of the ramp vehicle. Histograms of the relative speed and the

freeway vehicle are presented in Figure 6-7.


-5 0 5 10 15 20 25 30
Relative Speed between Freeway Vehicle and Ramp Vehicle (mi/h)


55 60 65 70 75
Freeway Vehicle Speed (mi/h)

Figure 6-7. Distribution of A) relative speed between the freeway vehicle and the ramp vehicle,
and B) freeway vehicle speed for initiation of cooperation.

The average freeway density was 22.1 veh/mi/ln, and it covers a wide range of values,

from 6.6 veh/mi/ln to 40 veh/mi/ln. The average freeway speed on the right lane was 63.2 mi/h

ranging from 46 to 70 mi/h. Histograms of the density and the speed difference between the

freeway vehicle and the average speed on the right lane (right lane average speed less the speed

of the subject-freeway vehicle) are shown in Figure 6-8.



















20


S15


10
.5-

0



8 16 24 32 40
Average Density (veh/mni/In)
A


25


20


S15


10


5


0 '
16 -12 -8 -4 0 4 8 12
Speed Difference of Freeway Vehicle and Average Speed on Right Lane (mi/h)
B


Figure 6-8. Distribution of A) average density, and B) speed difference between the freeway
vehicle and the average speed on the right lane for initiation of cooperation.

The speed difference histogram in Figure 6-8 shows the speed difference covers a wide


range suggesting that in many cases the participants were driving on greater or less speed than


their lane average.


The average distance between the ramp vehicle and the freeway vehicle before initiating a


cooperative maneuver was found to be 118 ft, ranging from 39.5 ft to 257 ft. Also, the average


position of the ramp vehicle, in terms of proportion of acceleration lane used was 0.21 (ranging


from -0.03 to 0.65). The negative sign of the minimum proportion suggests that the freeway












vehicle reacted before even the ramp vehicle entered the acceleration lane. The mean ramp

vehicles' position as a function of the remaining distance to the end of the acceleration lane is

821 ft, and its range is from 211.4 ft to 1675 ft. The average distance between the freeway

(subject) vehicle and the ramp vehicle is 118.7 ft ranging from 39.5 ft to 257 ft.

Dataset for initiation of forced merging

The dataset for the forced merging model contains twenty-four observations of forced

merging maneuvers performed by the participants. A forced merge was assumed to be initiated

as soon as the ramp vehicle starts to cross the line.

The dataset for this model includes the data used for the gap acceptance under forced

merging conditions (Table 6-4). Additional data obtained before the initiation of the forced

maneuver, as well as data where the ramp vehicle did not initiate a forced merge and the freeway

vehicle did not show any cooperation were also used. Summary statistics of the data used for the

development of the forced merging model are shown in Table 6-6.

Table 6-6. Statistics of dataset for forced merging model
Parameter Average St.dev. Minimum Median Maximum
Ramp vehicle speed 56.00 4.38 49.00 57.50 61.00
(mi/h) (50.79) (8.41) (24.00) (51.00) (62.50)
Ramp vehicle 2.57 2.18 0.00 2.20 7.33
acceleration (ft/s2) (0.63) (1.05) (0.00) (0.00) (4.40)
Lag vehicle relative 1.46 4.84 -3.27 0.50 14.41
speed (mi/h) (6.72) (6.82) (-4.61) (5.74) (27.36)
Average right-lane speed 58.67 6.33 50.00 57.50 68.00
(mi/h) (58.42) (6.75) (37.00) (58.00) (76.00)
Cluster size 1.67 0.78 1.00 1.50 3.00
(1.82) (0.89) (1.00) (2.00) (4.00)
Average density 36.45 12.16 18.21 37.09 52.80
(veh/mi/ln) (30.12) (10.72) (12.35) (30.80) (52.80)
Proportion acceleration 46.8% 13.3% 23.9% 46.6% 75.5%
lane used (23.0%) (14.0%) (5.0%) (25.1%) (49.4%)
Data in parenthesis are for the entire dataset.












Deceleration Model Due to Cooperative Merging

The freeway through vehicle is facing three choices when identifying a ramp vehicle

which is subject to merge. The freeway vehicle may decide to either provide cooperation to the

ramp vehicle by decelerating or by changing lanes, or to continue driving uninterrupted.

Based on the focus group discussions and the field observations the decision-making

process was modeled as a Multinomial Logit (MNL) Model, where the freeway vehicle has three

choices: to decelerate, to change lanes, to do nothing. If gaps are not available, then lane

changing is not an option, thus the freeway vehicles' choices are to decelerate or not yield to the

ramp vehicle.

The utilities of the choices for the freeway vehicle n are:

Ui,n = V,,n + Ei,, (6.4)
i = decelerate, change lanes, no-coop initiation

Where, Vi,~ are the deterministic components of the utilities of driver n to decelerate,

change lanes and to not initiate cooperation. For the estimation of the deterministic components

of the utilities the reference choice was the choice to decelerate. The utilities for the remaining

choices are:

Vi,n = Xi,n .i P,n (6.5)
i = decelerate, change lanes, no-coop initiation

Where Xi,n, are the vectors of explanatory variables that affect the utilities to change lane,

decelerate and do nothing. Pi,n are the corresponding vectors of the parameters. The vectors of

explanatory variables include only generic variables. The final model parameters of the MNL

model are presented in Table 6-7. The log-likelihood function for this model is -39.499 and the

adjusted rho-square is 0.216.












Table 6-7. Parameter estimates for MNL model.
Explanatory variables No cooperation Change lanes
Parameter t-statistic Parameter t-statistic
Constant 2.055 1.574 4.179 3.509
Distance to end of acceleration lane 0.002 2.107 0.002 2.107
Cluster size -0.724 -1.710
Min (0,Vavg-Vn) -0.144 -1.600
(non conservative drivers)
Distance to ramp vehicle 0.008 1.188
(conservative drivers)
Distance to ramp vehicle -0.018 -2.337
(all drivers)
Average density (veh/mi/ln) -- -0.071 -1.623

Both utilities of do nothing and change lanes depend on the position of the ramp vehicle

with respect to the end of the acceleration lane. Although the proportion of acceleration lane used

is a parameter more suitable to the data (due to observations at ramp junctions with different

geometry), the remaining distance was found to be more significant, probably because the

freeway vehicle is more sensitive to the distance left, irrespective of the how far on the

acceleration lane the ramp vehicle has traveled. As the ramp vehicle approaches the end of the

lane (distance decreases), the utilities of change lanes or do nothing decrease, and therefore, the

probability of decelerating increases. Figure 6-9 shows the probabilities of deceleration, lane

changing and no cooperation as a function of the remaining distance and driver type

(conservative and non-conservative). Average conditions were assumed for the development of

this graph.

















0 70
060 ------------------------------ - -------------
060 -

050

_" 0 40

030 -

o00 ------------------------------------------
020

010

00
0 200 400 600 800 1000 1200 1400 1600
Distance to end of acceleration lane (ft)
P(Dec)-Conservative P(NoCoop)-Conservative -- P(CL)-Conservative
P(Dec) -P(NoCoop) -P(CL)



Figure 6-9. Probability of decelerating, changing lanes or no cooperating as a function of the
distance to end of the acceleration lane for conservative and non-conservative drivers.


According to Figure 6-9, the probability of deceleration is not sensitive to driver types,


however non-conservative drivers are more likely to change lanes than conservative drivers.


The decision of the freeway vehicle also depends on the number of ramp vehicles present


(cluster size). Increased number increases the probability that the ramp vehicle will cooperate


(Figure 6-10).


1 00
090
080 ----
070------- -
S060 -
I 050 -- -
040 --
030 --- -
020 -
010 ----
000
0 1 2 3 4 5 6
Cluster size

P(Dec)-Conservative P(NoCoop)-Conservative P(CL)-Conservative
P(Dec) P(NoCoop) -P(CL)



Figure 6-10. Probability of decelerating, changing lanes or no cooperating as a function of the
cluster size for conservative and non-conservative drivers.














When the number of vehicles on the ramp is small, drivers are less likely to show any

cooperation. Figure 6-10 also shows that conservative drivers are less likely to change lanes,

however, the probability of decelerating is almost the same for all drivers.

As the distance between the ramp vehicle decreases, all drivers are more likely to change

lanes, and less likely to decelerate. Figure 6-11 shows the effect of the distance to the ramp

vehicle on the freeway vehicle decisions by driver type.


1.00
0.90

0.80 ----- -

0.70 -----------,- ,- -------
P0.60 *

0.40 --- -
0.40 %



0.10 -- -- - -
0.00
0 50 100 150 200 250
Distance to ramp vehicle (ft)
P(Dec)-Conservative P(NoCoop)-Conservative P(CL)-Conservative
P(Dec) P(NoCoop) -P(CL)


Figure 6-11. Probability of decelerating, changing lanes or no cooperating as a function of
distance to the ramp vehicle for conservative and non-conservative drivers.

Figure 6-1 also shows that when the distance between the two vehicles is large,

conservative drivers are more likely not to provide cooperation, whereas non-conservative

drivers have increased probability of initiating cooperation compared to conservative drivers.

Also, as the distance decreases, conservative drivers will become more aware and they are more

willing to change lanes.

The average density also affects the utility of changing lanes. Increase of the average

density reduces the probability of changing lanes and increases the probability of decelerating as

well as showing no cooperation. Also, increase of the negative relative speed between the












freeway vehicle and lane average speed increases the probability of decelerating or changing

lanes. This parameter concerns the non-aggressive drivers, and it suggests that when the freeway

vehicle speed is close to the average speed, the vehicle is more likely to cooperate.

The probability that any freeway vehicle n will select to decelerate is given in Equation

6.6:


P, (DEC, s,t, = coop / s,,, = normal) = exp(VDEC (6.6)
exp(VDEC,f) + exp(VCL,)) + exp(VNOcoop, )

Deceleration Model Due to Forced Merging

In the dataset, all observations of forced merging lead to decelerations of the freeway

vehicles. Therefore, the deceleration model is equivalent to modeling the probability that any

ramp vehicle r will initiate a forced merge.

Pn(DEC, St,n = forced/st-1,n = normal) = Pr(St,r = forced/st-,r = normal) (6.7)

The ramp vehicle will initiate a forced merge given that the freeway lag vehicle has not

shown any cooperation earlier (previous state is normal). This model can be expressed as a

binary choice model where the two choices of the ramp vehicle, are to initiate a forced merge or

not. The utilities of the two alternatives are:

V,, = xj,r j.r (6.8)
j = initiateforced, do not initiateforced

The parameter estimates for the utility to initiate a forced merge with the respective t-

statistics are presented in Table 6-8. The log-likelihood function for this model is -11.060 and the

adjusted rho-square is 0.619. All parameters are statistically significant at a 90% confidence

level.












Table 6-8. Parameter estimates for utility of initiation forced merge
Explanatory variables Initiate forced merge
Parameter value t-statistic
Constant -15.28 -2.76
Average density (veh/mi/ln) 0.10 1.93
Proportion of acceleration lane used 21.64 2.71
Number of ramp vehicles on ramp 1.14 1.61
(aggressive ramp driver)
Ramp acceleration (ft/s2) 0.88 1.64

Based on this model, the probability of initiating a forced merge and therefore the

probability that the freeway vehicle will decelerate is:


P, (DEC, s,, = forced / s,_1, = normal) = (6.9)
1+ exp(-VFoed,r)

As it was also concluded from the focus group experiment, aggressive drivers are more

likely to initiate a forced merge than average drivers. Conservative drivers did not show any

indication of initiating a forced merge. This was also confirmed from the instrumented vehicle

experiment, since none of the conservative drivers performed a forced merging maneuver. Ramp

drivers' aLili'i,, cnisc is captured through a dummy variable related to the number of ramp

vehicles ahead of the subject ramp vehicle. Aggressive ramp drivers become more eager to enter

the freeway if there are other vehicles in front of them waiting to merge. Due to their aggressive

nature, they might seek a gap and merge sooner, causing the freeway vehicles to decelerate.

Increase in average density also reduces the availability of gaps, therefore ramp vehicles

are more willing to force their way into the freeway. Assuming average conditions, the

relationship between traffic density and the forced merging probability considering drivers'

agglPc,'i\ cn'lc is shown in Figure 6-12.


















1 00 -

0 90 Aggressive Average
0 80

S0 70
060

o 050
Z 040

S030 -
a 020
010

000
10 20 30 40 50 60 70 80
Average Density (veh/mi/In)



Figure 6-12. Forced merging probability as a function of average density and driver's

aggressiveness.


In addition, the probability of initiating a forced merge increases as the ramp vehicle


travels on the acceleration lane. Figure 6-13 shows the relationship between the forced merge


probability and the proportion of acceleration lane used by the ramp driver as a function of its


aggressiveness.



1 00

0 90 Aggressive Average
080-

0 70 ----

E 060 -

60 50 -
0 40

030

020
010

000
000 010 020 030 040 050 060 070 080 090
Proportion of acceleration lane used



Figure 6-13. Forced merging probability as a function of proportion of acceleration lane used

and driver's aggressiveness.


Increased acceleration also suggests increase in the probability of performing a forced


merge. This is probably because of the ramp vehicles' effort to increase rapidly their speed on


the acceleration lane in order to decrease the speed difference with the lag vehicle and merge.














Figure 6-14 shows the relationship between ramp vehicle's acceleration and the probability of


initiating a forced merge. As expected, aggressive drivers are more likely to perform a forced


merge than average drivers.


1 00
0 90 Aggressive Average -
0 80 -
0 70
E 0 60
20 50 -
Z0 40
0 30
020
010
0 00
0 1 2 3 4 5 6 7 8
Ramp vehicle acceleration (ft/s2)



Figure 6-14. Forced merging probability as a function of the ramp vehicle acceleration and
driver's aggressiveness.

The Deceleration Probability Model

Considering the equations 6.3, 6.6, and 6.9, the model that describes the probability that

the freeway vehicle will decelerate at the merge area is summarized in the following equation:



P, (DEC,)= exp(VDE (6.10)
exp(VDEc, ) + exp(VcL, ) + exp(VNo-oo,, ) 1 + exp(-VForced,r)


The Merging Turbulence Model

The merging turbulence model transfers the deceleration probability model to the


macroscopic level. The merging turbulence model describes the probability (frequency) that N


freeway vehicles will decelerate due to the merging ramp flow over time.


1 N
P(MergingTurbulence) = -P (Dec) (6.11)
RampFlowRate .=


The data for the merging turbulence model were obtained through video observations of


two breakdown events at the J.T. Butler NB on-ramp. The first occurred during the morning peak















period and the second during the afternoon peak period. Vehicle decelerations due to merging,


lane changing, and also due to other reasons not easily identifiable through the videos were


recorded. The prevailing ramp and freeway flow was also obtained.


Typically, the decelerations became more frequent when the breakdown was imminent. A


speed threshold criterion was applied for identifying the breakdown events, since this criterion is


typically applied in capacity analysis studies. The breakdown events were identified when the


average freeway speed at the merging area would drop below the 60 mi/h threshold (posted


speed limit is 65 mi/h) for at least five minutes.


Time-series plots of speed were overlaid with the time-series of observed decelerations to


compare the identified times to breakdown of the two methods. Figure 6-15 shows an example of


the two time-series plots for one breakdown event.


800 07
-Average Speed
Right Lane Speed
70 0 T- otal Turbulence 0 6
Merging Turbulence

\ / 05

50 0
E 04
400 2
|,, /Breakdown \
S300o 3:48 PM

/ o 02
20 0

10 0

00 0
3 39 00 PM 3 44 00 PM 3 49 00 PM 3 54 00 PM 3 59 00 PM
Time



Figure 6-15. Time-series of speed and number of decelerations on October 9th, 2008.












Figure 6-15 shows an increasing trend of merging decelerations and total decelerations

along with decrease in average speeds in all lanes. Based on the applied definition of breakdown,

the breakdown is identified at 3:48 PM. Before the breakdown interval, the total decelerations

include mostly decelerations due to merging and few decelerations due to lane changing. No

decelerations are observed downstream of the merge. Two to three minutes before the

breakdown (starting at 3:45) the merging turbulence increases abruptly. The total turbulence also

increases slightly, indicating that most of the turbulence increase is due to merging decelerations.

The number of lane changes also increases, however, these were not observed to cause any

turbulence. The maximum merging turbulence observed before the breakdown exceeds 0.5,

indicating that more than 50 percent of the merging maneuvers caused decelerations.

During the breakdown minute, the total turbulence increases even more, and exceeds 0.4.

The proportion of vehicles decelerating due to merging remains high and over 0.5. Decelerations

downstream of the merge start to appear. After that minute, the decelerations are more frequent,

and some vehicles even stop at the middle and right lane for few seconds. The average speed has

dropped at 50 mi/h and all incoming traffic is reducing speed to join the queues.

Figure 6-16 shows the relationship between the total freeway and ramp flow, and the

merging turbulence probability for the same breakdown event. Generally, as the total flow

increases, the merging turbulence probability increases as there are more opportunities for

vehicle interactions. The highest merging turbulence observed one minute before the breakdown

(3:47PM) exceeded 0.5. After the breakdown, the merging turbulence remains at high levels,

however, the volume is decreasing. Several observations also resulted in zero merging turbulence

probability and these observations. These were observed approximately twenty minutes earlier

than the breakdown event.














0.8
Pre-breakdown
0.7 0 Post-breakdown
At breakdown
0.6 -- ---

0.5 -- 3:47 PM
S0.5

0.3

0.2
0) 0.3 ---------------------------------------------------------





0.0 -- -
0 20 40 60 80 100 120
Total Freeway and Ramp Volume (veh/min)

Figure 6-16. Relationship between total freeway and ramp flow and probability of merging
turbulence.

Based on the field observations during the breakdown event it was found that there is a

correlation between the merging turbulence and the speed reduction associated with the

breakdown event. From Figure 6-15 it can be concluded that the total turbulence and the merging

turbulence can serve as a precursor-indicator of the breakdown events, and could predict that the

breakdown is imminent one to three minutes before the speed decrease is recorded on the

detectors. Additional data are required to verify this conclusion.

The Breakdown Probability Model

This section discusses the proposed application of the merging turbulence model for

developing the breakdown probability model. For the development of the breakdown probability

model, field observations of merging maneuvers and the resulting merging turbulence frequency

are required. A large sample size is also necessary (e.g., breakdowns over a six-month period).

For the model development the breakdown intervals are identified considering the merging














turbulence criterion (e.g., when the turbulence exceeds 0.5). The Kaplan-Meier method could be

used, as this was also applied in Brilon (2005).

According to the Kaplan-Meier method, the distribution function of the breakdown volume


F(q) is:


F(q)= 1-f --; i {B} (6.12)
i:q, q ki


Where, q is the total freeway volume (veh/h), qi is the total freeway volume (veh/h) during

the breakdown interval i, (i.e., breakdown flow), ki is the number of intervals with a total freeway


volume of q > qi and {B} is the set of breakdown intervals (1-minute observations).

An illustration of the breakdown probability model is shown in Figure 6-17. The curve was

developed by applying the typical breakdown definition, where the speed drops below the 60-

mi/h threshold. The breakdown observations were during the am peak period and cover six

months of data.


0.35 1.00
-Breakdown Probability
0.90
0.30 0 AM-At breakdown -1
0.80
0.25 --- 0.70

17.2% 55.0% 0.60
0.20 ........-.. -. ...-. ..... ... .......... ... ....... ...............
2 0.50

S I
0 0.40

S 0.10 -0.30

0.20
0.05
0.10

0.00 0.00
0 20 40 60 80 100 120 140 160

Freeway and Ramp volume (veh/min)


Figure 6-17. Breakdown probability model and merging turbulence.












Figure 6-17 also displays the merging turbulence for one breakdown event, based on the

field data collection. The merging turbulence during the breakdown interval was 0.55 and it

corresponds to breakdown probability of 17.2%. Additional breakdown-related data were not

available, however, this graph shows the transferability of the breakdown probability model

considering the two breakdown definitions. Future research direction should be towards the

development of the breakdown probability model using the merging turbulence probability as the

breakdown identification criterion.

Summary and Conclusions

This chapter presented a gap acceptance model under different merging conditions and a

driver behavioral model that predicts freeway vehicles' interactions with the merging vehicles.

Driver characteristics (aggressiveness) and their variation based on traffic conditions have been

incorporated into both models. This chapter also presented the merging turbulence model which

evaluates the effect of vehicle interactions at the merge area on the freeway flow. Field

observations of one breakdown event showed that the merging turbulence increases before the

breakdown and it could serve as an indicator for identification of the breakdown events.

The final conclusions with respect to the data analysis and the model development are

offered here:

* The ramp design affects the merging position of the ramp vehicles. It was found that
compared to parallel type on-ramps drivers used more length on the tapered on-ramps
before merging. It was also found that the merging position on parallel on-ramps varies
significantly, ranging from almost the end of the acceleration lane to even before the end of
the solid white line.

* The gap acceptance model considers variations on the accepted gaps based on drivers'
aggressiveness as well as the type of the merging maneuver. Drivers were grouped to
aggressive and non-aggressive (average and conservative). It was found that aggressive
drivers accept smaller gaps than non-aggressive, under cooperative and forced maneuvers.
It was also found that the gap acceptance depends on the position of the ramp vehicle and
its acceleration, and the traffic density.












* The freeway vehicle's decision to decelerate, change lanes or not provide any cooperation
to the ramp vehicle was modeled as an MNL model. It was found that the freeway
vehicles' decisions depend on the ramp vehicle's position on the acceleration lane, the
distance with the ramp vehicle, the freeway density, and the number of vehicles on the
ramp. The driver behavior types were grouped to conservative and non-conservative
(aggressive and average).

* It was found that conservative drivers are more sensitive to their distance with the ramp
vehicle than non-conservative drivers. Although they are less likely to cooperate compared
to non-conservative drivers when the distance is large, they become increasingly concerned
and try to change lanes when the distance decreases to avoid conflict with the merging
vehicle.

* The forced merging assumes that all freeway vehicles will decelerate subject to the
initiation of a forced maneuver. Aggressive and average driver types are included in this
model since conservative drivers were not observed to perform forced merging maneuvers.
The initiation of a forced maneuver depends on the ramp vehicle's aggressiveness and
acceleration, its position on the acceleration lane, the number of ramp vehicles merging
ahead and the freeway density.

* Although three driver types were initially considered, these were grouped into two
categories for the model development. Also, for the models that describe the ramp
vehicle's behavior drivers were grouped to aggressive and non-aggressive, whereas for the
model that describes through drivers' behavior drivers were grouped to conservative and
non-conservative. This may indicate that driver behavior changes depending on whether
they are on the freeway or the on-ramp. This finding supports the focus group result, where
it was found that drivers' aggressiveness depends on their task.

* Evaluation of the merging turbulence model suggests its correlation with the time to
breakdown, as it was found to increase when the breakdown event was imminent, one to
three minutes before the breakdown event (i.e., before a speed drop is recorded on the
detectors).

The following recommendations are offered:

* The vehicle interactions and how these differ by driver type should be considered in
developing or refining existing analytical or simulation models for freeway operations.

* The variation of driver types depending on their task should be incorporated to simulation
models. This would also assist in developing more realistic tools for simulating the
freeway flow breakdown.

* The merging turbulence model needs to be verified with additional breakdown
observations. It is further recommended to use this measure for identifying and even
predicting the time to breakdown.












CHAPTER 7
CONCLUSIONS

This chapter summarizes the research conducted in this thesis and presents the most

important findings. Recommendations for future research are also offered.

Research Summary

A freeway-ramp merging model that considers vehicle interactions and their contribution

to the beginning of congestion was presented. Focus group discussions were conducted to attain

knowledge about drivers' thinking process when merging. There are three types of merging

maneuvers (free, cooperative, and forced), based on the degree of interaction between the

freeway and the ramp merging vehicle. Field data collection using an instrumented vehicle

experiment was performed to observe drivers' merging process. Behavioral characteristics of the

participants were also evaluated. The collected data were used for calibrating driver behavior

models that pertain to their decisions to decelerate, change lanes or not interact subject to the

ramp merging traffic, considering their behavioral attributes. A merging turbulence model was

developed that captures the triggers for vehicle decelerations at the merging areas. The merging

turbulence model due to vehicle interactions was evaluated through macroscopic observations at

near-congested conditions. It was shown that the merging turbulence increases before the

breakdown and it could be used as an indicator of the breakdown events.

Research Conclusions

The objective of this research was to develop a model that can capture vehicle interactions

and determine the probability of breakdown on the freeway given the behavior of both mainline

and ramp merging vehicles. The research conclusions based on the focus group discussions:

* Participants' responses were uniform with respect to the steps involved in merging, both
for non-congested and congested conditions.












* Ramp design appears to affect drivers' merging process. Most of the participants indicated
they would speed up and be more aggressive on taper ramps, compared to parallel design.

* Regarding gap acceptance, the participants would likely react differently, depending on
which factors each one considers. Some drivers indicated that they might choose any gap
(adjacent, upstream, or downstream), depending on the traffic conditions, while others
would be less flexible. This searching and targeting of the surrounding gaps has also been
described in Toledo (2003). Variables that affect gap acceptance have also been identified.

* Discussion on vehicle interactions showed that, if participants are on the freeway, their
preference is to change lanes and avoid decelerating. If this cannot be accomplished, they
will cooperate, depending on the speed/acceleration of the ramp vehicle, and its size/type.
If the ramp vehicle attempts to force its way in, they will consider their distance to the
upstream vehicle and the relative speed with the adjacent lane to decide whether to
decelerate of change lanes. Ramp vehicle's decision to initiate a forced merge depends
mostly on traffic-related factors, such as freeway speed, congestion and gap availability.

* Although the discussions captured a significant variability among participants', it is likely
that their reported actions are different than their actual actions, depending on the values of
each individual. For example, someone who values aggressiveness might respond as if
he/she is aggressive.

* The stated driver actions were analyzed to identify differences in driver behavior. The
criterion of "selfishness" was used to develop three behavioral categories: aggressive,
average and conservative. Given this definition, the degree of aggressiveness of each driver
varies as a function of their task and the traffic conditions.

* In congested conditions, driver behavior displays less variability; therefore, it may be more
predictable. This is consistent with findings (Persaud and Hurdle, 1991; Cassidy and
Bertini, 1999) indicating that the mean queue discharge flow displays smaller variability
than other capacity-related measures, and remains consistent from day to day.

The following conclusions are offered based on the field data collection effort:

* The steps involved in the observed merging process are found to be quite similar with that
identified during the focus group discussions (Chapter 4), for both congested and non-
congested conditions.

* When participants were on the freeway they were involved only in free and cooperative
merging maneuvers, and not in forced merges. Participants would show cooperation
through lane changing more often than through decelerating. This indicates drivers'
preference to change lanes if a gap is available. This finding is consistent with the relevant
discussion from the focus groups.

* When the participants were the merging vehicle the majority of observed merging
maneuvers were free. Cooperative and forced maneuvers were observed as well. When
drivers' received cooperation from the freeway vehicles, usually this was through












deceleration rather than lane changing. However, it is possible that cooperative lane
changes were not captured by the cameras since these would occur considerably upstream
of the merge area. In this case they would be observed and characterized as free
maneuvers.

* The participants' behavior was categorized as aggressive, average and conservative.
Participants were categorized based on the criterion of "selfishness" as this was introduced
in Chapter 4, and quantitative information about their speed and discretionary lane
changing activity. Both assessments are consistent and come in agreement.

* There were few differences between the resulting driver type categorization and the
participants' perceived aggressiveness. This inconsistency is most likely because
participants responses may not be objective as will respond by comparing themselves with
their peers.

* The resulting behavioral categorization showed that aggressive drivers belong to younger
average age group category, compared to the other two types. Also, men were most likely
to be aggressive than women.

* The field of view of the TMC cameras was very important for this study, as they dictate
whether the locations of interest (e.g., bottlenecks) can be considered for data collection.
However, there is a trade-off between the cameras field of view and the required zoom of
the merge area to identify potential vehicle interactions and reactions. If more cameras
were available, it would be possible to use multiple and capture the field of view with
acceptable resolution upstream, at the merge and downstream of the merge area.

* The participation of actual drivers was a very challenging task of the data collection. This
was primarily because several times drivers would fail to appear for the experiments,
without any prior notification. In addition to that, obtaining drivers' thinking process was
also challenging since drivers do not explicitly state their rationale behind their course of
actions.

The conclusions related to the model development are summarized here:

* The ramp design affects the merging position of the ramp vehicles. It was found that
compared to parallel type on-ramps drivers used more length on the tapered on-ramps
before merging. It was also found that the merging position on parallel on-ramps varies
significantly, ranging from almost the end of the acceleration lane to even before the end of
the solid white line.

* The gap acceptance model considers variations on the accepted gaps based on drivers'
aggressiveness as well as the type of the merging maneuver. Drivers were grouped to
aggressive and non-aggressive (average and conservative). It was found that aggressive
drivers accept smaller gaps than non-aggressive, under cooperative and forced maneuvers.
It was also found that the gap acceptance depends on the position of the ramp vehicle and
its acceleration, and the traffic density.












* The freeway vehicle's decision to decelerate, change lanes or not provide any cooperation
to the ramp vehicle was modeled as an MNL model. It was found that the freeway
vehicles' decisions depend on the ramp vehicle's position on the acceleration lane, the
distance with the ramp vehicle, the freeway density, and the number of vehicles on the
ramp. The driver behavior types were grouped to conservative and non-conservative
(aggressive and average).

* It was found that conservative drivers are more sensitive to their distance with the ramp
vehicle than non-conservative drivers. Although they are less likely to cooperate compared
to non-conservative drivers when the distance is large, they become increasingly concerned
and try to change lanes when the distance decreases to avoid conflict with the merging
vehicle.

* The forced merging assumes that all freeway vehicles will decelerate subject to the
initiation of a forced maneuver. Aggressive and average driver types are included in this
model since conservative drivers were not observed to perform forced merging maneuvers.
The initiation of a forced maneuver depends on the ramp vehicle's aggressiveness and
acceleration, its position on the acceleration lane, the number of ramp vehicles merging
ahead and the freeway density.

* Although three driver types were initially considered, these were grouped into two
categories for the model development. Also, for the models that describe the ramp
vehicle's behavior drivers were grouped to aggressive and non-aggressive, whereas for the
model that describes through drivers' behavior drivers were grouped to conservative and
non-conservative. This may indicate that driver behavior changes depending on whether
they are on the freeway or the on-ramp. This finding supports the focus group result, where
it was found that drivers' aggressiveness depends on their task.

* Evaluation of the merging turbulence model suggests its correlation with the time to
breakdown, as it was found to increase when the breakdown event was imminent, one to
three minutes before the breakdown event (i.e., before a speed drop is recorded on the
detectors).

Future Research

The following recommendations and directions for future research are offered:

* The merging process from the driver's perspective as well as the vehicle interactions and
how these differ by driver type should be considered in developing or refining existing
analytical or simulation models for freeway operations.

* The variation of driver types depending on their task should be incorporated to simulation
models. This would also assist in developing more realistic tools for simulating the
freeway flow breakdown.

* Differences in attitudes and driver behavior between non-congested and congested
conditions should be explicitly incorporated in traffic operational models.












* The merging turbulence model needs to be verified with additional breakdown
observations. It is further recommended to use this measure for identifying and even
predicting the time to breakdown.











APPENDIX A
PRESCREENING QUESTIONNAIRES

Focus Group Questionnaire

UNIVERSITY OF

FLORIDA
Transportation Research Center

Prescreening Questionnaire for Merging Behavior Research

To Participants: This questionnaire is used to select a diverse pool of drivers to participate in
the focus group experiment. Information collected in this form will be used for traffic
engineering research only. All responses will be held in complete confidential and exempted
from public disclosure by law. In accordance with the Confidential Information Protection and
Statistical Efficiency Act of 2002 (Title 5 of Public Law 107-347) and other applicable Federal
laws, your responses will not be disclosed in identifiable form without your consent. Since
drivers' diversities are highly encouraged, only the most fitful responders will be chosen. Please
answer as many as possible.

Return Address:

By Email: azk133@ufl.edu
By Mail: Alexandra Kondyli, 518C Weil Hall, PO Box 116580, Gainesville, FL 32601


1) What is your gender?
] Male 0 Female

2) What is your age range?
[ < 20 E 20 to 29 years 0 30 to 39 years
[ 30 to 39 years [ 50 to 59 years [ >= 60 years

3) Which of the following groups do you most identify yourself as?
[ Caucasian [ Native American [ African American
[ Hispanic
[ Asian 0 Pancific Islander 0 Other
(please specify)

4) Where did you begin your driving practice and obtained your driver's license?
[ North America [ Latin America [ Asia [ Europe
E Australia [ Other (please specify)












How long have you been driving in the U.S.?
< 1 year 0 1 to 3 years
Do you have a valid U.S. driver's license?
E Yes O No


What is your occupation?
Full time student 0 University faculty/staff
Other (please specify)

How often do you drive to work/school?
Everyday 0 Usually 0L


0 3 to 9 years


0 Professional driver


Sometimes


9) How much time do you spend driving per week?
[ < 4hr [ 4 to 8 hr [ 8 to 14 hr


0 Never


0 > 14hr


10) What time of the day do you usually drive?
[ Am/pm peak hour (6 am 10 am; 4 pm 7 pm) during work days
[ Non-peak hours (including holiday and weekend)

11) What type of vehicle do you usually drive?
0 Sedan/Coupe 0 Pickup/SUV 0 Jeep 0 Truck

12) What time are you typically available for participating in the focus group experiments?
Please check as many as possible.
F Monday morning (9:00 am to 12:00 pm) r Tuesday morning (9:00 am to 12:00 pm)
r Monday afternoon (1:00 pm to 4:00 pm) r Tuesday afternoon (1:00 pm to 4:00 pm)
r Monday evening (4:00 pm to 7:00 pm) r Tuesday evening (4:00 pm to 7:00 pm)
F Wednesday morning (9:00 amto 12:00 pm) r Thursday morning (9:00 amto 12:00 pm)
r Wednesday afternoon (1:00 pm to 4:00 pm) r Thursday afternoon (1:00 pm to 4:00 pm)
r Wednesday evening (4:00 pmto 7:00 pm) r Thursday evening (4:00 pmto 7:00 pm)
r Friday morning (9:00 am to 12:00 pm) r Saturday morning (9:00 amto 12:00 pm)
r Friday afternoon (1:00 pmto 4:00 pm) r Saturday afternoon (1:00 pmto 4:00 pm)
r Friday evening (4:00 pm to 7:00 pm) r Saturday evening (4:00 pm to 7:00 pm)
r Sunday morning (9:00 amto 12:00 pm)
r Sunday afternoon (1:00 pm to 4:00 pm)
r Sunday evening (4:00 pmto 7:00 pm)
r Any time by appointment


[ >= 10 years












13) Participant's contact information (at least 1 from phone/email/mail)

Name: (Required) Phone:

Email: Date:

Mail Address:











Instrumented Vehicle Questionnaire


UNIVERSITY OF
FLORIDA
Transportation Research Center

Prescreening Questionnaire for Merging Behavior Research

To Participants: This questionnaire is used to select a diverse pool of drivers to participate in
the 'in-vehicle' data collection experiment. Information collected in this form will be used for
traffic engineering research only. All responses will be held in complete confidential and
exempted from public disclosure by law. In accordance with the Confidential Information
Protection and Statistical Efficiency Act of 2002 (Title 5 of Public Law 107-347) and other
applicable Federal laws, your responses will not be disclosed in identifiable form without your
consent. Since drivers' diversities are highly encouraged, only the most fitful responders will be
chosen. Please answer as many as possible.

Return Address:

By Email: azk133@ufl.edu
By Mail: Alexandra Kondyli, 518C Weil Hall, PO Box 116580, Gainesville, FL 32601


14) What is your gender?
O Male 0 Female

15) What is your age range?
[ < 20 E 20 to 29 years [ 30 to 39 years
[ 30 to 39 years [ 50 to 59 years [ >= 60 years

16) Which of the following groups do you most identify yourself as?
[ Caucasian [ Native American 0 African American
[ Hispanic
O Asian 0 Pancific Islander 0 Other
(please specify)

17) Where did you begin your driving practice and obtained your driver's license?
[ North America [ Latin America [ Asia 0 Europe
E Australia [ Other (please specify)

18) How long have you been driving in the U.S.?












[ < 1 year [ 1 to 3 years
19) Do you have a valid U.S. driver's license?
E Yes No

20) What is your occupation?
O Full time student 0 University faculty/staff
O Other (please specify)


[ 3 to 9 years


0 Professional driver


21) How often do you drive to work/school?
[ Everyday 0 Usually 0 Sometimes

22) How much time do you spend driving per week?
[ < 4hr [ 4 to 8 hr O 8 to 14 hr


[ Never


0 > 14hr


23) What time of the day do you usually drive?
[ Am/pm peak hour (6 am 10 am; 4 pm 7 pm) during work days
[ Non-peak hours (including holiday and weekend)

24) What type of vehicle do you usually drive?
0 Sedan/Coupe 0 Pickup/SUV 0 Jeep 0 Truck


25) What time are you typically available for participating in these experiments? Please check as
many as possible.
r Monday morning (6:00 am to 7:00 am) r Monday evening (4:00 pm to 5:00 pm)
r Tuesday morning (6:00 am to 7:00 am) r Tuesday evening (4:00 pm to 5:00 pm)
r Wednesday morning (6:00 am to 7:00 am) r Wednesday evening (4:00 pm to 5:00 pm)
r Thursday morning (6:00 am to 7:00 am) r Thursday evening (4:00 pmto 5:00 pm)
r Friday morning (6:00 am to 7:00 am) r Friday evening (4:00 pmto 5:00 pm)
r Any time by appointment


26) Participant's contact information (at least 1 from phone/email/mail)


(Required)


Name:

Email:


Phone:


Date:


Mail Address:


[ >= 10 years












Participants Background Survey


.UNIVERSITY OF

TiK, FLORIDA [er

Participants' Background Survey Form


Participant's Name: Date:


Note: Information collected in this form will be used for traffic engineering research only. All
responses will be held in complete confidential and exempt from public disclosure by law. In
accordance with the Confidential Information Protection and Statistical Efficiency Act of 2002
(Title 5 of Public Law 107-347) and other applicable Federal laws, your responses will not be
disclosed in identifiable form without your consent. By law, every interviewer, as well as every
agent, is subject to a jail term, a fine, or both if he or she makes public ANY identifiable
information you reported.

27) If the speed limit on the freeway is 70 mph, what speed are you likely to drive (assuming
good visibility and good weather conditions)?
I <65mph D 65 to 70 mph D 70 to 75 mph D 75 to 80 mph D > 80
mph

28) How often do you change lanes if the vehicle in front of you is slower?
D Very often D Sometimes D Seldom

29) What type of driver do you consider your self?
D Very aggressive D Somewhat aggressive D Somewhat conservative OVery
conservative

30) What type of driver do your friends and family consider you?
D Very aggressive D Somewhat aggressive D Somewhat conservative DVery
conservative

31) When planning your driving trip, do you allow additional time for possible delays due to
congestion, construction, or bad weather? D Yes, always D Sometimes
D Never

32) You are approaching the acceleration lane from an entrance ramp, and traffic has already
started to appear on the freeway. When do you typically merge onto the freeway?
D Right after you enter the acceleration lane
D As soon as you see an appropriate gap on the freeway
D Just before you reach the end of the acceleration lane













33) You are driving in the right-most lane of a three-lane freeway and you are approaching an
entrance ramp merge area. You can see that there are several vehicles entering the freeway
from the entrance ramp. The vehicle in front of you changes lanes to avoid conflict with the
merging vehicles. What do you do?
I Do the same change lanes to avoid any interaction with the merging vehicles
D Remain in your lane, but accelerate and close the gap between you and the vehicle
further ahead, to discourage merging vehicles from cutting in front of you
D Do nothing, and maintain your current speed
D Slow down so that the vehicles from the entrance ramp can merge













APPENDIX B
ROUTES FOR INSTRUMENTED VEHICLE EXPERIMENT


AM Route


Description: 1- ELTiER R n
En1er I-95 3 tlu :utoh Pilh-:. Hwv on-inraip IiIi- It- j-
2. Exit at Ba.n,'ead.w. Rd. off-ramp
3. Enter I -5 NP tluh ou2h Bavmea.c.vs Rld. :n-t .amn
4. Exit at J.T. Butler Dff-t amp
5. Stop at designated check-point on J.T. Butler Bl-d

7. Exit at Bo'deni Rd
S. EnTer I-95 SB tlcIl: 3B-':vder. 7 ci:-raIp
9. Exit t PLullip- H-3 ctff-amp
10. Stop at designated check-point on Philhps Hwy (The Avenues Shopping Mall
parking lot)















PM Route


4. EXIt at
Barmnedow-
1---.


Description:
1. Entet I-S5 SB tl- :lgia Bowcle:l Rd o:i-:ai.ip
2. Exit at J.T. Butler Blvd off-ramp.
S Enter -95i SB fi J11.~ J.T. BI:tler Bl-d onl-rani
4. Exit at Bavmeadows Rd.
Enter -95 E; at B~rnveadcv:-
6. Exit at Bowden Rd. off-ramp.
7. Stop at designLated check point on Bowden Rd. (parking lot)












APPENDIX C
MEASURING LENGTHS ON DIGITAL IMAGES

The derivation of the correct scale for measuring lengths and distances from uncalibrated

moving cameras is a difficult task, because the geometry of the road is constantly changing as

the vehicle is traveling on the freeway segment. To address this issue, the method developed by

Psarianos et al. (2001) is adopted. This method has been developed for measuring lane widths

but it was modified to account for lengths along the road axis.

This basic geometry is described in Figure C-1, in which O is the perspective center and M

is the image center.



Y Y
-------"--- -------:-



I ,--- ----------
YBg -- horizon

Yo
BI \B


A Ax B

Figure C-1. Image geometry with A) horizontal camera axis and B) measurements on the digital
image. (Source: Psarianos et al., 2001).


In Figure C-l the camera constant is c, yB is the y image coordinate of points B and B' on

the road surface. If Yo is the camera height measured above ground level, then the scale of the

image at a distance ZB is:

c YB B (C-)
(C-l)
Z, Y, AX,

Where AXB is the lane width BB' and AXB is the corresponding length measured in the

image. Equation C-l was used first to estimate the camera height Yo from known widths (range












from 6 to 20 ft) measured with a tape. The camera height for the front camera is estimated as

3.96 ft 0.30 ft. The camera height for the rear camera is estimated as 6.65 ft 0.50 ft.

Next, the camera constant c was estimated for both cameras given known lane widths AXB

and distances ZB according to Equation C-2.


c = ZB B -ZB B (C-2)
AXB YO

Then, the constant c of the cameras was used for estimating the length Zx from any point of the
road X, by using the extracted images from the cameras.












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BIOGRAPHICAL SKETCH

Ms. Alexandra Kondyli is a research assistant at the Transportation Research Center of the

University of Florida, at the Department of Civil And Coastal Engineering. Ms. Kondyli received

her master's degree from the Department of Civil and Coastal Engineering from University of

Florida in December 2005. Ms. Kondyli also received her graduate diploma from the Department

of Rural and Surveying Engineering of the National Technical University of Athens, Greece, in

June 2003.





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1 BREAKDOWN PROBABILITY MODEL AT FREEWAY-RAMP MERGES BASED ON DRIVER BEHAVIOR By ALEXANDRA KONDYLI A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2009

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2 2009 Alexandra Kondyli

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3 To my parents

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4 ACKNOWLEDGMENTS I would like to thank my graduate advisor, Dr. Lily Elefteriadou of the University of Florida for her insights and guidance throughout th is dissertation and her valuable support throughout all my years of study. I would also like to thank the remaining members of the committee, Dr. Scott Washburn, Dr. Yafeng Yin, Dr. Siva Srinivasan, and Dr. Orit Shechtman, for their assistance and their advices. I would like to thank my friends and fellow student s of the University of Florida Transportation Research Center for their assistance during the data collection effort. Without them, it would be impossible to complete this effor t. Special thanks are addressed to Aaron Elias, George Chrysikopoulos, Dimitra Michalaka, Seokjoo L ee, Grady Carrick, Kevin Heaslip, Irene Soria, Daniel Sun, and Cuie Lu. I am also grateful to the staff at the Jacksonville Traffic Management Center for their assistance and accommod ations during the data collection effort. Above all, I am grateful to my parents, Apostolos a nd Maria for their love and support.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS.................................... ................................................... ........................4 LIST OF TABLES..................................... ................................................... ...................................8 LIST OF FIGURES.................................... ................................................... ..................................9 ABSTRACT........................................... ................................................... .....................................12 CHAPTER 1 INTRODUCTION..................................... ................................................... ..........................14 Traffic Operations at Freeway-Ramp Merging Segments ................................................... ...14 Driver Behavior at Freeway-Ramp Merging Segments... ................................................... ...17 Objectives of the Dissertation..................... ................................................... .........................19 2 LITERATURE REVIEW................................ ................................................... ....................20 Capacity and the Breakdown Process at Freeway Ramp Merging Segments........................20 The Nature of Capacity............................. ................................................... ...................21 Breakdown at Freeway Ramp Merging Segments and Its Causes..................................24 Driver Behavior Models for Merging Maneuvers....... ................................................... ........27 Modeling Acceleration Behavior for MLC............. ................................................... .....28 Modeling Gap Acceptance for MLC.................... ................................................... ........33 Integrated Models for MLC.......................... ................................................... ................42 Mandatory Lane Changing Models Used in Simulation P rograms........................................49 Merging Under Congested Conditions................. ................................................... ...............55 Using Instrumented Vehicles to Study Driver Behavio r.................................................. ......56 Summary of Literature Review....................... ................................................... ....................60 3 BEHAVIORAL BREAKDOWN PROBABILITY METHODOLOGY..... ...........................63 Merging Model Structure............................ ................................................... ........................63 Free Merge Model................................... ................................................... .....................65 Cooperative Merge Model............................ ................................................... ................66 Forced Merge Model................................. ................................................... ...................68 Breakdown Probability Model Formulation............ ................................................... ............68 Modeling the Behavior of the Freeway Vehicle....... ................................................... ....72 Merging Turbulence and the Probability of Breakdown .................................................77 Methodological Framework........................... ................................................... ......................77 Data Types for Models.............................. ................................................... ...................78 Research Tasks..................................... ................................................... ........................80 Step 1 Conduct focus group meetings:............. ................................................... ..80 Step 2 Conduct field data collection effort:..... ................................................... ...80

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6 Step 3 Calibrate the merging models:............. ................................................... ....81 Step 4 Develop merging turbulence models:........ .................................................81 Step 5 Develop breakdown probability model:...... ...............................................81 4 FOCUS GROUP EXPERIMENTS.......................... ................................................... ...........82 Setting Up the Focus Groups........................ ................................................... .......................82 Overview of Focus Group Questions.................. ................................................... ................84 Focus Group Key Questions.......................... ................................................... ......................85 Question 1 – Merging Process Under Free-Flowing Con ditions and Selection of Acceptable Gaps.................................... ................................................... ...................85 Question 2 Merging Process Under Decreased Speed (40-60 mi/h).............................87 Question 3 Cooperative Merging and Forced Merging Maneuvers Under Decreased Speed (40-60 mi/h)....................... ................................................... ...........87 Question 4 Merging Under Stop-and-Go Traffic..... ................................................... ..87 Question 5 Effect of other people on driving beha vior............................................... ..88 Assembly of Focus Group Data....................... ................................................... ....................88 Overview of the Freeway-Ramp Merging Process....... ................................................... .......88 Refining Merging Process Under Free-Flowing and Den se Traffic...............................88 Focus Group Results for Gap-Acceptance............. ................................................... ......89 Focus Group Results for Cooperative and Forced Merg ing............................................91 Relationships Between Driver Behavior and Driver Ch aracteristics.....................................9 5 Other Observations................................. ................................................... ...........................100 Conclusions........................................ ................................................... ................................100 5 FIELD DATA COLLECTION............................ ................................................... ..............102 In-Vehicle Data Collection......................... ................................................... .......................102 Description of Instrumented Vehicle................ ................................................... ..........102 Driving Routes..................................... ................................................... .......................103 Geometry of the Freeway Ramp Junctions............. ................................................... ...104 Selection of Participants.......................... ................................................... ...................106 Data Collection Procedures......................... ................................................... ...............109 In-Vehicle Data Processing......................... ................................................... ...............110 Gaps with adjacent vehicles and gap change rates... ..............................................110 Speeds and accelerations........................... ................................................... ..........111 Vehicle positions.................................. ................................................... ...............111 Average density and freeway speed.................. ................................................... ..111 Data Collection at the Jacksonville TMC............ ................................................... ..............111 TMC Data Processing................................ ................................................... .................113 Field Experiment Results........................... ................................................... ........................116 Overview of the Observed Merging Process........... ................................................... ...116 Distinction of Merging Maneuvers................... ................................................... .........116 Driver Behavior Types.............................. ................................................... .................119 Driver Decision-Making Process..................... ................................................... ..........124 Summary and Conclusions............................ ................................................... ....................124

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7 6 MODEL DEVELOPMENT................................ ................................................... ...............126 Development of the Gap Acceptance Model............ ................................................... .........126 Estimation Dataset for Gap Acceptance Model........ ................................................... .126 The Gap Acceptance Model........................... ................................................... ............133 Development of the Deceleration Model.............. ................................................... .............136 Estimation Dataset for Deceleration Model.......... ................................................... .....137 Dataset for initiation of cooperation.............. ................................................... ......137 Dataset for initiation of forced merging........... ................................................... ...140 Deceleration Model Due to Cooperative Merging...... ..................................................1 41 Deceleration Model Due to Forced Merging........... ................................................... ...145 The Deceleration Probability Model................. ................................................... .........148 The Merging Turbulence Model....................... ................................................... .................148 The Breakdown Probability Model.................... ................................................... ...............151 Summary and Conclusions............................ ................................................... ....................153 7 CONCLUSIONS...................................... ................................................... .........................155 Research Summary................................... ................................................... .........................155 Research Conclusions............................... ................................................... .........................155 Future Research.................................... ................................................... .............................158 APPENDIX A PRESCREENING QUESTIONNAIRES...................... ................................................... ....160 Focus Group Questionnaire.......................... ................................................... .....................160 Instrumented Vehicle Questionnaire................. ................................................... ................163 Participants Background Survey..................... ................................................... ...................165 B ROUTES FOR INSTRUMENTED VEHICLE EXPERIMENT....... ..................................167 AM Route........................................... ................................................... ...............................167 PM Route........................................... ................................................... ................................168 C MEASURING LENGTHS ON DIGITAL IMAGES.............. .............................................169 LIST OF REFERENCES................................. ................................................... .........................171 BIOGRAPHICAL SKETCH................................ ................................................... ....................177

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8 LIST OF TABLES Table page 2-1 Game matrix between freeway through vehicle and merging vehicle..............................39 4-1 Demographic characteristics of focus group part icipants........................................... ......83 4-2 Factors affecting cooperative merge decisions f or freeway vehicles...............................9 2 4-3 Factors affecting forced merge decisions for ra mp merging vehicles..............................93 4-4 Factors affecting deceleration and lane-changin g decisions of freeway vehicle, when a ramp vehicle has initiated a forced merge........ ................................................... ...........94 4-5 Behavioral categories based on focus group scen arios and background survey form......99 5-1 Demographic characteristics of instrumented veh icle experiment participants.............108 5-2 Merging maneuver categories.................... ................................................... ..................118 5-3 Driver behavior types based on actual observati ons and background survey form........122 5-4 Demographic characteristics by driver behavior type............................................... .....123 6-1 Statistics of merging position by ramp design.. ................................................... ...........130 6-2 Statistics of ramp vehicle gap acceptance param eters by driver type for free merges...130 6-3 Statistics of ramp vehicle gap acceptance param eters by driver type for cooperative merges............................................. ................................................... .............................131 6-4 Statistics of ramp vehicle gap acceptance param eters by driver type for forced merges............................................. ................................................... .............................132 6-5 Parameter estimates for total accepted gap..... ................................................... .............134 6-6 Statistics of dataset for forced merging model. ................................................... ...........140 6-7 Parameter estimates for MNL model.............. ................................................... .............142 6-8 Parameter estimates for utility of initiation f orced merge........................................ ......146

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9 LIST OF FIGURES Figure page 1-1 Critical ramp junction variables............... ................................................... ......................15 1-2 Bottleneck location at freeway-ramp merging seg ments.............................................. ....16 2-1 Lane changing model structure proposed by Ahmed (1999)............................................ 43 2-2 Lane changing model structure proposed by Toled o (2003)........................................... .45 2-3 Structure of proposed model by Choudhury et al. (2007)............................................ ....47 2-4 Extended model proposed by Choudhury et al. (20 07)................................................ ....49 3-1 Conceptual description of merging process...... ................................................... .............63 3-2 The lead, lag, and total gap................... ................................................... .........................64 3-3 The free-merge model........................... ................................................... .........................66 3-4 The cooperative-merge model.................... ................................................... ...................66 3-5 The forced-merge model......................... ................................................... .......................68 3-6 Interactions between the mainline vehicle N and the ramp merging vehicle R resulting to deceleration or lane change of vehicle N................................................. ......70 3-7 Following vehicle in shoulder lane (F) and inte racting mainline (M) and ramp (R) vehicles........................................... ................................................... ...............................70 3-8 Deceleration event due to ramp merging maneuver ................................................... ......71 3-9 Potential freeway vehicle decisions due to a ra mp merging maneuver............................73 3-10 Nested model for cooperative behavior of mainl ine vehicle N...................................... ..74 3-11 Methodological plan........................... ................................................... ...........................80 4-1 Figures discussed during scenario 1............ ................................................... ..................85 5-1 Inside view of the TRC instrumented vehicle.... ................................................... ..........103 5-2 Geometric characteristics of tapered entrance r amps on I-95....................................... ..105 5-3 Geometric characteristics of parallel entrance ramps on I-95...................................... ..105 5-4 Location of available cameras along I-95....... ................................................... .............112

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10 5-5 Camera field of view along I-95................ ................................................... ..................113 5-6 Observed breakdown locations and congestion pro pagation along I-95 SB direction, and NB direction................................... ................................................... .......................114 6-1 The ramp, lag and lead vehicle, their related g aps and positions.................................. .127 6-2 Distribution of ramp vehicle speed............. ................................................... .................128 6-3 Distributions of the lag, lead, and total gap.. ................................................... ...............128 6-4 Relationship between total gap and proportion o f acceleration lane used by driver type and maneuver type............................. ................................................... ..................135 6-5 Relationship between total gap and ramp vehicle ’s acceleration by driver type and maneuver type...................................... ................................................... ........................135 6-6 Relationship between total gap and average dens ity by driver type and maneuver type............................................... ................................................... ................................136 6-7 Distribution of relative speed between the free way vehicle and the ramp vehicle, and freeway vehicle speed for initiation of cooperation ................................................... .....138 6-8 Distribution of average density, and speed diff erence between the freeway vehicle and the average speed on the right lane for initiat ion of cooperation.............................139 6-9 Probability of decelerating, changing lanes or no cooperating as a function of the distance to end of the acceleration lane for conser vative and non-conservative drivers. ................................................... ................................................... ...................................143 6-10 Probability of decelerating, changing lanes or no cooperating as a function of the cluster size for conservative and non-conservative drivers............................................ 143 6-11 Probability of decelerating, changing lanes or no cooperating as a function of distance to the ramp vehicle for conservative and n on-conservative drivers.................144 6-12 Forced merging probability as a function of av erage density and driver’s aggressiveness..................................... ................................................... .........................147 6-13 Forced merging probability as a function of pr oportion of acceleration lane used and driver’s aggressiveness............................ ................................................... ....................147 6-14 Forced merging probability as a function of th e ramp vehicle acceleration and driver’s aggressiveness............................ ................................................... ....................148 6-15 Time-series of speed and number of deceleratio ns on October 9th, 2008.......................149 6-16 Relationship between total freeway and ramp fl ow and probability of merging turbulence......................................... ................................................... ............................151

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11 6-17 Breakdown probability model and merging turbul ence............................................... ...152 C-1 Image geometry with horizontal camera axis and measurements on the digital image..169

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12 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy BREAKDOWN PROBABILITY MODEL AT FREEWAY-RAMP MERGES BASED ON DRIVER BEHAVIOR By Alexandra Kondyli August 2009 Chair: Ageliki Elefteriadou Major: Civil Engineering A freeway-ramp merging model that considers vehicle interactions and their contribution to the beginning of congestion was presented. Focus group discussions were conducted to attain knowledge about drivers’ thinking process when merg ing. Three types of merging maneuvers were considered (free, cooperative, and forced), ba sed on the degree of interaction between the freeway and the ramp merging vehicle. Field data co llection was undertaken to quantify the effect of individual driver characteristics on thei r merging decisions and associate those with the breakdown occurrences at the freeway-ramp junctions The data collection entails observations of participants driving an instrumented vehicle and simultaneous video observations of the freeway during these experiments. Behavioral charac teristics of the participants were also evaluated. The collected data were used for calibrating driver behavior models that pertain to ramp vehicles’ gap acceptance decisions and freeway vehi cles’ decisions to decelerate, change lanes or not interact subject to the ramp merging traffic, c onsidering their behavioral attributes. A merging turbulence model was developed that capture s the triggers for vehicle decelerations at the merging areas. The merging turbulence model due to vehicle interactions was evaluated

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13 through macroscopic observations at near-congested conditions. It was shown that the merging turbulence can be used as an indicator of the break down events.

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14 CHAPTER 1 INTRODUCTION Traffic Operations at Freeway-Ramp Merging Segments Freeway-ramp merging segments are important compone nts of the freeway facilities since they connect the freeway system and the adjacent ar terial network, and also they feed traffic into the freeway. These segments are also the source of dynamic interactions, as they involve the merging of two traffic streams. Conflicts occur bec ause these segments usually serve as physical bottlenecks (acceleration lane is dropped after som e length), and the two traffic streams are competing for the same space. The literature has de scribed the dynamic interactions between the two traffic streams as either cooperative (through vehicles move to the inner lanes, or yield to create gaps for the merging vehicles) or competitiv e (merging traffic forcing its way into the freeway, causing the through vehicles to decelerate ). It has also been observed that the composite behavior of acceleration and gap acceptance of the merging traffic and the cooperative behavior of the freeway traffic can result in conflicts and even congestion. In the current version of the Highway Capacity Manu al (HCM 2000), the analysis of a freeway facility is based on segmenting the facilit y to basic freeway segments, ramps and rampjunctions and weaving segments, neglecting possible interdependencies between the different freeway segments, and the impact of these on capaci ty (TRB, 2000). The Ramps and Ramp Junctions methodology (Chapter 25, HCM 2000), defin es the ramp influence area to be a 1,500 ft long segment downstream of the gore (which includes the acceleration lane and the two outmost lanes of the freeway) and the operations of vehicle s within that segment is the focus of the analysis. An illustration of the ramp influence ar ea as well as other important variables used in the HCM methodology is provided in Figure 1-1.

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15 Figure 1-1. Critical ramp junction variables (Sour ce: HCM 2000–Chapter 25). In addition, the HCM 2000 provides a clear connecti on between the definition of capacity and the breakdown occurrence. According to the man ual, capacity is defined as “… the maximum hourly rate at which persons or vehicles re asonably can be expected to traverse a point or a uniform section of a lane or roadway during a given time period, under prevailing roadway, traffic and control conditions” (HCM 2000, p. 2-2). Inherent to this definition is the notion that once capacity is achieved, the freeway facility wil l break down (transition from free-flowing conditions to congestion, i.e., level of service F) ; otherwise there is still the potential of observing higher maximum flows. This is also assoc iated with the development of queues upstream of the bottleneck, indicating excess of de mand. In the field, capacity at ramp junctions is typical ly measured at the bottleneck (as shown in Figure 1-2), where vehicles are in discharge state. Capacity cannot be measured inside the queue because the flow there is restricted by the downstr eam capacity (beyond the front of the queue) (Elefteriadou et al., 2006). On the other hand, cap acity at basic freeway segments cannot be measured in the field, as the literature has not sh own any evidence that these segments can break down without the presence of a bottleneck or other sources of demand restriction.

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16 Figure 1-2. Bottleneck location at freeway-ramp me rging segments. In addition to the measurement issues of capacity, the literature has examined various definitions of capacity. Suggested flow rates from the literature that define capacity are: (1) the maximum pre-breakdown flow; (2) the average pre-bre akdown flow; and (3) the flow rate after the upstream queue has formed (Elefteriadou et al., 2006). Irrespective of whether capacity is defined as the maximum or the average pre-breakdown flow or queue discharge flow, the literature has shown that this is not a fixed numbe r, but rather a random variable (Persaud and Hurdle, 1988, 1991; Agyemang-Duah and Hall, 1991; M inderhoud et al., 1997; Lorenz and Elefteriadou, 2001; Brilon, 2005). Regarding the breakdown events and the beginning of congestion at freeways, research has shown that breakdown does not always occur at the s ame demand levels (Elefteriadou et al., 1995; Okamura et al., 2000). Moreover, the HCM 200 0 states that (pp. 25-3) “… the turbulence due to merging and diverging maneuvers does not aff ect the capacity of the roadways involved, although there may be local changes in lane distrib ution and use”, but field observations show the opposite. The data show that at merging segmen ts, the presence of platoons of ramp vehicles that want to merge and “squeeze” on the freeway (El efteriadou et al., 1995; Kerner and Rehborn, 1996, 1997; Yi and Mulinazzi, 2007) may have “invas ive influences” on the freeway vehicles, such as decelerations and lane changes. These obser vations lead to the conclusion that

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17 breakdown events at freeway merging segments are as sociated with the interactions between the two competing traffic demands, and this might expla in the observed variability in capacity. Driver Behavior at Freeway-Ramp Merging Segments In the previous section it was shown that driver be havior affects capacity and traffic operations at freeway-ramp merging segments. Based on Rasmussen’s model (1986) driver behavior can be divided into a hierarchical structu re with three levels: Strategic level: At this level the driver determine s its goals and plans its route. The decisions made at this level, are affected by drive r’s familiarity with the transportation network and by any available real-time information. Tactical level: At this level the driver selects c ertain maneuvers to achieve short-term objectives (e.g. interactions with other drivers). Here, driver behavior is influenced by both the most recent action, and the driver’s goals at the highest level. Operational level: At this level, the driver perfo rms real actions such as steering, accelerating, and gearing. These actions are skill -based and mostly done automatically, with little conscious effort. Several interactions can be observed between the di fferent driving tasks: At the strategic level, the driver makes decisions related to the pa th choice and to determine a schedule for the trip (e.g. in terms of desired arrival time). Tact ical decisions are affected by the vehicle’s drivin g neighborhood and by the strategic concerns. For ex ample, the driver has to be in the correct lanes in order to follow the path plan. If the tri p schedule is not kept or in the presence of traffi c information the driver may decide to reevaluate the path plan and switch paths. The choices of speed and lane are translated to mechanical actions to control the vehicle. In turn, the outcome of these actions affects the positioning of the veh icle within its neighborhood. Travel behavior researchers study drivers’ strategi c choices (level 1) while the operational behavior (level 3) is studied in human factors rese arch. Driving behavior models capture tactical decisions at level 2. The most notable driving beh avior models are acceleration and lane changing models. Other important driving behaviors include negotiation of intersections and

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18 merging areas and response to signals and signs. T wo of the most important microscopic models in traffic engineering, car-following and lane chan ging, are tactical-level models. Car-following models describe the vehicle’s behavio r while following the leading vehicle. Car-following models assume that the subject vehicl e reacts to the leader’s actions. Recent research developed general acceleration models that also capture the behavior of drivers in other situations; such as in car following and free-flow conditions. Based on these models, drivers that are not close to their leaders may apply free-flow acceleration to reach their desired speed. Lane changing models have mostly been developed for micr o-simulators. The lane changing process is normally modeled in two steps: (i) the decision to consider a lane change and (ii) the execution of the lane change. Lane changes are further class ified as either mandatory (MLC) or discretionary (DLC). MLC are performed when the dr iver must leave the current lane, such as in freeway-ramp merging segments. DLC are performed t o improve vehicles’ driving conditions. In the vicinity of freeway-ramp junctions, mandator y, but also discretionary lane changes take place (DLC are performed upstream to avoid conflict s with the ramp merging vehicles). Recent research categorizes lane changes depending on the degree of interference with the adjacent vehicles, to free, cooperative and forced lane chan ges. Lane changes are usually modeled using gap acceptance models. Existing driving behavior models have several limit ations. An important limitation is that inter-dependencies between vehicles’ behaviors are not addressed, as different behaviors are modeled separately. Most significantly, the combin ation of merging and lane changing behavior on the traffic operations of the freeway is ignored Similarly, factors that influence drivers’ decisions while performing (or being affected by) m erging maneuvers have not been studied from the drivers’ perspective. Lastly, although dri ver behavior parameters are crucial for the

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19 investigation of breakdown occurrences at freeway-r amp merges and gap acceptance decisions, these are not explicitly incorporated in current mo dels. The unavailability of driver-related data may lead to inaccurate models since decisions at th e tactical level are very much dependent on the interactions between individuals. Objectives of the Dissertation The objectives of this research can be summarized a s follows: 1. To develop a ramp merging model that considers the merging process near congested conditions, as it is perceived by individual driver s. The scope of this objective includes the following elements: The ramp merging model should address all different types of merging maneuvers, such as free, cooperative and forced merging. The model should capture the vehicle interactions t hat occur during the merging process. It should also account for stochasticity of driver behavior in accepting gaps and in making decisions, for the same driver and across all drive rs. An in-depth analysis of the drivers’ perspective is required to collect information abou t factors that affect their decision process and their behavioral differences. The model should also consider the geometry of the merging area as a factor. The behavior of the freeway vehicles upstream of th e merge point (lane changing activity) should be addressed in all relevant components of t he merging model. Evaluation of the effect of the lane changing behavior on the distrib ution of gaps, and therefore the merging process, will be performed. The effect of cooperative and forced merging on the traffic conditions should also be addressed. The research will quantify the impact o f these maneuvers on the probability of breakdown. 2. To develop an analytical model that can determine t he probability of breakdown on the freeway given the behavior of both mainline and ram p merging vehicles.

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20 CHAPTER 2 LITERATURE REVIEW The chapter summarizes past research related to the estimation of capacity at freeway ramp merging segments and the description of the breakdo wn phenomenon at these locations, either through observational studies or through modeling o f the driver behavior. The first section describes previous research efforts to model the be havior of the merging vehicle (acceleration, lane changing, and gap acceptance) and discussion o n specific models that have been used in microsimulation programs follows. The next section presents findings regarding the merging process under complete congested conditions. Follo wing that, a summary of literature review on driver behavior-related studies is presented. This chapter concludes with a summary of the literature findings and their limitations. Capacity and the Breakdown Process at Freeway Ramp Merging Segments According to the current version of the Highway Cap acity Manual (HCM 2000) the capacity of a facility is defined as “…the maximum hourly rate at which persons or vehicles reasonably can be expected to traverse a point or a uniform section of a lane or roadway during a given time period, under prevailing roadway, traffi c and control conditions (HCM 2000, p. 2-2).” This definition implies that once capacity is achie ved, the facility will break down; otherwise capacity has not been attained (HCM 2000 also notes that capacity is the upper boundary of LOS E). Thus, the observation of breakdown is closely related to the capacity of a facility. Several studies that focused on the capacity of fre eway segments and the investigation of the speed/flow/density relationships have observed traffic flow and the breakdown process in the vicinity of ramp merges that usually serve as freew ay bottlenecks. The findings of these studies vary significantly, and this indicates that (i) cap acity is stochastic in nature, (ii) individual drivers’ behavior may trigger the breakdown phenome non, (iii) vehicles merging onto the

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21 freeway from an on-ramp may create traffic turbulen ce, which can result in freeway flow breakdown. The Nature of Capacity According to the definition of capacity used by the HCM 2000, each facility type has different capacity values; however these remain inv ariable for facilities with similar geometric and traffic conditions. For example, capacity valu es are given as 2,250 passenger cars per hour per lane (pcphpl) for freeways facilities with free -flow speeds of 55 miles per hour (mph), and 2,400 pcphpl when the free-flow speed is 75 mph (un der ideal geometric and traffic conditions). While the current version of the HCM treats capacit y as a deterministic value that depends on the geometric conditions of the facility, there is a significant amount of recent literature based on field data observations, which contradicts this argument, and proposes that capacity is stochastic in nature. Researchers have come to ack nowledge the stochasticity of capacity, however this has raised several other questions rel ated to which value of flow rate should be measured (maximum pre-breakdown flow rate, pre-brea kdown flow rate, discharge flow rate), where and when it should be measured, what time int erval should be used, and if it is a random variable what percentile of the distribution should be used as the descriptive statistic. The remaining of this section presents proof from the l iterature that capacity rather stochastic than deterministic in nature. Persaud and Hurdle (1991) examined various definiti ons and measurement issues for capacity; such as maximum flow, mean flow, and expe cted maximum flow definitions. Based on observations of field data at a three-lane freew ay site, over three days, they recommended that the mean queue discharge flow is the most appropria te, partly due to the consistency they observed in its measurement.

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22 Agyemang-Duah and Hall (1991) collected data over 5 2 days on peak periods to investigate the capacity drop issue when a queue fo rms, and to recommend a numerical value for capacity. They showed that the distribution of pre -queue flows and queue discharge flows in 15minute intervals, with the first one slightly more skewed toward higher flows. They recommended two capacity values: one for pre-breakd own conditions at 2,300 pcphpl, and one for post-breakdown conditions at 2,200 pcphpl. The y recognized the difficulty in defining and measuring capacity, given the variability observed. Wemple et al. (1991) also collected near-capacity d ata at a freeway site and discussed various aspects of traffic flow characteristics. H igh flows (above 2,000 vphpl) based on fifty 15min time periods were identified, plotted, and fitt ed to a normal distribution, with a mean of 2,315 vehicles per hour (vph), and a standard devia tion of 66 vph. Elefteriadou et al. (1995) developed a model for de scribing the process of breakdown at ramp merge junctions. Observation of field data sh owed that, breakdown may occur at flows lower than the maximum observed, or capacity flows. In addition, it was observed that, at the same site and for the same combination of ramp and freeway flows, breakdown may or may not occur. Elefteriadou et al. developed a probabilisti c model for describing the process of breakdown at ramp merges, which gives the probabili ty that breakdown will occur at given ramp and freeway flows, and it is based on the occurrenc e of ramp-vehicle clusters. Minderhoud et al. (1997) also studied the random na ture of capacity by considering stochastic theories for estimating capacity. Simil ar to Wemple et al. they proposed a normal distribution to describe the statistical properties of capacity. They were also the first who proposed to estimate the distribution of capacity u sing the Product Limit Method based on field observations. They borrowed the theory from lifeti me statistics analysis, assuming that a system

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23 failure (traffic breakdown) occurs when there is tr affic spillback from the bottleneck; however, they used flow observations taken from the upstream location. Thus, in this way they included congested data points in the analysis, that are ins ide the queue, and volumes at that location may be lower than the maximum possible. Brilon and Zur linden (2003) and Brilon (2005) built upon this method, although they assumed as events of fai lure cases of distinct breakdown observed at the bottleneck and not upstream (also assuming that congestion does not propagate from downstream). Brilon and Zurlinden (2003) evaluated various mathematical functions and they concluded that the Weibull distribution provides th e best fit to the empirical data. Sarvi and Kuwahara (1999) performed an evaluation s tudy of the merging capacity in Tokyo Metropolitan Expressway to determine the impa ct of geometric design and traffic characteristics on the capacity of seven merging se ctions. Based on their research, capacity is positively related to the taper length, but no corr elation with the length of the acceleration lane was found. This may occur because under congested conditions the drivers try to merge soon after entering the acceleration lane. Sarvi and Ku wahara also found that the merging capacity increases slightly with increasing relative grade ( ramp grade minus the freeway grade). With respect to the merging ratio (percentage of merging flow), the evaluation concluded that capacity increases when the merging ratio increases up to 0. 32 and then decreases. Therefore, the maximum capacity was observed for a 0.33 merging ra tio, but it is noted that additional data are required to identify the maximum capacity. Okamura et al. (2000) collected data on several fre eway sections in Japan over a whole year where they observed several breakdown events. They considered that freeway capacity is the average of the breakdown volumes (i.e., traffic volume immediately before the breakdown event), which varied over a wide range.

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24 Lorenz and Elefteriadou (2001) conducted an analysi s of speed and flow data for two freeway bottlenecks in Toronto, Canada. They sugge sted incorporating a probability of breakdown in the definition of freeway capacity, su ch as: “...the rate of flow (in pcphpl and for a particular time interval) along a uniform freeway s egment corresponding to the expected probability of breakdown deemed acceptable under pr evailing traffic and roadway conditions in a specified direction.” The value of the probabili ty component should correspond to the maximum breakdown risk deemed acceptable for a part icular time period. According to this definition, on the average, highest flows occur bef ore the breakdown. Sarvi et al. (2007) performed an analysis of the ma croscopic observations on driver behavior, and showed that capacity (measured after the onset of congestion: i.e., discharge rate) varies from one bottleneck location to another, and its range is between 1,679 and 2,068 vphpl. An important finding of this research is that capac ity at merge junctions were generally lower than capacity at other freeway segments. Breakdown at Freeway Ramp Merging Segments and Its Causes Buckley and Yagar (1974) observed the breakdown phe nomenon at an entrance ramp or lane drop. According to their observations, at the entrance ramp drivers merge into minimal gaps in the adjacent lane, and as they move downstr eam, they tend to increase their spacing to a more acceptable distance. This occurs when initial ly drivers decelerate in a car-following mode, and consequently, if one driver slows down then tho se upstream will need to decelerate more rapidly. They suggested that this shock wave movin g upstream is seen as the flow breakdown, which becomes the long-term slow-and-go traffic con dition observed upstream of the lane drop. Elefteriadou et al. (1995) collected data using fou r video cameras along the ramp merge area at two bottleneck locations, and they conclude d that the breakdown was associated with the presence of vehicle clusters coming from the on-ram p. Based on their observations, the ramp

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25 vehicle clusters would “force” their way into the f reeway and this would result in vehicles slowing down and eventually the following vehicles would reduce their speed, creating an overall sudden speed drop. Similar to Elefteriadou et al. (1995), Yi and Mulinazzi (2007) found that the infl uences of ramp vehicles on freeway vehicles (also defined as “invasive-influences”) are related to the presence of persistent platoons on the ramps. More specifically, they found that the number of evasive events (slow down or change lanes) increase s and the standard deviation decreases with the merging platoon size. The note that these inva sive-influences of the ramp vehicles may cause the freeway vehicles to slow down and even ch ange lanes. For the model development, they observed the brake-light indications and lane change maneuvers to account for the evasive behavior of the freeway vehicles that travel on the shoulder lane. They also defined the following three merge situations depending on the a rrival patters: Free Merge (FM): random arrival of ramp vehicle tha t does not interact with the freeway vehicle, Challenged Merge (CM): ramp vehicles conflict with freeway vehicles on the shoulder lane before merging, and Platoon Merge (PM): clusters of ramp vehicles force their way ignoring the priority order, and trigger invasive-influences to the freeway vehi cles. The significance of the invasive-influence on the s houlder lane traffic was estimated by considering: (i) the distribution of traffic on tha t lane; i.e., less traffic on the shoulder lane mea ns higher invasive-influence, and (ii) the speed decre ase of the shoulder lane caused by the persistent platoons. Lastly, the authors proposed alternative LOS indicators that correspond to these relationships between the invasive-influence with volume shift and the speed reduction. Kerner and Rehborn (1996, 1997) defined the breakdo wn phenomenon as the transition from free-flow to synchronized flow (average speeds are almost synchronized in different lanes).

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26 Based on data from German highways, the free-flow t o synchronized flow transition was detected from the abrupt changes in the average spe ed. They stated that in bottlenecks, breakdown occurs due to local speed decrease and de nsity increase that is observed when onramp vehicles “squeeze” on the highway or due to un expected speed decrease and lane changing activity. Daganzo et al. (1999) presented a model describing traffic behavior, which assumes that vehicles respond to changes in the speed of the lea d vehicle in the same fashion, irrespective of the past history. They defined the “deceleration d isturbance” as occurring when one of the vehicles in the platoon decelerates and allows a ga p to grow in front of it to allow another vehicle to merge in. This causes the following vehicles in the platoon to decelerate as well. Eventually, the entire platoon returns back to the original spe ed, causing a wave to travel within the platoon and propagate upstream. This results in further in stabilities and perturbations, which lead to higher densities and the development of “jam” state s. They also defined “acceleration disturbance” to occur when a vehicle accelerates an d closes the gap in front of it. They concluded that if the acceleration disturbances are persistent, then the queue disturbances could propagate forward and reduce the flow through the b ottleneck. Daganzo (2002), assuming two types of drivers (fast -moving and slow-moving), modeled the freeway breakdown event at a freeway ramp merging s egment, as follows: Fast moving vehicles stay in the passing (left) lane, willing to accept shorter headways, while on-ramp vehicles enter and stay in the shoulder lane. Further downstream of t he merge, fast-moving vehicles that had entered from the on-ramp leave the shoulder lane and merge into the passing lane; thus they increase the passing-lane flow (this is defined as the “pumping mechanism” as the drivers are willing to accept reduced headways and let the on-ramp vehicles merge ). In high and uncongested flow, fast-moving

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27 vehicles follow each other in small headways, sugge sting that they are “motivated” by their desire to pass. When the through and/or the merging flow is high, the passing lane becomes saturated downstream of the merge (because of the merging fas t-moving vehicles), and a shockwave will move further upstream. This also means that the pa ssing-lane speed will decrease near the merge, causing the fast-moving vehicles to lose their “mot ivation” to follow closely and change lanes to equalize speeds; thus the queue on the passing lane eventually spills over to the shoulder lane. An evaluation study of Daganzo’s theoretical model was performed by Banks et al. (2003), where it was concluded that some of the phenomena described in Daganzo’s theory do occur, but not at all locations, and that the underlying assumptions were oversimplified. More specifically, Banks et al. verified the increase in time gaps (loss of motivation) but only at one site, but contrary to Daganzo’s model (and other literature), the speed e qualization does not take place at all locations. In addition, they did observe redistrib ution of flow among lanes, even though the speeds were not equalized, and distinction between capacity and discharge flow were not observed downstream from queues (as predicted by Da ganzo). Driver Behavior Models for Merging Maneuvers Several studies have investigated the maneuvering d ecisions in order to model driver behavior. These models are mostly valuable to micro scopic simulators but also to safety and capacity analysis where aggregate traffic flow char acteristics can be obtained from modeling individual drivers’ behavior. Generally, the literature on driver behavior models has studied mainly three significant topics: acceleration, lane changing and gap accepta nce. The acceleration models try to capture the parameters that affect drivers’ acceleration de cisions and process, while the drivers are either in a car-following situation or not. Therefore, th ese models can be grouped (Toledo, 2003) into (1) car-following acceleration models (drivers reac ting to the behavior of their leaders), and (2)

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28 general acceleration models. This chapter provides an overview of the acceleration models that were specifically developed to describe the acceler ation of vehicles involved in merging situations (usually, these models are focused on th e ramp vehicles and the lag vehicles that approach the merge area). Typically, the lane changing models found in the li terature contain two steps: the lane selection process and the lane changing execution p rocess, where gap acceptance formulations are used for the model development. In addition to that, these models distinguish lane changes into two categories: (1) discretionary lane changes (DLC) and (2) mandatory lane changes (MLC). Discretionary lane changes are performed in order for drivers to improve their position in the traffic stream. Mandatory lane changes are performed when drivers must leave the current lane, in order to follow a specific route, such as in merging from the acceleration lane on the freeway, or because of a lane drop or lane closure due to work zone activity. The literature review included in this section, pro vides a discussion on all models related to MLC, since this type of lane changes describes the ramp merging behavior. A description of specific DLC models that were developed in conjunct ion with components for MLC is also available, because this type of lane changes can be observed at the vicinity of ramp junctions, as the mainline vehicles may choose to avoid any disru ption from the merging vehicles. Past research focused on the development of merging mode ls integrating both gap acceptance and acceleration decisions is also provided in this sec tion. Modeling Acceleration Behavior for MLC Significant amount of research has focused on model ing the acceleration of either the ramp or the freeway vehicles near the merge area. Kou a nd Machemehl (1997) presented a methodology for modeling the acceleration-decelerat ion behavior of ramp vehicles. Merging vehicle position data and freeway and ramp volume d ata from both parallel and taper ramps were

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29 obtained and analyzed (both long and short segments ). The volume data cover off-peak and peak periods; however fully congested conditions were no t included. In short acceleration lanes, most of the traffic (a pproximately 70 percent) merges at the section where the acceleration lane width decreases from 12 ft to zero (parallel-type) or at the section immediately after the gore, where the accel eration lane width drops from 12 ft to 9.5 ft (taper). At long acceleration lanes it was found t hat the merging position is not affected by the flow levels, which does in fact contradict the init ial hypothesis that the larger the freeway and ramp flow rates the longer the distance ramp vehicl es travel in the acceleration lane. No significant relationship was found between ramp vehicles’ speed and distance to complete the maneuver, or between time to complete the maneuver and time lags with the freeway lead/lag vehicles; however, this may be the result of limited data availability. Finally, they did conclude that as the speed differential be tween the ramp vehicle and the freeway lag vehicle increases, the merging percentage decreases The ramp vehicle acceleration-deceleration model wa s based on the stimulus-response concept implemented in the car-following models, wi th respect to the distance lag, D The methodology was expanded linearly to incorporate th e influence of the freeway vehicles and the ramp geometric constraints. Solving for the non-li near regression for D = 0, 18.29, and 36.58 m (0, 60, and 120 ft) yielded that the best calibrate d acceleration-deceleration model was for D =18.29 m (60 ft): (d) X (d) X L ) (d X (d) X (d) X (d) X (d) X ) (d X (d) X (d) X (d) X (d) X ) (d X ) (d Xr r r flead r r flead r r flag flag r r r 726 1 092 1 699 0 092 1 135 0 092 129 18 484 3 29 18 020 0 29 18 002 0 145 2 29 18 (2.1)

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30 Where: Xri(dj) : Location of ramp vehicle i when it passes the fiducial mark j Xflagi(dj) : Location of corresponding freeway lag vehicle for ramp vehicle i when vehicle i passed the fiducial mark j, Xfleadi(dj) : Location of corresponding freeway lead vehicle fo r ramp vehicle i when vehicle i passed the fiducial mark j, ) (d Xj i r: Velocity of ramp vehicle i when it passes the fiducial mark j, ) (d Xj i flag: Velocity of the corresponding freeway lead vehicl e i when vehicle i when it passes the fiducial mark j, D) (d Xj i r: Acceleration rate of ramp vehicle i at location dj+D, The relevant R-square value was 0.566. A weakness of the propose d model is that it was calibrated with a limited amount of field data. In addition, the ramp merging position was found not to depend on any traffic parameter, which is co ntroversial with common expectations and requires further examination. Research conducted along the Tokyo Metropolitan Exp ressway in Japan (Sarvi et al., 2002) has focused on modeling ramp vehicle accelera tion-deceleration behavior during the merging process in congested conditions. This meth odology also, uses the stimuli-response equation to model the acceleration-deceleration beh avior. In their research they introduce three stimuli to evaluate the ramp vehicle response. The se are the relative speed regarding the freeway leader, the relative speed regarding the freeway la g vehicle and the spacing regarding the freeway leader. The hypothesized expression of the ramp vehicle acceleration-deceleration behavior of a ramp platoon leader entering the free way is given as: v(t) f S(t) (t) X (t) X a (t) V (t) V (t) X (t) X T) (t V a (t) V (t) V (t) X (t) X T) (t V a a T) (t al R Flead Flag R l Flag R m R R Flead l R Flead m R R 3 2 113 2 1 0 (2.2) Where: aR(t+T) : Acceleration rate of the ramp vehicle at time t+ T (m/s2)

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31 XR(t) : Location of the ramp vehicle at time t (m) XFlead(t) : Location of the freeway lead vehicle at time t ( m) XFlag(t) : Location of the freeway lag vehicle at time t (m ) VR(t) : Speed of the ramp vehicle at time t (m/s) VFlead(t) : Speed of the freeway lead vehicle at time t (m/s ) VFlag(t) : Speed of the freeway lag vehicle at time t (m/s) S(t): Spacing between the ramp vehicle and the freeway l eader vehicle at time t (m) ( XFlead(t)-XR(t)) f[v(t)] : Desired spacing as a function of speed (m) T : Time lag or driver reaction time (s) Although the data collected were not enough to cove r all geometric conditions, they were used to calibrate the acceleration models. Two set s of models were investigated, linear and nonlinear acceleration models, and these were proven t o be equally significant. Sarvi and Kuwahara (2005) have also developed an ac celeration-deceleration model for the lag vehicle that approaches the merge area from the freeway under congested flow. They investigated the lag vehicle behavior in terms of i ts relative speed and spacing with its corresponding ramp and freeway lead vehicles. In t heir method, they used a non-linear specification to the stimuli-response equation. Field data were collected through videotapes and im age processing techniques during congestion periods. Based on the data, the lag veh icle has higher speed than the ramp vehicle in the beginning of the acceleration lane, but the lag vehicle either decelerates (to accommodate the merging) or the ramp vehicle accelerates (to force the merging). Next, the vehicle continues to accelerate to reach the leader vehicle. The leader and ramp vehicles have higher speeds than the lag vehicle. The modeling of the lag vehicle is built upon previ ous work for modeling the ramp vehicle merging (Sarvi et al. 2002). The main stimuli identified are the relat ive speed and spacing between the lag vehicle and its leading and ramp ve hicles. The lag vehicle accelerationdeceleration behavior is given by the following exp ression:

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32 v(t) f S(t) (t) X (t) X a v(t) f S(t) (t) X (t) X a (t) V (t) V (t) X (t) X T) (t V a (t) V (t) V (t) X (t) X T) (t V a a T) (t al Flag R l Flag Flead Flag R l Flag R m Flag Flag Flead l Flag Flead m Flag Flag 2 4 1 3 2 1 04 3 2 11 1 (2.3) Where: AFlag(t+T) : Acceleration rate of the freeway lag vehicle at t ime t + T (m/s2) XR(t) : Location of the ramp vehicle at time t (m) XFlead(t) : Location of the freeway lead vehicle at time t (m) XFlag(t) : Location of the freeway lag vehicle at time t (m) VR(t) : Speed of the ramp vehicle at time t (m/s) VFlead(t) : Speed of the freeway lead vehicle at time t (m/s) VFlag(t) : Speed of the freeway lag vehicle at time t (m/s) S(t)1: Spacing between the freeway lag vehicle and the f reeway leader vehicle at time t (m) ( XFlead(t)–XFlag(t) ) S(t)2: Spacing between the freeway lag vehicle and the r amp vehicle at time t (m) ( XR(t)–XFlag(t) ) f[v(t)] : Desired spacing as a function of speed (m) T : Time lag or driver reaction time (s) a0,a1,a2,a3,a4: Parameters m,l1,l2,l3,l4 : Parameters This acceleration model was calibrated through line ar and non-linear regression. Even though the non-linear model has greater R-sq value than the linear model, this difference was not significant, thus the linear model is sufficient fo r replicating the vehicle interactions. Sarvi et al., (2000) developed a simulation program that was used for calibrating and validating the ramp vehicle acceleration model (Sar vi et al., 2002) and the lag vehicle acceleration model (Sarvi and Kuwahara, 2005), in c onjunction with field measurements. In both cases the authors compared the vehicle traject ories from simulation data and the field data and it was shown that there is agreement between th e two trajectories.

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33 Kesting et al. (2007) presented a car-following mod el that includes the lag vehicle in the decision-making process and it is focused on modeli ng the acceleration. Safety constraints are also considered in the lane changing decision. The utility of a lane changing increases if the gap with the lead vehicle increases; however, if the sp eed of the lead vehicle is lower, then the subject vehicle may decide to stay on the present l ane. They proposed a lane changing utility function that considers the difference in the accel erations (or decelerations) after the lane changing. For example, higher acceleration on a gi ven lane suggests that this is closer to the “ideal” acceleration on an empty road; thus, it is more appealing to the driver. Another important feature of the proposed model is that it considers a “politeness” factor, which denotes in essence the (dis-)advantage of the lag vehicle ( degree of cooperativeness). Moreover, the model considers a safety threshold which guarantees that after the lane change the deceleration of the follower will not exceed a given safe limit. Examination of the lane changing rate through simul ation showed that this primarily depends on the politeness factor. The politeness f actor is an important model parameter, however, the proposed model represents only the las t decision of whether to change lanes or not. Thus, information related to the decisions prior to the final lane-changing step, is not provided. Lastly, it is suggested that varying the safety thr eshold changes the “critical” lane change and this could further affect the breakdown probability Modeling Gap Acceptance for MLC During the past 20 years, research has been involve d with the study of gap acceptance during the merging process. Michaels and Fazio (19 89) developed a freeway ramp merging model based on driver behavior. The concept of the model is that ramp drivers accept a gap based on an angular velocity. Michaels and Fazio n ote the continuous process of acceleration and gap-acceptance, and they distinguish several di screte tasks during the merging maneuver.

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34 These are (1) the ramp curve tracking, (2) the stee ring transition from the ramp to the acceleration lane, (3) acceleration, (4) gap search and (5) steering transition from acceleration lane to freeway or abort. During the gap search ta sk the angular velocity is defined as the first order motion vector relative to the ramp driver and it is estimated as: n 2/l V V k wr f (2.4) Where: w: Angular velocity (rad/sec) Vf: Freeway vehicle speed (ft/sec) Vr: Ramp vehicle speed (ft/sec) l: Distance separation (ft) k: Lateral offset (ft) The angular velocity may have three different value s, depending on the relative velocity and the distance. When the speed of the ramp vehic le is greater than the speed of the freeway vehicle (angular velocity is negative), this is an opening condition, and the ramp driver can merge as long as there is sufficient gap from the l ead vehicle. When the speed of the ramp driver is less than the speed of the freeway driver (angul ar velocity is positive), this is a closing condition, and the merging decision depends on the angular velocity of the following vehicle, as long as the ramp vehicle is always behind the lead vehicle over the whole segment of the change speed lane. The third situation occurs when the rel ative speed and distance generate angular velocity below the threshold of 0.004 rad/sec (angu lar velocity is zero). An important hypothesis made, is that the merging maneuver can be an iterat ive process under congested conditions, where the ramp vehicle accelerates and searches for a gap iteratively, until its speed reaches that of the freeway. In their model, they also incorporated the ramp cur vature and the gap distribution function of the freeway traffic. Under heavy traffic condit ions it was found that: (1) the median angular velocity is consistent with the literature, (2) dri vers tend to decrease their speed between

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35 successive accelerations as they are in a gap searc h process and not in speed control, and (3) the probability of merging increases with successive tr ials. Based on the proposed model, the authors present a procedure for estimating the length of th e acceleration lane to provide adequate gaps. These findings indicate that the length is independ ent of freeway volume over a range of 1,200 to 2,000 pcphpln and that 650-800 ft is a sufficient l ane length to ensure 85% or more merging opportunities for ramp drivers (for most used ramp design speeds). The proposed model however does not consider the interactions between the merg e vehicles and the freeway vehicles as it assumes that the merging traffic has no influence o n the mainline traffic. Kita (1993) examined the merging behavior on an onramp section in the case where the merging vehicles are running slower than the throug h vehicles. The author developed: (1) a gap acceptance model that describes the merging behavio r based on the merging probability and (2) a method to relate the safety level in a merging sect ion with road and traffic characteristics. The gap acceptance model (only sections with parall el acceleration lanes and not tapered were used) was based on a binary logit model of “ac cept” or “reject” choices of a sequential gap choice process. This model also considers the infl uence of the merging lane length on the driver’s decision process. The two alternative cho ices are formulated as: a r r a aP P U U P 1 ) ( exp 1 1 (2.5) Where: Pi: Probability that a driver chooses the alternativ e i Ui: Deterministic part of the drivers utility to the alternative i i : Alternatives (i = a: accept; i = r: reject) and, J j j j r ax U U1 0 (2.6)

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36 Where: xj: Explanatory variables j: Parameters (j = 1, …, J) Data from a three-lane freeway and one-lane ramp me rging section were used for the model calibration. The data included measurements of speed, gap length, and merging position of each vehicle (distance from the merging nose to the point where the vehicle performs the merging maneuver). The first gap is defined as the time difference between the time when the merging vehicle reaches the merging nose and the fo llower vehicle reaches the merging nose. The second gap is defined as the time headway betwe en the first vehicle and the second vehicle in the through traffic when the first vehicle reach es the same position as the merging vehicle. Cases where the through vehicle would change lane t o avoid a conflict with the merging vehicle were excluded from the analysis. Additionally, whe n multiple merging occurred, only the data of the first merging vehicle were considered. The explanatory variables selected for the model ca libration are the gap length (sec), the remaining distance of the acceleration lane (m), an d the relative velocity of the merging vehicle to the corresponding through vehicle (m/sec). The resulted goodness-of-fit measure was considered satisfactory (2 = 0.785). Kita also developed models for the distribution of the merging position and the time-tocollision after merging, depending on the accelerat ion lane length. A case study to test the effect of the acceleration lane length on the distribution of time-to-collision was also developed. It was shown that the probability of a vehicle merging int o a dangerous gap with shorter time-tocollision decreases when the acceleration lane leng th is longer.

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37 Ahmed et al. (1996) developed a lane changing model which captures the gap acceptance process using discrete choice models. Lane changes were categorized as mandatory (MLC) and discretionary (DLC). A driver that needs to perfor m an MLC may either respond immediately or delay. This depends on the remaining distance, num ber of lanes to cross, and traffic density. If the driver does not respond to an MLC situation (or MLC does not apply), then he/she decides whether to consider a DLC or not, and its satisfact ion with the current lane is evaluated. This decision depends on speed differences, deceleration heavy vehicle presence and presence of ramps. Ahmed et al. developed a desired lane choice model (for both ML C and DLC) when both the adjacent lanes are candidate lanes. The e xplanatory factors are the speed differentials, deceleration, heavy vehicles, ramp presence and nee d for mandatory response. The last parameter forces the vehicles to perform an MLC sho uld they be in this situation and they postpone the response. The developed model was applied to the case of merg ing (MLC case). The gap acceptance model presented by Ahmed et al. (1996) addresses is sues of heterogeneity and state dependence. The heterogeneity in the driver population was capt ured by introducing a random term in the critical gap specification, which varies across dif ferent components of a gap for the same individual, across different gaps for the same indi vidual and across individuals. The lane changing model is assumed to be binary logit. The probability that a lane changing takes place given a gap is acceptable depends on several explan atory variables such as the time delay (since the gap searching process began), the remaining dis tance to the point where the lane change must be completed, the lag relative speed and a first ga p dummy (captures the initial hesitation of the drivers to merge as soon as they appear at the begi nning of the acceleration lane). The model formulation estimates both the lead and lag gap par ameters separately. The lead critical gap was

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38 found to be insensitive to traffic conditions, wher eas the lag critical gap was found to be a function of the relative speed, remaining distance to the point at which the lane changing must be complete, and whether the gap is the first one cons idered or not. Ahmed et al. research captures the structure of the decision process and it also a ccounts for the stochasticity in driver behavior, but it does not capture any inter-dependence relati on between the subject vehicle and the freeway vehicles. Kita (1999) modeled the interactions between the me rging vehicle and the through vehicle on on-ramp merging sections, using game theory. Th ese interactions occur when the freeway through vehicle on the shoulder lane, changes lane to accommodate the merging maneuver of the ramp vehicle. Giveway behavior occurs when traffic conflict with a merging vehicle is likely to happen, and it deals with low-speed merging where t he speed of the merging vehicle is lower than that of the through vehicle. This study suppl ements a previous study performed by the author (Kita, 1993) which dealt with the influence of the freeway through vehicles to the merging behavior of the ramp vehicles. The interac tion is modeled as a zero-sum noncooperative game, where each driver chooses their b est action considering the forecast of the other drivers, and its validity is tested through f ield data. Kita (1999) considers only the merging and the through vehicles as their interaction is th e most dominant, but their behavior may affect the surrounding vehicles as well. It is also assum ed that the number of games is one for each of the through vehicles in conflict and these games ar e independent. The game can be characterized as non-cooperative (the drivers cannot exchange any information) with perfect information (both drivers know the situation that the other driver is facing). By solving for the equilibrium condition the model derives the merging probabiliti es of a merging vehicle and the giveway probabilities of a through vehicle.

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39 Even though the merging vehicle may monitor the tra ffic conditions in a much wider area, the model estimates the payoff functions (utility f unctions) for both merging vehicle and through vehicle based only on their position and speeds rel ative to the neighboring vehicles, but it indirectly accounts for the influence of the adjace nt through lane in the equilibrium solution. The concept behind this model is based on the assum ption that the driver selects the action with the lower risk level, where the risk is the time to collision (TTC). However, this assumption is oversimplified and unrealistic, as it does not acco unt for other factors such as the presence of the leader in the through lane that creates unsafe cond itions for merging directly. Kita et al. (2002) presented an improved giveway be havior model based on game theory. Kita et al. developed a method to estimate the payo ff functions of merging and through vehicles without any information about equilibrium selection (which is rather difficult to estimate), and then analyzed the merging and giveway behavior by u sing the estimated method. In their analysis, the merging-giveway behavior is described by the through vehicle that gives way and the merge vehicle that merges in front of the throu gh vehicle. In this situation, both vehicles attempt to take best action by forecasting the othe r’s behavior. This behavior is modeled as a two-person non-zero-sum non-cooperative game under complete information. The actions of the merge vehicle are either merging or passing up the specific gap and the actions of the through vehicle are either to go with giveway or without gi veway. The game matrix is defined as: Table 2-1. Game matrix between freeway through veh icle and merging vehicle (source: Kita et al., 2002) Through vehicle actions Merging vehicle action Go with giveway Go without giveway Merge (F11,G11) (F12,G12) Pass up (F21,G21) (F22,G22)

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40 In this method a set of probabilities is assigned t o each action. If the probability of the merge vehicle merging is p and the probability that the through vehicle goes with giveway is q, then the expected payoffs of the merge driver (EF(p,q)) and the through driver (EG(p,q)) are: 22 21 12 11 22 21 12 11) 1( ) 1( ) 1( ) ( ) 1( ) 1( ) 1( ) (G q G q q G q G q p q p EG F q F q q F q F q p q p EF r r r r r r r r r r r r (2.7) Thus, the best response of a driver, which is the p robability that maximizes their expected payoff under the probability chosen by another driv er, can be obtained from the derivative of the equations above and by checking if it is positive o r negative. The equilibrium condition is the intersection point between the best responses of th e drivers. The intersection point can be found if both drivers know the payoffs, however the exter nal observer cannot estimate these deterministically. For this reason, Kita et al. co nsider that the equilibrium to be utilized is selected in a probabilistic manner. The probabilit ies that each type of best response is given are a function of the payoffs and also of factors that characterize the environment. They examined three models for the payoff functions : a standard Time-To-Collision (TTC) model, a log TTC model and a model that considers t he influence of leading vehicles. The estimation results showed that the model’s capabili ty of estimating the probabilities of equilibrium selection are fairly good, and can be u sed for the analysis of phenomena with strong interactions. This model however does not consider a minimum safe gap between the vehicles. Another limitation is that it does not account for the fact that the merging vehicle will slow down and stop at the end of the acceleration lane if it cannot merge safely. Also, it is assumed that all vehicles travel at a constant speed, with no provis ion for slowing down for the through vehicle when staying in the through lane. Lastly, it is as sumed that the merging vehicle does not take any action to improve its merging position.

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41 Goswami and Bham (2007) studied the gap acceptance behavior using the NGSIM data, along I-80 in Emeryville, California. Their focus was to obtain statistical distributions for the accepted and rejected gaps (and therefore, the crit ical gaps) in MLC maneuvers. Their motivation to study the distribution of acceptable gaps derives from the fact that the minimum acceptable gap does not represent the critical one, but only the gap acceptance behavior of an aggressive driver. The data consisted of vehicle trajectories between an on-ramp and an off-ramp, under both uncongested and congested conditions. They examine d the vehicle trajectories and considered vehicle interactions to occur when their distance i s 250 ft or less. The Gamma and Lognormal distributions were tested for the (lag and lead) ac cepted gaps, and it was found that in some occasions the gaps are Gamma-distributed, while in some others they are Lognormal-distributed. They also used both deterministic (cumulative frequ encies, acceptance curve) and stochastic methods (maximum likelihood, logit, probit) for est imating the critical gaps and conclude that the results from the logit and probit methods fit b est to the data. Analysis of the critical gaps as a function of the location of lane changes indicates that in uncongested conditions the critical gaps (from the shoulder to the adjacent lane) are smalle r than in congested conditions. Zhang and Kovvali (2007) used the NGSIM data as wel l, to develop a gap acceptance model for the mainline vehicles. They considered t he mandatory lane changes (MLC) but only from the vehicles exiting the freeway from the offramp at the study area. They evaluated 24 explanatory variables for the gap acceptance model, among these are: speeds, accelerations, vehicle types, etc., for the subject vehicle and al so the lead and lag freeway vehicles. Two variables were also introduced, that are MLC-relate d, and these are the number of lane changes required to exit from the off-ramp and the distance to the MLC point.

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42 Comparison between accepted gaps in MLC and DLC sho wed that these are statistically different (drivers in MLC situations select smaller gaps than in DLC). It was also found that the gap size decreases with increasing number of MLC, a nd that there is correlation between the acceptable time gaps and the distance to the MLC po int (reveals drivers’ urgency to change lanes). They also showed a correlation between the vehicle size and the accepted gap between the subject and the lag vehicles, (i.e., heavier ve hicles accept larger gaps). Moreover, relative speeds were found to have little effect on acceptab le gaps in MLC. Examination of the accelerations showed that the accepted distance gap s are smaller with higher subject vehicle accelerations, and that relative accelerations do n ot affect gaps significantly. Regression models of gap acceptance for both MLC and DLC were develop ed, however the regression coefficients are 0.495 and 0.389 respectively, which shows that there are still other unidentified factors that influence the gap acceptance process. Integrated Models for MLC Recent studies have developed models incorporating acceleration decisions to the merging models. Ahmed (1999) developed a lane changing mod el and an acceleration model to describe merging behavior under congested traffic. The stru cture of the lane changing model is presented in Figure 2-1. The lane changing process is describ ed in three-steps through discrete choice framework: a decision to consider a lane changing, choice of a target lane and acceptance of gaps in the target lane.

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43 Figure 2-1. Lane changing model structure proposed by Ahmed (1999). Ahmed (1999) proposed a lane changing model for unc ongested conditions and a forced merging model for congested conditions based on his previous work (Ahmed, 1996). The lane changing model includes the lane selection model an d the gap acceptance model. Ahmed introduces the term “courtesy yielding” of th e lag vehicle and “forced merging” of the subject vehicle to describe the proposed forced merging model. The merging vehicle evaluates the traffic environment in the target lan e continuously, to decide whether to merge in front of the lag vehicle. The merging vehicle also communicates with the lag vehicle to check whether his/her right of way is established. If bo th of these occur, then the vehicle initiates a forced merging. If not, then the vehicle continues this process at the next time interval. Using a binary logit model, the probability of switching fr om the “start a forced merging state” to the “do not start a forced merging state” is modeled. Expl anatory variables are the lead relative speed when the lead vehicle is slower, the lag relative s peed, the remaining distance to the point that

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44 the merging must be completed, the delay, the sum o f lead and lag gaps, and the presence of heavy vehicles. An important addition of Ahmed to the acceleration model was to include two components: the car-following model and the free-fl ow acceleration model. Ahmed defined a headway threshold to differentiate between the carfollowing regime and the free-flow regime. Another improvement of the acceleration model propo sed by Ahmed (1999) was that he relaxed the assumption that the car-following stimulus is a linear function of the lead vehicle relative speed and used the density in front of the subject vehicle to capture the impact of traffic conditions. However, this model does not capture e xplicitly the impact of the lane changing decisions on the acceleration decision. Toledo (2003) developed an integrated driver behavi or model that captures lane changing and acceleration behaviors. The method is based on short term goals and plans. Drivers that target a lane change but cannot change lanes immedi ately, choose a short-term plan, and adapt their acceleration behavior to facilitate the lane changing. The model’s structure searches for interdependencies between the different decisions o f lane changing and acceleration. The model considers four levels of decision-making: target la ne (lane choice), gap acceptance (lane changing), target gap (gap choice) and acceleration Toledo introduces three mechanisms that allow captu ring interdependencies between the various decisions. These are causality, unobserved driver/vehicle characteristics and state dependency. The causality captures the effect of l ower level choices on higher level decisions, because, the lower level choices are modeled condit ional on those made at higher levels (e.g. the acceleration is conditional on the short-term plan) This was done by introducing variables that capture the expected maximum utility (EMU) of the a lternatives at the lower level in the

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45 specification of higher-level choices. A driver/ve hicle specific variable was introduced in the model to capture correlations between observations obtained from a given driver. Finally, the state dependency mechanism aims in re-evaluating an d potentially modifying the short-term goals and plans due to changes in driving condition s. This also addresses the fact that different combinations of short-terms and plans may result at the same observed conditions. The target lane model integrates MLC and DLC into t he same utility function for each target lane, rather than considering separate utili ty functions (Ahmed, 1999). The conceptual structure of the model is illustrated in Figure 2-2 Toledo integrated the two lane changing situations to capture potential trade-offs between mandatory and discretionary considerations. Figure 2-2. Lane changing model structure proposed by Toledo (2003). The gap acceptance model captures the decision whet her to change lanes immediately using the adjacent gap, conditional on the target l ane choice. Explanatory variables for this model are the subject’s speed, the relative speeds with respect to the lead and lag vehicles, the traffic density and the urgency of the lane changin g. If the adjacent gap is rejected the driver does not change lanes and he is assumed to create a short term plan by choosing a target gap on

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46 the target lane. The driver chooses between the ad jacent, the backward and forward gaps. The explanatory variables affecting the utilities of ea ch gap are the gap size, the gap trend, the subject’s relative speed, and the distance to the p oint where the lane change must complete. Three acceleration models were developed: the stayin-the-lane acceleration, the acceleration during a lane changing (when the adjac ent gap is accepted) and the target gap acceleration (when the driver does not change lane immediately). Additionally, two driving regimes are considered, depending on whether the op erations are constrained or unconstrained. The stay-in-the-lane acceleration model is based on the model developed by Ahmed (1999). The constrained and unconstrained driving regimes assum e car following and free-flow behaviors, respectively. For the lane changing acceleration m odel it is assumed that the driver determines the acceleration by evaluating the relations with t he target lane leader. For the target gap acceleration model, the driver constructs and execu tes a short-term plan which depends on the target lane and the target gap choices. If unconst rained, the driver targets a desired position with respect to the target gap, which would allow the la ne change to be performed. In this case the stimulus is the difference between the vehicle’s de sired and current position. Although the proposed integrated model incorporates many different features and accounts for drivers’ planning capabilities, behavior-relate d data were not used for the model validation. In addition, there is no accountability for lane ch anging during congested conditions, where courtesy yielding and even forced maneuvers take pl ace. Choudhury et al. (2006, 2007) present a lane changi ng model for merging and weaving that considers four levels of decision making proce ss: normal gap acceptance, decision to initiate courtesy merging, decision to initiate forced mergi ng, and gap acceptance for courtesy and forced merging. The structure of the proposed model is given in Figure 2-3.

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47 Figure 2-3. Structure of proposed model by Choudhu ry et al. (2007). The data collected for this model are part of the F ederal Highway Administration (FHWA) Next Generation Simulation (NGSIM) project. The da ta include vehicles’ trajectories (position, acceleration and speed) along the Interstate I-80 i n Emeryville, California, during transition to congestion and congested conditions. Observations of the lead, lag and the subject vehicle were recorded in a second-by second basis. The distribu tions of the relative speeds and gaps show that when a gap is accepted, the subject vehicle is traveling slower than the lead vehicle and faster than the lag. For the gap acceptance model, a gap is accepted if it is greater than the critical gap, which is modeled as a random variable following lognormal distribution. n ig nt n ig nt ig ig ntu a X GT ln (2.8) forced courtesy normal i lag lead g , ig ntG: Critical gap g of individual n at time t for merge type i, ntX: Vector of explanatory variables, Tig: Corresponding vector of parameters that depend o n the merge type,

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48 ig nt: Random term for gap acceptance for merge type i of individual n at time t, nu: Driver-specific random term, iga: Coefficient of the driver-specific random term o f gap g, and merge type i. The model assumes that the driver must accept both lead and lag gaps in order to perform a lane change. Explanatory variables are the relativ e speed between the subject and lead/lag vehicles, the remaining distance to the MLC point a nd the acceleration of the lag vehicle. If the gaps are unacceptable the driver evaluates the spee d, acceleration, and relative position of the freeway vehicles and anticipates a gap that will be available in a later time. If these gaps are stil l not acceptable, then the subject vehicle will consi der initiating a forced merge. Variables that affect the decision to initiate a forced lane chang ing are related to the status of the merging driver (distance to the MLC point, delay (intolerance), an d speed), the lag vehicle status (vehicle type, speed and acceleration), and the traffic conditions (congestion level and tailgating dummy). Choudhury et al. (2007) recently extended their mod el by integrating drivers’ acceleration and deceleration actions to facilitate their mergin g maneuvers. They incorporated three different acceleration models (Figure 2-4), which are: lane c hange acceleration and target gap acceleration (similar to Toledo, 2003), and initiated courtesy/f orced merging acceleration. The lane change acceleration occurs when the existing gaps are acce ptable and it is based on the relative speed with the leader. The target gap acceleration is pe rformed when the subject vehicle seeks an improved position with respect to the lead and lag vehicles (can select forward, adjacent or backward gap). The initiated courtesy/forced mergin g acceleration seeks to obtain an improved position while in the subject lane, with respect to the lead and lag vehicles. These acceleration models are still under development and have not bee n finalized to this moment.

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49 Figure 2-4. Extended model proposed by Choudhury e t al. (2007). Mandatory Lane Changing Models Used in Simulation P rograms Lane changing rules and models have been extensivel y used in microsimulation programs to provide a more realistic representation of traff ic operations. Yang and Koutsopoulos (1996) presented the MIcroscopic Traffic SIMulator (MITSIM ) where they implemented a rule-based lane changing model. They presented a merging mode l, separately from the lane changing model. The merging model is classified into: (i) p riority-based merging and (ii) merging without priority, while the lane changing model distinguish ed between MLC and DLC lane changes. In contrast to other models, merging from on-ramps is modeled through the merging model and not through the MLC model. More specifically, the prior ity-based merging includes merging from on-ramps or dropped lanes to the freeway, and from minor to major streets, and the merging without priority includes merging downstream of tol l plazas. They define that MLC occurs when vehicles have to change lanes to (i) connect t o the next link on their path, (ii) bypass a lane

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50 blockage, (iii) avoid entrance to a restricted use lane, and (iv) respond to LUS or VMS. DLC occurs when a driver wants to increase speed, or ov ertake a heavy vehicle, or to avoid the lane connected to an on ramp. For the priority-based merging model, the merging v ehicle checks whether there is an upcoming vehicle and executes the maneuver only if the projected headway gap is acceptable. If the headway gap is not acceptable, the vehicle eith er calculates the acceleration rate (by treating the freeway vehicle as leader) or stops at the end of the acceleration lane, depending on which case is the critical one. In addition, the merging model incorporates a court esy yielding parameter in case the vehicle decides to decelerate to create space for a nother vehicle to merge. This is done by assigning a probability of courtesy yielding to the drivers, and applying the deceleration rate calculated from the car-following model; however no t enough details are provided about this process. The lane changing algorithm in MITSIM (based on Gip ps model) is implemented in three steps: (i) check the necessity of lane change and d efine its type (mandatory or discretionary), (ii) select desired lane, (iii) execute lane changing if gaps are acceptable. For DLC, the decision to change lane is based on traffic conditions on both current lane and adjacent lanes. The model introduces an impatience factor and a speed indiffe rence factor, to determine whether the speed is low enough and the speeds at the adjacent lanes are high enough for considering a lane changing. A lane change is executed only if both t he lead and lag gaps are acceptable. The critical gaps used in MITSIM are assumed to follow the lognormal distribution. Hidas (2002) presented a lane changing and merging algorithm implemented in the simulator named Simulation of Intelligent TRAnsport Systems (SITRAS). Key aspects of these

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51 algorithms are the forced and cooperative lane chan ging modules, which are significant for modeling congested traffic conditions. The necessi ty of a lane change is evaluated in each simulation interval, and depending on the situation (turning movement, incident, end-of-lane, transit lane, speed advantage, queue advantage), it can either be essential, desirable, or unnecessary. Next, the feasibility of the lane cha nge is examined, depending on the gap availability at the target lane. A lane change is considered feasible if (i) the deceleration/acceleration needed for the subject ve hicle is acceptable, and (ii) the deceleration required by the potential follower is acceptable. An aggressiveness parameter is incorporated to the deceleration calculation, to differentiate betw een driver types. When an MLC is warranted, the lane selection proces s is terminated. Hidas incorporated the driver courtesy in the case of forced lane chan ges. This concept deals with the reduction in acceleration required for the potential new followe r to allow the subject vehicle to move to the target lane. Other important elements presented by Hidas (2002) with respect to the merging model, are: acceptance of shorter critical gaps than those that derive from the car-following model, implementation of acceleration in order for the sub ject vehicle to better position during the lane change, implementation of lane changing behavior for the ri ght-lane freeway vehicles approaching the ramp merge, if ramp vehicles are present, in or der to avoid any friction, application of lower deceleration when ramp vehicle s try to merge into the freeway using very short gaps, instead of using large deceleratio n that could potentially disturb the freeway flow, and, application of the driver courtesy function only to congested traffic conditions. In 2005, Hidas presented an updated version of SITR AS (renamed to ARTEMiS), for simulating lane changing and merging models under c ongested conditions. The objective of the lane changing model in ARTEMiS is to determine unde r which conditions a vehicle is allowed to

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52 move into the target lane, and consider the issue t hat the drivers are willing to tolerate much shorter gaps when they can anticipate the actions o f other drivers, and do not use the maximum but a moderate deceleration. Data collected in the field showed that in congesti on, lane changes occur at short gaps and that the accepted gaps are more closely related to the relative speed between the leader and the follower than to the absolute speed of the follower vehicle. It was also shown that when the leader is faster than the follower, the minimum acc epted gap was constant, but if the leader is slower than the follower, the minimum accepted gap increases with the speed difference. Analysis of gap acceptance led to the classificatio n of lane changing maneuvers as free, forced and cooperative. Free lane changing occurs when there is no significant change in the relative gap between the leader and follower, which means that there is no interference between the subject and the follower vehicle. Generally, i n a free lane change there is no interaction between the vehicles. Forced lane changes are asso ciated with apparent change in the gaps before and after the merge point, i.e., the gap bet ween the leader and the follower was either constant or narrowing before the merge and it widen s after the merging vehicle enters. Thus, the subject vehicle forces the follower to decelerate. In essence, the subject vehicle plays an active role by initiating the merge, and the follower reac ts to that action. In cooperative lane changes the gap between the leader and the follower is incr easing before the entry point and it decreases afterwards, which indicates that the follower decel erates to allow the vehicle to merge. In cooperative lane changes, at first, the subject veh icle indicates its willingness to move to the target lane, then the follower acknowledges the sit uation and cooperates by slowing down, and eventually, the subject vehicle realizes that the f ollower gives way and when the gap is long enough, it merges.

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53 Wang et al. (2005) present a model of freeway mergi ng behavior that considers the acceleration and gap acceptance behavior. The auth ors introduce two plausible behaviors/reactions of the freeway traffic approach ing the merge: cooperative lane changing (to allow vehicles to merge) and courtesy yielding (dec elerate to create gaps). The following series of sub-models are introduced to capture the merging behavior and to develop the simulation model: Cooperation model: It captures the cooperative yiel ding behavior and the cooperative lane changing, that essentially facilitates the merging process by creating gaps for the ramp vehicles. Acceleration model: It captures the acceleration-de celeration decisions of the merging vehicle. It is influenced by the target gap on the freeway, the leading vehicle on the acceleration lane and the remaining distance to the end of the acceleration lane. They modeled the ramp vehicle’s acceleration to reach th e speed of the leading vehicle, as well as the deceleration of the vehicle based on the rel ative speed and gap with the leader. If the speed of the merging vehicle is very close to t he speeds of the follower or the leader (small relative speeds), another acceleration model is employed which aims in creating larger lead or lag gaps. A parameter for the drive r aggressiveness is also introduced. The model incorporates a maximum acceptable deceleratio n as an urgency, to prevent the merging vehicle from running into the vehicle in fr ont or the end of the acceleration lane. Gap selection model: It is based on the speed of th e merging vehicle and its position relative to the freeway leader and follower. The t arget gap is assumed to be the adjacent gap, unless different situations occur, such as a f ast moving vehicle that overtakes the leader on the acceleration lane and takes the previ ous gap as its target gap, or a slow moving vehicle that chooses to take the following g ap. Gap acceptance model: It is based on the game theor y idea proposed by Kita et al. (2002) where the merging vehicle makes a decision consider ing the forecast of the other vehicles’ actions and its own actions. The model calculates t he acceptable lead and lag gaps as a function of the speed, merging driver’s reaction ti me and maximum decelerations of the merging, the leader, and the follower vehicles, dep ending on their projected reactions to the merging process. Merge model: It captures the presence of an accepta ble gap and the merging process. However, if the vehicle is reaching towards the end of the acceleration lane and an acceptable gap is not found then a merge failure is registered. The model was tested through simulation and a sensi tivity analysis was performed to evaluate how the parameters affect the merging proc ess. The model was found to be sensitive to

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54 the length of the acceleration lane and the average freeway flow. For long acceleration lanes and low speed on the freeway, the merging failures were fewer and there is a greater chance that a following gap will be chosen. The optimal accelera tion lane length for smooth merging (accepting the adjacent gaps) was found to be appro ximately 100 meters (330 ft.). With longer acceleration lanes vehicles tend to take the follow ing gaps and not the adjacent gaps. It was also found that the accepted lead and lag gaps decrease with increasing flows but these do not vary with increasing merging flows. The authors tested a range of values for the gap acceptance factor and the driver’s reaction time and compared the der ived outputs with field data from the literature; however, a direct calibration of the pr oposed model parameters was not performed. CORSIM (Halati et al. 1997) distinguishes three typ es of lane changing: (i) mandatory, (ii) discretionary and (iii) anticipatory lane changes. Mandatory lane changes are considered in the following situations: (i) merging traffic entering on the freeway, (ii) lane changing for diverging traffic to exit the freeway, (iii) leaving a blocke d lane due to an incident, (iv) vacating a dropped lane. In CORSIM, a lane change is performed if bot h lead and lag gaps are acceptable. The gap acceptance process involves a risk factor. More sp ecifically, the model compares the acceptable level of risk (acceptable deceleration) for avoidin g collision, between the potential follower and the merging vehicle. The acceptable risk factor de pends on lane changing type, driver type, and urgency of lane changing. In addition, vehicles initiate the merging as soon as they enter the acceleration lane. Merging vehicles’ acceleration is determined by con sidering that it car-follows a stopped ‘dummy’ vehicle at the end of the acceleration lane and this is compared with the deceleration required to stop at that location. The minimum of the two decelerations is applied. CORSIM

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55 also models the anticipatory lane changes of the fr eeway vehicles that give up the shoulder lane to avoid potential conflict and speed reduction cau sed by the merging traffic. VISSIM applies a psychophysical model that presents critical gaps as thresholds depending on the relative speeds of the subject vehicle and t he assumed leader and follower. Lane changing vehicles may accept progressively higher decelerati on rates as an urgency to complete the merging maneuver. At the same time, the merging ve hicles may cause the through vehicles to accept higher deceleration rates as the merging veh icle approaches the end of the acceleration lane. During lane changes the subject vehicle may accelerate to facilitate its maneuver, and there is provision for cooperation between the vehicles. Merging Under Congested Conditions Various researchers have contributed to the investi gation and modeling of merging behavior during congested traffic conditions. Sarv i et al. (2002) performed research for modeling ramp vehicle acceleration-deceleration beh avior during the merging process in congested conditions. Based on the field data coll ected at two ramp junctions along the Tokyo Metropolitan Expressway, Sarvi et al. observed that the merging behavior under congested conditions occurs on a one-by-one basis regardless of the length of the available gap (also referred to as zip merging or zipper effect). The authors do not make use of the gap acceptance methodology because previous research (Sarvi and Ku wahara, 1999) found that during heavy congestion, unstable or stop-and-go traffic flow ap pears to take place, and the gap searching and acceptance maneuvers do not occur. This zip mergin g behavior has been characterized also as turn-taking merging by Cassidy and Ahn (2005), who showed that the merging occurs in an almost one-by-one basis, and this ratio remains con stant at each site, irrespective of the merge outflow. Furthermore, Sarvi et al. (2007) performe d an analysis of macroscopic observations on driver behavior, and they showed that under congest ed conditions, the ratio of ramp flow over

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56 the total flow does not affect the capacity of the merging segment. They further observe that the opposite occurs during merging under free flowing c onditions, where the distribution of these two volumes is related to the easiness of the mergi ng operation: i.e., all else held constant, fewer ramp vehicles suggests easier merging. Lastly, aft er examining the lane distribution they conclude that the shoulder lane is being under-util ized, i.e., the shoulder lane volume was approximately 1/3 of the median lane, and the ramp shoulder lane volume was half of the volume on the ramp median lane. Using Instrumented Vehicles to Study Driver Behavio r Various studies have been conducted with the partic ipation of subjects and the use of instrumented vehicles to study closely a variety of driver behavior-related issues. Researchers in psychology have deployed instrumented vehicles to s tudy physiological responses of drivers and how these relate to the driver-vehicle-environment system (Helander, 1978). Measurement of the electrodermal response (EDR) and heart rate (HR ) in the occurrence of various external factors showed that a vehicle merging in front of t he subject vehicle may induce great difficulty in the driving task. Lane changing activity may ha ve similar psychological implications. Recently, Chang et al. (2001) showed that driver’s load in acceleration lane before merging is higher than the freeway section and that it was mai ntained after the completion of the merging maneuver. Other researchers in the field of robotics and cont rol theory have collected behavioral data using instrumented vehicles, aiming in modeling and predicting driver’s maneuvers that can potentially be used in automated driver assistance systems and ITS applications (Salvucci et al. 2007; Hegeman et al. 2005; Oliver and Pentland, 200 0; Pentland and Liu, 1999). In the same context, Shimizu and Yamada (2000) studied the effe ctiveness of the AHS (Advanced and cruise-assist Highway System) in merging behavior u nder non-congested conditions, using an

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57 instrumented vehicle. Their results indicated that the system could result in smoother merging behaviors, given that the driver recognizes the tra ffic flow on the mainline in advance. Traffic safety and driver performance is another re search field where instrumented vehicles have been used. Such example is the 100-car natura listic study performed by Virginia Tech’s Transportation Institute, where the purpose was to collect pre-crash naturalistic driving data. Additional research performed by the 100-car natura listic study (Hanowski et al. 2006), focused on the interactions between light and heavy vehicle s. In their study, video cameras and other equipment were installed to one hundred light vehic les and the analysis entailed recording of each light vehicle-heavy vehicle interaction event. Sayer et al. (2007) performed a naturalistic driving study using 36 drivers in order to examine their engaging in secondary behaviors (conversation, grooming, cell phone use, eating/dri nking, etc.) and to explore the effect of these behaviors on the driving performance. Horrey et al (2007) have gone beyond exploring the effect of secondary behaviors on drivers’ responses and they examined to which degree drivers are aware of these distraction effects (namely, the cell phone use). Classen et al. (2007) used an instrumented vehicle and surveys to evaluate the safety effects of geometric improvements at intersections, on the driving ability of older drivers. Analysis of the data indicated that at the improved intersections the average speed was increased and also drivers made fewer errors compared to the unimproved intersections. Further comparisons between younger and older drivers indic ated that older drivers make more mistakes than the younger ones, however, all drivers benefit from the geometric improvements. In addition, a significant amount of research has b een involved with the examination of microscopic traffic characteristics. Brackstone et al. (1999) performed a study using an instrumented vehicle for developing and calibrating models of driver behavior. The vehicle was

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58 equipped with various sensors such as: optical spee dometer, microwave radar which measures distances to the adjacent vehicles, and two video c ameras (one rear-facing and one front-facing) with audio recording system. Information from all sensors was stored at a PC for further analysis. Seven subjects were used where each was instructed to follow another test vehicle. Analysis of the data showed that the front and rear gaps, and the time to collision (TTC) are important factors that affect lane changing decisio ns. Brackstone et al. also found two thresholds for TTC: one of 45 seconds above which a gap is alm ost always accepted and a second at about 20 seconds, below which a gap is almost always reje cted. The authors hypothesize that there might be an intermediate threshold for which the de cision for a lane change would mostly depend on lane and local flow and density, among ot her parameters. Lastly, in-vehicle interviews with a limited number of subjects were p erformed to investigate their perception of relative speed (denoting as “closing”, “constant” o r “opening”). Brackstone (2003) used an instrumented vehicle to c ollected data for a car-following study. He applied the same instrumented vehicle in this re search which is relevant to the classification of drivers’ attributes. Brackstone examined correl ations between different indicators of driver personality/ experience and found that at low speed s, drivers with high externality (measures drivers feelings regarding locus of control and res ponsibility) will have high following distances, while drivers who score high on the sensation scale would have lower following distances. They did not conclude to anything similar at high speeds Recently, Wu et al. (2007) examined the effect of r amp metering on the driving performance of merging vehicles, using the instrume nted vehicle described in Brackstone et al. (1999). More specifically, they examined whether r amp metering can reduce the stress of the merging vehicles and whether it can smooth traffic downstream of the merge junction. In

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59 addition to the vehicle sensors, loop detector data were available on the freeway (upstream of the merge junction) and on the on-ramp. All data (in-v ehicle, loop and video data) were used for the investigation of gap acceptance, speed at merge and merge location during the merge process. The subjects were instructed to follow both a mergi ng route and a through route. Wu et al. performed three investigations: (i) the behavior of the through traffic, (ii) the behavior of the merging vehicles at the merge point, and (iii) the behavior of the freeway through vehicles upstream of the merge. The research finding showed that ramp metering has insignificant effect on the behavior of the through traffic (mean speed, acceleration, and time headway). It was also found that ramp metering resulted in increased lane changing activity and higher headways from the outside lane to the middle lane, which indicate s a flow reduction upstream of the merge. Speeds and headways on the middle and median lanes were not found to be statistically different. Lastly, the effect of ramp metering on the merging traffic included increase of acceptable gaps, and reduction in merging speeds, which indicates ea sier merging conditions for merge traffic. There are other studies as well that collected data using instrumented vehicles to establish microscopic driver behavior relationships. Cody et al. (2007) used instrumented vehicles to examine the gap acceptance decision making during l eft-turn maneuvers from an intersection. Ma and Andreasson (2007) also used an instrumented to collect car-following data on Swedish roads. The authors also developed a fuzzy clusteri ng algorithm to distinguish between the different car-following regimes. Henning et al. (2007) examined several behavioral a nd environmental indicators that predict drivers’ intent to change lanes. Data coll ected from an instrumented vehicle include speed, acceleration/deceleration, yaw rate and incl ination, eye movement, steering wheel position, pedal use and turn signal use, distance t o the car in front and GPS positioning. Cameras

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60 were also set to record 5 different views around th e vehicle. The indicators considered for the lane change maneuver are the first glance to the le ft mirror, the turn signal and the actual lane crossing, all three of which were found in the data collected. In concluding, instrumented vehicles have been wide ly implemented for data collection in transportation-related studies. By combining data from vehicle sensors (gear, acceleration, throttle, etc) in-vehicle cameras either facing the driver or the roadside environment or both, and loop detectors, researchers have gathered useful in formation for understanding and modeling driver behavior at the operational and also tactica l level. Although the use of instrumented vehicles can provi de useful information about driver behavior, the experiments should be designed with c are, and the results should be analyzed with caution, as research has shown that human behavior may change even if very subtle indication exists of being watched. Not only is this true, bu t it has been also shown that the behavior becomes more altruistic as people, and even some an imals are being observed (Milinski and Rockenbach, 2007). This derives from the fact that by observing (or rather “snooping on”) other people, we actually work out how to behave in the f uture. Consequently, people (and also animals) try to deceive the observers in order to s ecure future gains (e.g., positive reputation). The authors further comment that: Watchful eyes induce altruistic behavior and an ‘ar ms race’ of signals between observers and the observed. Summary of Literature Review According to the literature, capacity associated wi th breakdowns at freeway ramp merging segments is a stochastic variable, because the brea kdown events can occur over a wide range of traffic conditions. It has been also shown that the se breakdown events are the result of conflicts that occur during the merging process, when traffic moves towards congested conditions. For

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61 example, Elefteriadou et al. (1995) and Yi and Muli nazzi (2007) discuss vehicle platoons; Kerner and Rehborn (1996, 1997) mention of vehicles “squeezing” on the highway. Further observations in the vicinity of ramp merges note th at the consequence of these interactions between the on-ramp and the freeway vehicles may be for several vehicles to decelerate and cause other vehicles to reduce their speed as well, leading towards the occurrence of breakdown. Merging behavior during complete congestion (queues on the freeway and the on-ramps) appears to follow the “zipper effect” or is describ ed by taking turns (Cassidy and Ahn, 2005). This behavior could potentially be easy to model, g iven that the queue lengths are known. The merging process has been studied to a significa nt degree in the literature, and the developed models are typically applied in microscop ic simulators to provide a more realistic representation of traffic operations. Most of the MLC models are based on gap acceptance rules. Recent refinements of the models include the additi on of the cooperative behavior of the freeway through vehicles (cooperative merging), and also th e competition between freeway and ramp vehicles (forced merging). Recent research has als o incorporated acceleration-deceleration decisions of the merging vehicle, to provide a more complete outlook of the merging process. Important parameters identified to affect drivers’ choices of acceptable gaps during the merging process pertain to traffic conditions, geometric at tributes, relative speeds, and also individual driver characteristics (impatience factor, aggressi veness). The merging process on freeway-ramp merging segment s has been studied in a significant extent during the past twenty years, however many l imitations are identified to date. For instance, decisions that occur during the merging p rocess have been established by various researchers, but these have not been evaluated by a ctual drivers. As such, the effect of individual drivers’ characteristics on the decision-making pro cess is still unknown. Generally, driver

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62 behavior has been considered an important factor in the literature, but this has not been examined closely. This also means that there are no data sh owing if the merging process differs by driver’s aggressiveness, e.g., if an aggressive driver makes different acceleration and gap acceptance decisions differently than a timid driver. In addition, current research has included the effe ct of traffic conditions on the merging decisions, but has not studied the opposite; the im pact of individual drivers’ merging maneuvers on the overall traffic stability. This type of res earch could provide some answers concerning the breakdown events and the resulting capacity at free way ramp merges. Thus, how the behavioral characteristics of drivers can trigger instabilitie s affect at a given freeway-ramp junction can give insights regarding the occurrence of a breakdown.

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63 CHAPTER 3 BEHAVIORAL BREAKDOWN PROBABILITY METHODOLOGY This chapter presents the methodological framework for the development of the breakdown probability model at freeway merges consi dering driver behavioral characteristics. First, the structure of the merging process with th e respective decision-making steps is presented. Following that, the breakdown probability model is formulated, which accounts for the effect of driver interactions and merging maneuvers on the fr eeway operations. Merging Model Structure This section presents the proposed structure of the merging process. The conceptual framework of the merging process is illustrated in Figure 3-1. n r n r r n r r nn nn r r n n nn n nn n r n r n n r r Figure 3-1. Conceptual description of merging proc ess. The conceptual merging process combines ideas from previous models in the literature (Toledo, 2003; Choudhury, 2007), with the data coll ected through this thesis. The model presents 4 levels of decision-making: gap acceptance, decisi on for free merge maneuver, decision to initiate cooperative merge, and decision to initiat e forced merge maneuver.

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64 As it is shown in Figure 3-1, the merging model is based on gap acceptance. The critical gaps depend on driver’s aggressiveness, the traffic conditions and the geometry of each site. The critical gaps are typically the minimum acceptable gaps. The gap acceptance model checks which gap is accept able for merging. Each gap is defined by the lead and lag gaps in the shoulder la ne, as depicted in Figure 3-2. Figure 3-2. The lead, lag, and total gap. The available lead, lag and total gaps are compared to the ramp driver’s critical (i.e., minimum acceptable) gaps, and these are accepted if they are greater than the critical gaps. The critical gaps are assumed to follow a lognormal dis tribution to ensure their non-negativity. i lag i lag R i lag R i lead i lead R i lead RX G X G, , ,* ) ln( ) ln( (3.1) Or equivalently, i total i total R i total RX G, ,* ) ln( (3.2) forced e cooperativ free i Where, i lead RX,, i lag RX, and i total RX, are vectors of explanatory variables affecting the lead, lag and total critical gaps under the different types o f merging maneuvers, respectively. i lead,, i lag,and i total,are the corresponding vectors of parameters. The ga p acceptance model assumes

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65 that both the lead gap and the lag gap or the total gap must be acceptable in order for the ramp vehicle to merge, under any merging maneuver. The p robability of accepting a gap and performing any of the possible merging maneuvers is given by: forced e cooperativ free P m P or G G P G G P P P m PR i R i cr lag R i lag R R i cr lead R i lead R R R R i R, i gap) al accept tot ( ) ( ) ( ) ( ) gap) lag accept (( ) gap) lead accept (( ) (i , i i r r (3.3) Assuming that critical gaps follow a lognormal dist ribution, the conditional probability that the lead gaps and the lag gaps are acceptable is gi ven respectively by: r i total i total i total R i total R i cr total R i total R R i cr total R i total R RX G G G P G G P, , , ,) ( ) ln( ) ln( ) ln( ) ( (3.4) Where [.] is the cumulative standard normal distribution. If the gap is rejected, then the ramp vehicle needs to re-examine the situation, by evaluating the mainline lag vehicle’s reaction. If the mainline vehicle initiates cooperation (decelerate or change lanes), the ramp vehicle may decide to accept the gap and merge. If the mainline vehicle is not willing to yield or its dec eleration is not enough, the ramp vehicle may decide to initiate a forced merge. The following sections present the basic elements o f the three preliminary merging models in more detail. Free Merge Model This section presents the detailed free merge proce ss. The structure of the proposed free merge model is illustrated in Figure 3-3.

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66 n r nn nn r n n r r n r n Figure 3-3. The free-merge model. If the gap is larger than the critical gap, or if t he freeway vehicle yields by changing lanes, then the ramp vehicle initiates a free merge. The c ritical gap is the minimum acceptable gap under free gap acceptance conditions. The critical gap is the critical total gap between the potential freeway lead and lag vehicles, as shown i n Figure 3-2. Cooperative Merge Model Figure 3-4. The cooperative-merge model.

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67 During this decision level, both ramp and mainline lag vehicles need to evaluate the situation ahead. Frequently, a mainline vehicle th at is approaching the on-ramp will evaluate whether it should change lanes or decelerate to mak e room for the ramp vehicle, or continue its course. If the freeway vehicle changes lanes, then the ramp vehicle will merge under free-merge conditions. However, if the freeway vehicle deceler ates, then the ramp vehicle will evaluate the situation and depending on its perception of the ma inline vehicle’s actions, it will react by accepting the freeway vehicle’s cooperation and mer ge. The decision to accept the gap formed after the coo peration depends on whether the mainline vehicle is willing to decelerate or not. T he freeway vehicle’s willingness to decelerate (Hidas, 2005) may depend on several factors such as the driving experience, the freeway vehicle’s degree of aggressiveness, the mental stat e of the driver (being in a hurry, disconcerted about other things, etc), the urgency of the maneuv er as this is perceived by the freeway vehicle, and the downstream traffic conditions. Given that the mainline vehicle slows down, the pot ential gap size increases; thus, the ramp vehicle evaluates whether the current gap is ( or will be) acceptable for cooperative merging. If the mainline vehicle does not slow dow n, the ramp vehicle will decide whether to perform forced merge or to search for next gap. At this step, it is considered that the acceptable gap for cooperative merging is a random variable, w ith a mean value less than the critical gap.

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68 Forced Merge Model Figure 3-5. The forced-merge model. The ramp driver will initiate a forced merge maneuv er in two situations: (i) the courtesy that the mainline vehicle is providing (by slowing down) is not enough for the development of an acceptable gap for cooperative merge and the ramp v ehicle decides to force its way so that the follower will decelerate more, and (ii) no action o f cooperation is perceived, however, the ramp vehicle will attempt to force its way, waiting for the follower to comply. Alternatively, the ramp vehicle may decide to evaluate the next gap and ret urn to the initial state. Breakdown Probability Model Formulation This section presents the structure of the breakdow n probability model. As it was previously stated, the goal of this model is to bri dge the gap between individual drivers’ behaviors and traffic characteristics, and to provi de an explanation of how the drivers’ choices and actions related to merging can trigger the brea kdown phenomenon at ramp junctions.

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69 In this research it is assumed that all vehicles at tempting to merge can create a certain degree of traffic instability in the freeway traffi c stream. The magnitude of the turbulence depends on the maneuver type that the ramp vehicle will perform. This magnitude also depends on the degree of interaction between the ramp vehic les and the freeway through vehicles. As it was shown in the conceptual description of the merg ing process (Figure 3-1), there are three types of merging maneuvers: free, cooperative and f orced. In terms of explaining vehicle interactions, these maneuvers can be defined as: Free merges: No obvious interaction exists between the merging vehicle and the mainline vehicle. The free merge maneuver does not affect t he driving behavior of the mainline vehicle, and vice versa. Cooperative merges: The mainline vehicle yields to the ramp merging vehicle by either slowing down or changing lanes, to create an accept able gap. Forced merges: There is a clear conflict between th e merging vehicle and the mainline vehicle. The merging vehicle initiates this intera ction and the mainline vehicle reacts by slowing down or changing lanes. Based on these definitions of merging maneuver type s, it is clear that the free merging maneuver does not create any disruption to the free way traffic stream. However, the cooperative or forced merging maneuvers can create instabilitie s due to vehicle interactions which may lead to a series of vehicles slowing down to accommodate the merges and eventually, to a sprawling speed reduction (i.e., breakdown) at the location o f the merge. The models developed in this thesis account for all three merging maneuver types Typically, the likelihood of cooperative or forced merging maneuvers increases as traffic operations move towards congested conditions, becau se vehicle conflicts become more frequent. Figure 3-6 shows the reaction of the mainline vehic le N, in response to the merging maneuver of the ramp vehicle R. At time t = 0 the mainline veh icle N at the shoulder lane identifies the intention of the ramp vehicle R to merge into the f reeway. In anticipation of that fact, at time t =

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70 t1, the mainline vehicle M may be involved in a coope rative or a forced merge maneuver with vehicle R. vehicle. The resulting action of the veh icle N would be either to decelerate, or to change lanes. It is also possible that the mainline vehicle N will not yield to the ramp vehicle R, and continue with the same speed or even accelerate to avoid any interaction. Figure 3-6. Interactions between the mainline vehi cle N and the ramp merging vehicle R resulting to deceleration or lane change of vehicle N. It is also useful to know how the behavior of the u pstream vehicles is affected by the merging maneuver downstream. Figure 3-7. Following vehicle in shoulder lane (F) and interacting mainline (M) and ramp (R) vehicles. For example, assume that a cooperative or a forced maneuver takes place and the mainline vehicle N decelerates to X mph (Figure 3-7). The v ehicle upstream of N (vehicle F) may react to the situation ahead by decelerating as well. At th is point it is clear that the merging maneuver was the cause of the speed drop for both vehicles N and F, which eventually can lead to braking

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71 for several of the through vehicles. However, depe nding on spacing between vehicles F and N, it is possible that the following vehicle F does not r espond at all to the situation downstream (continues with constant speed) or moves to the ins ide lane depending on the gap availability. Thus, vehicle decelerations as a result of the coop erative and forced merging maneuvers at a ramp junction, may affect not only the interacting vehicles but the following vehicles as well. Depending on the extent of this impact, it is possi ble that this interaction might trigger a chain reaction of braking and lane changing activity near the merge, which may eventually result in a breakdown. To describe the aggregate effect of the merging veh icle’s maneuvers on the traffic stream over a certain period of time, a new term is introd uced, called merging turbulence: Merging turbulence is defined to occur when there is a seri es of cooperative or merging maneuvers, capable of affecting the speed choice of either the freeway vehicles (vehicle N or F). Thus, merging turbulence represents the frequency of ramp merging maneuvers that cause the freeway vehicles to decelerate, over a specific period of t ime (e.g., one minute). An illustration of turbulence is shown in Figure 3-8. Figure 3-8. Deceleration event due to ramp merging maneuver.

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72 At time t = 0, Figure 3-8 shows vehicle R entering the on-ramp. At that time, vehicles N and F are faced with three options: to continue dri ving with same speed, to move to the inside lane, or to decelerate. At time t = t1 vehicle N decides to decelerate, and potentially f orces the following vehicle F to decelerate as well. If the p robability that any freeway driver N decelerates due to a cooperative or forced merging maneuver is Pn(DEC), then the probability of merging turbulence can be expressed as: N n nDec P te RampFlowRa bulence MergingTur P1) ( 1 ) ( (3.5) The following two subsections discuss the proposed models for modeling the behavior of vehicle N, to predict their contribution in the dev elopment of turbulence due to merging maneuvers, and the relationship between the merging turbulence model and the probability of breakdown. Modeling the Behavior of the Freeway Vehicle The probability of merging turbulence depends on th e decision-making process of the freeway vehicles as they are approaching the merge area. During the ramp merging event, vehicle N has three alternatives: (i) to decelerate (and remain in the current lane), (ii) to change lanes, and (iii) to continue with the same speed in the current lane. The first two alternatives are associated with the cooperative or forced merge man euvers. The third alternative suggests that the freeway vehicle does not yield (no cooperation is provided) or the ramp vehicle does not initiate a forced merge. In this case, the ramp veh icle will have to merge after vehicle M, and possibly interact with vehicle F. Figure 3-9 descri bes the potential interactions between the ramp vehicle and the freeway vehicle and the resulting d ecisions of the freeway vehicle. Whether the deceleration or lane changing occurs as a result of a cooperative merge or a forced merge

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73 depends on who initiates the interaction (as descri bed in the definitions of merging types presented in the previous section). nr n rnn n nr rn n n n n n n n n Figure 3-9. Potential freeway vehicle decisions du e to a ramp merging maneuver. As illustrated in Figure 3-9, the behavior of the f reeway vehicle can be modeled considering two components. The first component des cribes the event that the freeway vehicle will decelerate by initiating a cooperative merge, indicating the transition from the normal state (no interaction) to the cooperative state. The seco nd component captures the event that a freeway vehicle will decelerate as response to a forced mer ge by the ramp vehicle, given that no cooperation was provided earlier. This assumes the transition of the freeway vehicle from the normal state (no interaction) to the forced state. These two events are mutually exclusive, i.e., they cannot occur simultaneously. Therefore, the pr obability that the freeway vehicle will decelerate can be described by the following expres sion: Pn(DECt) = Pn(DEC, st,n = coop/st-1,n = normal) + Pn(DEC, st,n = forced/st-1,n = normal) (3.6) Where st is the state of the freeway vehicle n at time t which can be normal (no interaction), cooperative, or forced. Both componen ts of this model are developed in a discrete choice framework. The exact structure of both discr ete choice models is dictated by the freeway

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74 vehicle’s decision-making process. A discussion on the modeling specifications of both components follows. Freeway vehicle behavior under cooperative merging: Assuming that the freeway driver decision-making process is a two-step proces s, nested structures of the model were evaluated initially. An example of a nested structu re related to the cooperative merges is given in Figure 3-10. Figure 3-10. Nested model for cooperative behavior of mainline vehicle N. According to this structure, at the first level the driver evaluates the situation and makes the decision whether to cooperate or not. If the dr iver is willing to cooperate, then they evaluate which form of cooperation to provide (level 2). Thi s structure was found to be supported by the data; however, no significant explanatory variables were identified. Other nested structures were evaluated as well, but these were not supported by the data. Therefore, the driver behavior under cooperation is modeled as a Multinomial Logit (MNL) model where the freeway vehicle has three cho ices: to decelerate, to change lanes, to do

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75 nothing. If gaps are not available, then lane chang ing is not an option, thus the freeway vehicles’ choices are to decelerate or not yield to the ramp vehicle. Freeway vehicle behavior under forced merging: If the freeway vehicle does not show cooperation towards the ramp vehicle, then the ramp vehicle may attempt to force its way into the freeway (Figure 3-9). In this case, the role of the freeway vehicle is reactive. They can either decelerate or move to the inside lane, provided tha t there is a gap available. The freeway vehicle’s decision is also modeled as a Multinomial Logit (MNL) model. For the development of both behavioral models under cooperative, forced or normal state, the utility functions (U) of the choices for the fr eeway vehicle N have the property that an alternative is chosen if its utility is greater tha n the utility of all other alternatives in the individual’s choice set. These functions are: s n i s n i s n iV U, (3.7) i {decelerate, change lanes, no action} s {cooperative, forced, normal} In Equation 3.7 s n iV, represent the observable (deterministic) portion o f the utilities of driver n to decelerate, change lanes and do nothing under e ither state. The terms s n i are the error terms associated with the three utilities. The erro r terms are assumed to be Gumbel distributed and also identically and independently distributed across the alternatives and across the individuals. The deterministic components of the utilities for a ll three choices are: s n CL s n CL s n CLX V, ,r (3.8) s n NoAction s n NoAction s n NoActionX V, ,r (3.9) s n DEC s n DEC s n DECX V, ,r (3.10)

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76 Where s n CLX,, s n DECX, and s n NoActionX, are the vectors of explanatory variables that affe ct the utilities to change lane, decelerate and do nothing s n CL ,, s n DEC and s n NoAction are the corresponding vectors of the parameters. Generally, the explanatory variables are related to : (1) alternative-specific attributes, (2) characteristics of the drivers, and (3) interaction s between the attributes of the alternatives and the characteristics of the drivers. The function t hat describes the decision of vehicle N to decelerate, change lanes or do nothing has the foll owing form: ) (* *0 n n n n s nZ X Z X V (3.11) s {cooperative, forced, normal} In Equation 3.11, ao are the alternative-specific constant parameters, Xn is the vector of explanatory variables related to the traffic condit ions and the environment of the subject vehicle, are the parameters associated with explanatory var iables Xn, Zn is the vector of variables related to the characteristics of the driver, are parameters associated with explanatory variabl es Z, are parameters associated with the interaction ter ms between the explanatory variables, X, and driver characteristics variables, Z. The final expressions for the probabilities of all three alternatives are: ) exp( ) exp( ) exp( ) exp( ) / (, 1 j n Action No j n CL j n DEC j n DEC t t nV V V V normal s j s DEC P (3.12) ) exp( ) exp( ) exp( ) exp( ) / (, 1 j n Action No j n CL j n DEC j n CL t t nV V V V normal s j s CL P (3.13) ) exp( ) exp( ) exp( ) exp( ) / (, 1 j n Action No j n CL j n DEC j n Action No t t nV V V V normal s j s Action No P (3.14)

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77 Merging Turbulence and the Probability of Breakdown The merging turbulence model accounts for the effec t of the merging maneuvers on the occurrence of the freeway flow breakdown. The mergi ng turbulence model should be compared with a breakdown probability model to evaluate thei r relationship. To account for the stochastic nature of the breakdo wn, the method for developing the breakdown probability model is based on the lifetim e data analysis, and particularly the KaplanMeier estimation method, as this was introduced by Brilon (2005). For the development of this model, historic speed-flow data at the breakdown lo cation are required. The distribution function of the breakdown volume F(q) is: B i k k q Fq q i i ii ; 1 1 ) (: (3.15) In Equation 3.15 q is the total freeway volume (veh/h), qi is the total freeway volume (veh/h) during the breakdown interval i, (i.e., breakdown flow), ki is the number of intervals with a total freeway volume of q qi and {B} is the set of breakdown intervals (1-minute observations). The breakdown interval is typically identified as t he interval when the average speed at that location drops below a specific threshold (e.g ., 10 mi/h lower than the posted speed limit). Methodological Framework This section presents the data that are required fo r the development of the driver-behavior models and the macroscopic models of merging turbul ence and breakdown probability, as these were described in the previous sections of this cha pter. The chapter concludes with a step-bystep summary of the methodology pertained in this t hesis.

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78 Data Types for Models The development of the microscopic driver behavior models require data related to the drivers’ thinking process, the interactions with th e adjacent vehicles and the traffic conditions on the freeway. The drivers’ thinking process is required to invest igate when they start (or fail) to interact and cooperate with their adjacent drivers, what act ions they are performing to accomplish their decision (decelerate, change lanes or do nothing), how they perceive the adjacent vehicles and if they see any cooperation (or not) from the adjacent vehicles. In additions, drivers’ characteristics are also important to examine how their decisions v ary across traffic conditions and across different drivers. To obtain driver behavior-relate d information, actual input from different drivers is required. This could be through conversa tions with drivers in the format of focus group sessions, as well as actual driving observations, w here driver actions and reactions are observed from the inside. Data that describe the relationship between the sub ject vehicle and the adjacent vehicles in the traffic stream are also required to produce the variables used in the models. This type of data include the gaps and gap change rates between the r amp vehicle and the freeway lead/lag, their relative speeds and accelerations, the positions of the freeway lag when the ramp vehicle enters the acceleration lane, the percent of acceleration lane used, the position of the freeway lag and lead vehicles during the merging maneuver. Other ty pes of information, such as the type of the interacting vehicles are also required. These data can easily be obtained through video observations, however this should be at the individ ual vehicles level. Video observations taken from inside the vehicle can provide the quantitativ e data that are related to drivers’ actions and triggers.

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79 Data related to the prevailing traffic conditions a re required to quantify their effect on the choices of the interacting vehicles. These data inc lude measurements of densities and average speeds during the merging maneuver, as well as the availability of gaps in the adjacent lanes. The number of ramp vehicles at the time of the merge is also considered as this may affect both the decisions of the freeway lag and the ramp vehicle. Data taken from cameras (e.g., traffic monitoring cameras) that cover the entire merge are as are required to obtain the macroscopic information. For the development of the turbulence model video d ata at the merge junction before the occurrence of the breakdown are required to disting uish between the different sources of vehicle interactions (due to merging, lane changing or due to speed reduction downstream), and to quantify the effect of those interactions to the fr eeway vehicles. These effects include decelerating or lane changing activity for each lan e. In addition, information about the ramp volume and the freeway volume are required to provi de correlation between the turbulence model and the breakdown occurrence. To verify the b reakdown occurrence speed time-series plots need to be constructed from the detector sens ors close to the merge area. Historic detector data for the breakdown locations are also required to construct the breakdown probability model as this was described in the previous section. In summary, various sources of data are required to observed driver behavior and its relation to the development of the breakdown. Focus group discussions, as well as simultaneous data collection using an instrumented vehicle and t raffic monitoring cameras are appropriate sources for identifying how merging decisions affec t traffic operations and the breakdown occurrences on freeway merges.

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80 Research Tasks The step-by step procedure performed in this thesis is summarized in this section. An illustration of the entailed tasks is shown in Figu re 3-11. Figure 3-11. Methodological plan. Step 1 Conduct focus group meetings: In the first step, focus group surveys were conducted to attain knowledge about how drivers per form merging maneuvers and what are their concerns. During this step, all important factors indicated from the drivers were used to finalize the merging process and to formulate the merging mo dels that are calibrated as part of Step 3. A detailed description of this data collection effort and results is provided in Chapter 4 of this thesis, while the questionnaires used during the fo cus group discussions is provided in Appendix A. Step 2 Conduct field data collection effort: In this step, drivers were asked to participate in in-vehicle driver behavior studies. Typically, drivers’ intention and process of thinking related to the merging task cannot be capt ured by observing field operations, because only the result of their actions is captured this w ay. Drivers’ thinking process can only be

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81 obtained through questionnaires, where they can exp licitly describe their intention about a maneuver. These studies aim at obtaining such driver behavior data from participants during their driving task (merging on the freeway and driving on the mainline). Additional field data (flow, speed, density) were collected concurrently with th e in-vehicle data at the study ramp merging sections. The combination of in-vehicle and traffi c data is used to infer vehicle interactions in two ways: how the driver merging decisions influenc e and are influenced by the prevailing traffic conditions. The field data collection was p erformed at near-to-congestion conditions to capture the impact of these interactions on the fre eway operations. Information relevant to the in-vehicle and field data collection and results is presented in detail in Chapter 5. Step 3 Calibrate the merging models: This step includes the calibration of the gap acceptance and the driver behavior models. All data collected in the field, from both the invehicle study and the external traffic data were us ed for the model calibration. The gap acceptance model considers the different types of m erging maneuvers and evaluates the impact of driver behavior attributes on those maneuvers. T he driver behavior models capture freeway drivers’ decisions to decelerate, change lanes or n ot interact with the ramp merging traffic. Step 4 Develop merging turbulence models: During this step, the contribution of individual drivers’ action on the freeway traffic s tability is evaluated. The external traffic data were used to quantify the effect of individual vehi cle deceleration decisions and associate those with the beginning of congestion. Step 5 Develop breakdown probability model: This step includes the proposed application of the turbulence model to develop a br eakdown probability model.

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82 CHAPTER 4 FOCUS GROUP EXPERIMENTS The first part of the data collection plan undertak en for this research is presented in this chapter. The focus of this research is to look at merging behavior and vehicle interactions from the drivers’ perspective, and to investigate the ef fect of individual behavioral characteristics on drivers’ decisions. Focus groups were used as a fir st step to understand the drivers’ thinking process when merging. The forms as well as the meth odology used for the focus group meetings were pre-approved by the Institutional Review Board (IRB) of the University of Florida. This chapter describes the formulation of the focus groups and presents the questions discussed during these sessions. Important focus gr oup findings and conclusions from the discussions are also presented. Setting Up the Focus Groups The focus group study was advertized through local organizations in Gainesville, FL, and candidates completed a pre-screening questionnaire. The pre-screening questionnaires assembled information on gender, age-group, ethnicity, years of driving experience, occupation, frequency of driving and time of day, and vehicle type. The i nformation was used to select a diverse set of participants for focus group participation. Sevente en participants were invited to join three 2hour focus groups, and an attempt was made to selec t drivers with different demographics, in terms of their gender, age-group and race. The demo graphics of all participants are presented in Table 4-1.

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83 Table 4-1. Demographic characteristics of focus gr oup participants ID Gender Age group Race Experience Occupation Driving frequency Hours per week Peak/ non-peak Vehicle ownership Focus Group 1 1_03 Female 25-35 Caucasian >=10 years Teacher Ever yday >14 hrs Peak Sedan/Coupe 1_05 Male 25-35 Caucasian >=10 years Teacher Usuall y <4hrs Peak Pickup/SUV 1_09 Male 45-55 Caucasian >=10 years Community design Sometimes 4-8 hrs Non-peak Sedan/Coupe 1_22 Male 25-35 Caucasian >=10 years Student Everyd ay 4-8 hrs Peak Sedan/Coupe 1_01 Female 25-35 Caucasian >=10 years Student Ever yday 4-8 hrs Peak Sedan/Coupe 1_15 Female 25-35 Caucasian >=10 years Legal assist ant Everyday 4-8 hrs Peak Sedan/Coupe Focus Group 2 2_13 Female 55-65 Caucasian >=10 years Accountant E veryday 8-14 hrs BOTH Sedan/Coupe 2_12 Female 35-45 Caucasian >=10 years Massage therapist Everyday 8-14 hrs Peak Pickup/SUV 2_16 Female 18-25 Afr/American 3-9 years Student So metimes >14 hrs Non-peak Sedan/Coupe 2_07 Male 18-25 Caucasian 3-9 years Attorney Everyd ay 4-8 hrs Peak Sedan/Coupe 2_25 Female 35-45 Caucasian >=10 years Student Ever yday 8-14 hrs Peak Sedan/Coupe Focus Group 3 3_26 Male 35-45 Caucasian >=10 years US Navy Everyd ay 4-8 hrs Peak pickup/SUV 3_04 Male 18-25 Caucasian 3-9 years Student Everyda y >14 hrs Peak Sedan/Coupe 3_06 Male 18-25 Afr/American 3-9 years Student Some times 4-8 hrs Peak Sedan/Coupe 3_14 Male 35-45 Caucasian >=10 years Manager Everyd ay 4-8 hrs BOTH Sedan/Coupe Truck 3_27 Female 55-65 Caucasian >10 yrs Retired economist Usually 4-8 hrs Non-peak Sedan/Coupe 3_28 Female 25-35 Hispanic >10 yrs Real-estate Eve ryday 4-8 hrs Peak Sedan/Coupe

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84 Prior to each session, the participants completed a background survey form, which contained seven multiple-choice questions related t o their driving habits. These questions solicited the subjects’ desired freeway speed (assu ming good visibility and weather conditions and a 70-mi/h speed limit), lane-changing habits, h ow aggressive they consider themselves, how aggressive their friends/family consider them, when and where they typically merge onto the freeway, how they react if a vehicle merges onto th e freeway while they are driving on the rightmost lane, and whether they plan their trips allowi ng for additional time to mitigate possible delays. Overview of Focus Group Questions Typically, focus group discussions contain five cat egories of questions, all of which have their specific purpose and function (Krueger and Ca ssey, 2000): opening, introductory, transition, key, and ending. The opening question i s designed to get people talking and make them feel comfortable. They were asked if they enjo y driving and if they spend a lot of time driving. The next question is the introductory ques tion which helps people relate to the topic. Here, the participants were asked “What is the firs t thing that comes to mind when you hear the phrase ‘Merge into the freeway’?”. The transition q uestion moves the conversation to the key questions. The transition question used was phrased as follows: “Do you believe the way you merge is different from other drivers? Why or why n ot?”. The key questions are the ones that typically drive the study. The key questions are op en-ended situation-based scenarios, and the central idea is to obtain the thinking process and potential actions in a merging maneuver. These scenarios are discussed in detail in the following section. The ending question ensures that all important topics have been covered. A handout conta ining all key questions and ending question was given to the participants to fill out throughou t the session.

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85 Focus Group Key Questions The goal of the key questions is to obtain the part icipants’ thinking process and potential actions in various scenarios, either as the merging vehicle or the freeway vehicle. Scenarios under different amounts of congestion were discusse d. The effect of other factors (e.g., ramp geometry, vehicle type, driver’s urgency) on driver behavior was also discussed. Participants were asked to report (up to five) factors that affe ct their decisions and assign an importance level (“very important”, “somewhat important”, and “not a s important but may consider”) to each factor. These three levels were transcribed into th e following importance values for analysis purposes: “very important” value = 3, “somewhat imp ortant” value = 2, and “not as important” value = 1. The following five scenarios were discus sed Question 1 – Merging Process Under Free-Flowing Con ditions and Selection of Acceptable Gaps Participants were shown Figure 4-1A and B and were asked to provide their actions and thinking process assuming they are the merging vehi cle just entering an on-ramp, while the freeway vehicles are traveling at their desired spe eds. Both cases of parallel and taper ramps were discussed. A Figure 4-1. Figures discussed during scenario 1 A) Merging process under parallel type onramp. B) Merging process under tapered type on-ramp C) Lagged position of merging vehicle with respect to freeway vehicle. D) Parallel position of merging vehicle with respect to freeway vehicle.

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86 B C r !" n !# r D Figure 4-1. Continued. Participants were asked to list and discuss their a ctions and thought process when merging into the freeway, given the presence of freeway veh icles (vehicles 1, 2, and 3) at the locations shown in Figure 4-1C and D. The participants discus sed their preferable gaps in each case, as well as the factors affecting their preference. The effect of vehicles 1, 2, or 3 being trucks in the gap decision was also discussed.

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87 Question 2 Merging Process Under Decreased Speed (40-60 mi/h) For this question the participants were asked first to assume that they are the merging vehicle reaching the acceleration lane, where traff ic is denser and vehicles’ speeds are low (4060 mi/h). They were also asked to report their thin king process in merging under those conditions, and how this would change if there was another vehicle present on the acceleration lane (moving towards the end of the lane). Then, th ey would list their actions assuming they are the freeway vehicle on the right lane reaching the merging section and observing at least one vehicle on the ramp trying to merge. Question 3 Cooperative Merging and Forced Merging Maneuvers Under Decreased Speed (40-60 mi/h) This question investigated the likelihood of initia ting a cooperative merge (as the freeway vehicle), and a forced merge (as the merging vehicl e), as well as factors (up to five) that affect each decision. In both cases participants had to se lect between the “very likely”, “somewhat likely”, and “not so likely” responses. Participant s were asked to rank their stated factors as “very important”, “somewhat important”, and “not as important but may consider”. The definitions of cooperative and forced merges used i n this question derive from the literature (Hidas, 2005), but modified to consider specificall y the freeway vehicle actions after the merge: Cooperative merge: the gap between the freeway lead er and follower is increasing before the merge, indicating that the follower decelerates or changes lanes to allow the ramp vehicle to enter. Forced merge: the gap between the leader and follow er is either constant or narrowing (follower maintains speed or accelerates) before th e initiation of the merge, and starts to increase as the ramp vehicle enters, indicating tha t the ramp vehicle has “forced” the follower to either decelerate or change lanes. Question 4 Merging Under Stop-and-Go Traffic Participants were asked to assume that the freeway is congested (stop-and-go traffic). The discussion concerned participants’ actions when sta rting a forced merge (as the ramp vehicle),

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88 and when giving way to a ramp vehicle that initiate d a forced merge (as the freeway follower). They were also requested to express the likelihood of performing these maneuvers (“very likely”, “somewhat likely”, and “not so likely”). Question 5 Effect of other people on driving beha vior This last question obtained information related to the effect of other people’s presence in the vehicle, in driving performance. Assembly of Focus Group Data The data from the focus groups contained: (i) voice recordings of the 2-hour sessions, (ii) documentation of the participants’ background surve y form, and (iii) documentation of participants’ responses on distributed handouts dur ing the session. Before analyzing the data, the voice recordings for each focus group were transcri bed, and matched with the responses obtained from the handouts. Overview of the Freeway-Ramp Merging Process This section presents the focus group findings rela ted to participants stated actions and thinking process while merging. Refining Merging Process Under Free-Flowing and Den se Traffic Based on participants’ responses, a series of steps was developed for merging under both free-flowing and dense traffic conditions. The proc ess was found to be similar for all participants. These steps are summarized below: Step 1: As drivers arrive on the on-ramp, most of t hem first think about merging when they have a clear view of the freeway traffic (this depe nds on the ramp design). Others when they are half way on the on-ramp, or when they have accelerated to a speed of 50-55 mi/h. Step 2: Most of the drivers become aware of their s urroundings. They check: (i) their side to assess the speed and flow of traffic on the righ t lane (possibly the left lanes too), (ii) their front to evaluate the length of the accelerat ion lane and the time left for merging, and (iii) their rear to acknowledge potential followers

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89 Step 3– free-flowing conditions: All drivers start to accelerate when arriving at the beginning of the acceleration lane. The acceleratio n and speed adjustment may be related to targeting a specific gap that was visible from t he on-ramp, which could be used for merging. If there is no vehicle in front, all drive rs want to reach a speed close to the freeway speed or the speed limit, as the optimal sp eed for merging. Some drivers indicate they target a specific gap at this stage. Step 3– dense conditions: Several drivers indicated they would accelerate as soon as entering the acceleration lane to match or even dri ve 5 mi/h faster than the freeway traffic. Due to the denser traffic (speeds are lower), there is less variability in speeds, therefore the vehicle can adjust its speed immediately, and there is no need for fast acceleration. Step 4 – free-flowing conditions: This step include s the gap acceptance and merging process. If a gap has not been targeted through the acceleration process, the drivers select a gap and may adjust their speed to fit the gap. Task s such as actuating the turn signal and checking of the mirrors or blind spots follow. Most of the participants (16 out of 17) indicated they would accept a minimum gap of 2 – 3 vehicle lengths, while only one participant indicated they would accept a gap of ab out 5 vehicle lengths. Step 4 – dense conditions: The gap acceptance and m erging process is similar. Additional considerations: if the acceleration lane is long en ough, they might consider going faster than the rest of traffic and decelerate if necessar y, to allow more opportunities to get in (one participant). On the other hand, another parti cipant stated that if speed was low (about 40 mi/h) she might consider letting 1-2 vehicles pa ss before merging, to assess the traffic conditions downstream (e.g., presence of stopped ve hicles). All participants agreed that the acceptable gap size in this case ranges from 1.5 to 2 car lengths. Step 5: After merging, several drivers may consider moving to the inside lane, especially if the right-most lane is slow. Focus Group Results for Gap-Acceptance When participants were asked to compare their mergi ng process (Figure 4-1A and B), several suggested that, in taper ramps they would b e more cautious and anxious to merge. Fourteen also indicated they would accelerate soone r and faster than in the parallel type on-ramp, and that they would be more aggressive in selecting a gap. However, two participants suggested being less aggressive, and less worried about their acceleration, but more worried about finding a gap to merge with lower speed. Both these participa nts drive manual cars, and indicated so independently, as they were in different focus grou ps.

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90 When participants were asked to select a preferred gap (Figure 4-1C and D) their answer differed as a function of several parameters. In Fi gure 4-1C, almost all participants (16 out of 17) chose the gap between vehicles 1 and 2, while one c hose the gap after vehicle 1. Participants’ decision to choose the gap between vehicles 1 and 2 depends on: Speed of vehicle 1 Speed/deceleration of vehicle 2 Presence of vehicles behind vehicle 1 Whether vehicle 1 changes lanes Six participants that initially chose the gap betwe en vehicles 1-2 might consider merging in front of vehicle 2. This depends on: Speed of vehicle 1 Speed/deceleration of vehicle 2 Change rate of gap between 1 and 2 Whether vehicle 2 is a truck Alternatively, the decision (of 12 participants) to merge after vehicle 1 depends on: Speed of vehicle 1 Whether vehicle 1 is a truck Presence of vehicles behind vehicle 1 Whether vehicle 2 is a truck Relative speed between merging vehicle and vehicle 2 Acceleration capabilities of merging vehicle Freeway speed Almost all participants (16 out of 17) would merge between vehicles 1 and 2 or after 1, while only a few (6 out of 17) would merge between 2 and 3. This selection changes if the merging vehicle is approximately at the same lateral positi on with vehicle 2 (Figure 4-1D). In this case, drivers would prefer to merge between vehicles 2 an d 3 (12 out of 17), depending on: Relative speed between merging vehicle and vehicle 2 Speed/deceleration of vehicle 2 Acceleration capabilities of the merging vehicle Change rate of gap between 2 and 3 Whether vehicle 2 is a truck Comparison of the two figures showed that the major ity of the participants (14 out of 17) would merge between vehicles 1-2 or 2-3 (Figure 4-1D) giv en that previously they selected gaps after 1

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91 and 1-2, respectively (Figure 4-1C). The remaining three would select the same gaps in both cases. In summary, it was observed that under the same sit uation, drivers would likely react differently, and that each driver considers differe nt factors for making their decision. Some drivers are more likely to choose a specific gap, w hile others may choose any of the three gaps, depending on the traffic conditions. Focus Group Results for Cooperative and Forced Merg ing A significant portion of the focus group discussion aimed in understanding the drivers’ thought process while being either on the freeway a pproaching a merging section, or the onramp. The purpose of this discussion was to identif y factors that affect: Cooperation of the freeway vehicle towards the ramp vehicle by decelerating or changing lanes. Whether the ramp vehicle forces its way onto the fr eeway. Whether the freeway vehicle yields to a ramp vehicl e by decelerating or changing lanes when the later initiates a forced merge. Throughout the discussion, several factors that aff ect drivers’ decisions were identified and grouped into the following categories: Environmental Factors: These include the roadway, w eather and lighting conditions. Freeway Vehicle Factors: These are associated only with the freeway vehicle/driver. Ramp Vehicle Factors: These are associated only wit h the ramp vehicle/driver. Interaction Factors: These pertain to the relation between the subject vehicle and another vehicle of the immediate environment (e.g., relativ e speed). Traffic Factors: These are associated with the gene ral traffic conditions of the merging segment (e.g., average speeds, gap availability). Table 4-2 presents all factors reported to affect v ehicle decisions to cooperate towards a merging maneuver, their frequency, and average impo rtance. The average importance is a

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92 measure of both frequency and importance value and it is calculated as the frequency-weighted average of importance. Table 4-2. Factors affecting cooperative merge dec isions for freeway vehicles Factors for cooperative merging Frequency Avg. impo rtance (max=3) Weather 2 2.5 Lighting conditions 1 2.0 Speed of vehicle 1 3 3.0 Emotional status 1 3.0 Route selection 1 3.0 Headway between vehicle 1 and upstream vehicle 5 2. 2 Speed of upstream vehicle 2 2.5 Vehicle 1 ramp vehicle relative speed 1 3.0 Speed of vehicle 2 1 2.0 Speed/acceleration capabilities 9 2.7 Vehicle size/type 6 2.5 Distance traveled/position on acceleration lane 4 2 .8 Competency Erratic behavior 2 2.5 Traffic awareness (eye-contact) 2 2.5 Previous unsuccessful merges 1 3.0 Attempt to start a forced merge 1 3.0 Gap availability on left lane 8 2.8 Speed in all/left lanes 5 2.8 Traffic congestion 2 2.0 Coop. behavior of other freeway vehicles 1 3.0 Lane-changing activity 1 2.0 In the cooperative merge case, the participants are assumed to be the freeway vehicle (vehicle 1, Figure 4-1C). The three most important factors highlighted in this table are: Speed/acceleration capabilities of the ramp vehicle : If the participants perceive that the ramp vehicle has achieved a reasonable merging spee d, they are willing to yield. This perception depends on the make/type of the vehicle, but also the driver (primarily age). Gap availability on left lane: Participants are ver y likely to give way to the ramp vehicle, if they can move to the inside lane. This is consisten t with the responses to Question 2, which investigated participants’ actions when approaching the merge area from the freeway (right lane). Size/type of the merging vehicle: Participants that consider this factor are reluctant to cooperate with trucks, especially if these are open -bedded or if they are stopped at the end of the acceleration lane. One participant indicated willingness to decelerate for a motorcycle.

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93 Table 4-3 presents the stated factors that affect d rivers’ decisions to initiate a forced merge maneuver. In the forced merge case, the participant s are assumed to be the ramp vehicle. The three most important factors highlighted in Table 4 -3 are: Average speed on the freeway: ramp vehicles are mor e likely to force their way in if freeway speeds are low and traffic is dense. Amount of congestion and gap availability on the ri ght lane: These two factors are grouped together because they are correlated. The more cong ested the freeway, the less available gaps exist, and drivers are more willing to perform a forced merge. Table 4-3. Factors affecting forced merge decision s for ramp merging vehicles Factors for forced merging Frequency Avg. importan ce (max=3) Roadway conditions 3 2.3 Weather 2 3.0 Speed of vehicle 2 3 2.7 Vehicle size-type 5 3.0 Relative speed between vehicle 2 and ramp vehicle 2 3.0 Coop. behavior of vehicle 2 1 2.0 Speed/acceleration 6 2.7 Emotional status 1 3.0 Position on acceleration lane 1 3.0 Speed in all/right lanes 9 2.6 Gap availability on right lane 7 3.0 Traffic congestion 7 2.9 Number of following vehicles on ramp 2 2.0 Number of leading vehicles on ramp 1 3.0 Gap availability farther upstream 1 2.0 Table 4-4 presents the factors that affect drivers’ decisions to yield to a ramp vehicle that forces its way in, by either decelerating or changi ng lanes. Participants were asked to assume they are freeway vehicle 1 of Figure 4-1C. Table 44 includes all factors reported by the participants. The three most important factors for the decision to decelerate or change lanes are shown in italics.

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94 Table 4-4. Factors affecting deceleration and lane -changing decisions of freeway vehicle, when a ramp vehicle has initiated a forced merge Factors for deceleration Frequency Avg. importance (max=3) Roadway conditions 1 3.0 Weather 1 2.0 Headway between vehicles 1 and 2 5 2.8 Speed of vehicle 1 4 2.8 Relative speed between vehicle 2 and ramp vehicle 1 3.0 Headway between vehicles 2 and 3 1 2.0 Speed/ acceleration/ deceleration capabilities 5 3. 0 Vehicle size/type 3 2.3 Position on acceleration lane 1 3.0 Gap availability on left lane 12 2.9 Speed/relative speed in all/left lanes 8 2.4 Traffic congestion 2 2.5 Factors for lane-changing Frequency Avg. importanc e (max=3) Roadway conditions 1 3.0 Speed 2 3.0 Route selection 2 2.5 Trip urgency 1 2.0 Headway between vehicles 1 and 2 5 2.8 Relative speed between vehicle 2 and ramp vehicle 1 3.0 Speed/acceleration 8 2.9 Vehicle size/type 2 2.0 Gap availability on left lane 12 2.9 Speed/relative speed in all/left lanes 9 2.3 Traffic congestion 4 3.0 The most important factors shown in Table 4-4 are: Gap availability in the left lane: If there are gap s in the inside lane they will change lanes, otherwise they will decelerate. Freeway speed (or relative speed between lanes): If the speed of the left lane is less than the speed of the right-most lane, then there is not much incentive for the freeway vehicle to change lanes, thus, it will remain to the right lan e and decelerate. However, if the speed in the inside lanes is higher, they would be more will ing to change lanes. This factor is related to the amount of deceleration that the free way vehicle is willing to accept. The

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95 freeway vehicle is not willing to decelerate signif icantly, thus, if the merging vehicle forces them to, they will likely move to the left l ane. Speed/acceleration capabilities of the ramp vehicle : Similar to the cooperative merge, the freeway vehicle is more likely to change lanes if i t perceives that the ramp vehicle cannot accelerate to the merging speed, or will not match the freeway speed quickly once it has merged onto the freeway. Relationships Between Driver Behavior and Driver Ch aracteristics Driver behavior is related to the individual’s char acteristics, vehicle capabilities, the traffic/geometric environment, and also the task pe rformed. This section identifies differences in driver behavior, categorizes the stated behaviors a s aggressive, average and conservative, and evaluates whether drivers are consistent in degree of aggressiveness under various scenarios. Based on focus group analysis aggressive behavior c an be described by “selfishness” and consideration of factors that affect mostly the sub ject vehicle. An average behavior can be defined as considering both the subject vehicle sta tus and the other vehicles. A conservative behavior is assumed to occur when the subject vehic le will only act as a response to the other vehicles’ actions. For the purposes of evaluating d riving behaviors vs. driver characteristics, the focus group scenarios of cooperative and forced mer ging maneuvers under both dense and stopand-go traffic conditions were considered. An attempt was made to categorize different behavio rs in the case where the participants are on the ramp, under dense traffic conditions. Pa rticipants were asked to discuss how likely they are to initiate a forced merge. These response s, along with the discussion on how competitive and considerate of other vehicles they are, were grouped. The following categories are distinguished: Aggressive behavior: participants would not hesitat e to cut somebody off if they only had one chance. They have a sense of pressure and eager ness to get in, and not run out of space. They assume that others will let them in. Th ese participants consider mostly factors associated with their own individual status when ma king the decision to merge.

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96 Average behavior: participants will consider a forc ed merge, but their decision also depends on the prevailing traffic (available gaps, speeds) and their perception of the freeway vehicles. Their decision to merge depends e qually on their own status and the surrounding traffic conditions. Conservative behavior: they are less likely or not likely at all to attempt a forced merge under any situation. These participants will probab ly wait for a large gap to merge without causing any disruption on freeway vehicles. Participants’ responses were also grouped for the s cenario of the cooperative merge under dense traffic conditions. Even though both options of deceleration and lane-changing were given, all of the participants responded that lane-changin g is their first choice. In fact, some participants reported they would be moving to the inside lane “o ut of habit”. Thus, the distinction of the different behaviors was based on the event that lan e-changing is not a feasible option (no available gaps on the left lane). Given that, behav ior was categorized as follows: Aggressive behavior: participants are not very like ly to start a cooperative merge by decelerating. They will at least maintain their spe ed so the ramp vehicle merges behind them. Also, they are not likely to initiate a coope rative merge if the ramp vehicle is stopped at the acceleration lane. They might decelerate onl y if the merging vehicle is approaching the end of the lane but still moving, and traffic p ermits. Average behavior: these drivers are willing to dece lerate and create gaps for the ramp vehicle to merge; however, they are not willing to decelerate significantly. These drivers appear to be more cautious about stopped vehicles a t the end of the ramp, because they believe these could make poor judgments at merging. Conservative behavior: these drivers will firstly c onsider decelerating, than changing lanes. This behavior was not represented in the focus grou p. Similar analysis was performed for the remaining sc enarios that deal with congested conditions. The first case deals with ramp vehicles ’ willingness to wait on the on-ramp for a larger gap instead of forcing their way in. Driver behavior was categorized as follows: Aggressive behavior: Participants feel that forcing their way in is their only option, thus there is a high probability that they will force th eir way into the freeway. They also feel that the freeway vehicles are more willing to give way, because everybody is in the same position, sharing the same motivation. They will mo stly consider themselves when making the decision to merge.

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97 Average behavior: Participants prefer making eye-co ntact with the freeway vehicle and wait for them to signal, or a gap to form. Their th inking process involves the surrounding freeway vehicles as well. They feel that this situa tion yields for cooperation rather than forcing their way in. Conservative behavior: Conservative drivers are not likely to perform forced merge, as they would wait for a substantive gap to form; olde r drivers might fall in this category. However, no such behavior was identified from the f ocus group, as the sample did not include older drivers. Lastly, the case that involves freeway vehicles’ wi llingness to give way to a ramp merging vehicle under congested conditions showed a small d ifferentiation among participants’ responses. The following categories are drawn from this case: Aggressive behavior: Drivers are not willing to let any vehicle in. All participants reported that they do not react in this manner, however, the y have seen such behaviors from others. Average behavior: Drivers are not willing to let mo re than one vehicle in. Conservative behavior: Drivers may let one or two v ehicles in. High probability of giving way to the merging vehicles. Table 4-5 summarizes the results related to behavio ral categories of the participants for each question (columns 1 to 4). This table also pre sents participants’ responses from the background survey. As shown in columns 1 to 4, the same participant might exhibit different degrees of aggressiveness depending on the situatio n. For example, under dense traffic, a ramp driver that hesitates to perform a forced merge (co nservative behavior – column 2), might become aggressive under congested traffic (aggressi ve behavior – column 3). Likewise, in dense traffic, the same driver may be equally or more agg ressive when they are on the freeway than when they are the merging vehicle. This may be expl ained by the fact that ramp vehicles do not have the right-of-way or speed advantage compared t o the freeway vehicles, thus, they seem to feel less entitled to receive priority. Freeway veh icles are more likely to change lanes than decelerate to accommodate a merging vehicle. Anothe r significant result is that congested conditions yield less variability in driver behavio r. Under these conditions, ramp vehicles will

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98 either force their way in, or they will wait for th e freeway vehicle to yield, and freeway vehicles become more accommodating and are willing to let at least one vehicle to merge in front of them. Cross-tabulation between gender and behavioral cate gories shows that, in dense traffic conditions, men appear to be more aggressive than w omen (Table 4-5). Also, there are inconsistencies regarding drivers’ stated aggressiv eness between the focus group results and the background surveys. For example, drivers that indic ated they consider themselves as ‘somewhat aggressive’ in the background survey did not show a ny indication of aggressiveness based on their responses during discussion.

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99 Table 4-5. Behavioral categories based on focus gr oup scenarios and background survey form Behavioral categories Background survey responses Pre-screening Dense traffic Congested traffic ID Start coop. (1) Start forced (2) Start forced (3) Yield forced (4) Speed (mi/h) (5) Lane change frequency (6) Driver type (7) Driver type by friends (8) Gender (9) Age group (10) 1_03 Av C Av C 70-75 Sometimes V.C. V.C. Female 2535 1_05 Av Av Ag C 70-75 Sometimes S.C. S.C. Male 25-3 5 1_09 Ag Av Ag C 65-70 Very often S.A. S.C. Male 4555 1_22 Av Ag Av C 75-80 Very often S.A. S.C. Male 2535 1_01 Av Av Av C 75-80 Sometimes S.A. S.A. Female 25 -35 1_15 Av Av Ag C 65-70 Very often S.A. S.A. Female 2 5-35 2_13 Av C Ag Av 75-80 Sometimes S.A. S.A. Female 55 -65 2_12 Av Av Av C 75-80 Very often S.A. S.A. Female 3 5-45 2_16 Ag C Ag C >80 Very often S.A. S.A. Female 18-2 5 2_07 Ag Ag Ag Av 75-80 Sometimes S.A. V.A. Male 1825 2_25 Av Av Ag Av 70-75 Very often S.C. V.C. Female 35-45 3_26 Av C Av C 70-75 Seldom S.C. V.C. Male 35-45 3_04 Av Av Ag C >80 Sometimes S.A. S.C. Male 18-25 3_06 Ag Ag Ag C 75-80 Very often S.A. S.A. Male 1825 3_14 Av Av Av C 65-70 Sometimes S.A. S.A. Male 35-4 5 3_27 Av C Av C 65-70 Very often S.C. S.A. Female 55 -65 3_28 Av C Av C 75-80 Very often S.A. S.A. Female 25 -35 C: Conservative, Av: Average, Agr: Aggressive V.C.: Very conservative, S.C.: Somewhat conservativ e, S.A.: Somewhat aggressive, V.A.: Very Aggressive

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100 Other Observations Five participants indicated that urgency might caus e them to accept smaller gaps. The remaining responded that urgency would affect their speed selection and lane-changing activity on the freeway, but not the way they merge. With re spect to the trip purpose, many participants responded that for casual driving, they drive more relaxed compared to commuting. The last question entailed differences in driving a lone vs. having passengers. Many participants stated that they are more cautious whe n they have passengers, because they feel responsible for them. Conversely, they drive faster when they drive alone. However, if they are involved in a conversation they are less focused an d more distracted. Conclusions Several important conclusions were drawn from the f ocus group study: Participants’ responses were uniform with respect t o the steps involved in merging, both for non-congested and congested conditions. Ramp design appears to affect drivers’ merging proc ess. Most of the participants indicated they would speed up and be more aggressive on taper ramps, compared to parallel design. Regarding gap acceptance, the participants would li kely react differently, depending on which factors each one considers. Some drivers (14 out of 17) indicated that they might choose any gap (adjacent, upstream, or downstream), depending on the traffic conditions, while others (3 out of 17) would be less flexible. This searching and targeting of the surrounding gaps has also been described in Toledo (2003). Variables that affect gap acceptance have also been identified. Discussion on vehicle interactions showed that, if participants are on the freeway, their preference is to change lanes and avoid deceleratin g. If this cannot be accomplished, they will cooperate, depending on the speed/acceleration of the ramp vehicle, and its size/type. If the ramp vehicle attempts to force its way in, t hey will consider their distance to the upstream vehicle and the relative speed with the ad jacent lane to decide whether to decelerate of change lanes. Ramp vehicle’s decision to initiate a forced merge depends mostly on traffic-related factors, such as freeway speed, congestion and gap availability. Although the discussions captured a significant var iability among participants’, it is likely that their reported actions are different than thei r actual actions, depending on the values of each individual. For example, someone who values ag gressiveness might respond as if he/she is aggressive.

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101 The stated driver actions were analyzed to identify differences in driver behavior. The criterion of “selfishness” was used to develop thre e behavioral categories: aggressive, average and conservative. Given this definition, th e degree of aggressiveness of each driver varies as a function of their task and the traffic conditions. In congested conditions, driver behavior displays l ess variability; therefore, it may be more predictable. This is consistent with findings (Pers aud and Hurdle, 1991; Cassidy and Bertini, 1999) indicating that the mean queue disch arge flow displays smaller variability than other capacity-related measures, and remains c onsistent from day to day. The following recommendations are offered: The merging process solicited by focus group partic ipants should be considered in developing or refining existing analytical or simul ation models for freeway operations. Similarly, the factors stated as contributing in ga p selection should be considered when developing or revising gap acceptance models. Differences in attitudes and driver behavior betwee n non-congested and congested conditions should be explicitly incorporated in tra ffic operational models.

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102 CHAPTER 5 FIELD DATA COLLECTION This chapter presents the second part of the data c ollection effort for this research. The focus of the field data collection is to quantify t he effect of individual driver characteristics on their merging decisions and associate those with th e breakdown occurrences at the freeway-ramp junctions. The data collection undertaken for this task entails observations of participants driving an instrumented vehicle and simultaneous video obse rvations of the freeway during these experiments. All survey instruments as well as the methodology used for the field experiments were pre-approved by the Institutional Review Board (IRB) of the University of Florida. This chapter describes the formulation of the instrument ed vehicle experiments and the simultaneous collection of traffic data, and presents findings a nd results related to the field observations of the merging process. In-Vehicle Data Collection The following section provides information on the o rganization and the setup of the instrumented vehicle experiment. The section also p rovides a description of the methods used for the data collection as well as the selection of the participants. Procedures used to process the invehicle data are also discussed. Description of Instrumented Vehicle The instrumented vehicle used in this study is a Ho nda Pilot SUV, owned by the University of Florida – Transportation Research Cen ter (TRC). The vehicle is equipped with a Honeywell Mobile Digital Recorder (HTDR400) system. The vehicle has an inbuilt GPS where all information about vehicle position and speed da ta is displayed and recorded on the HTDR400. In addition to the GPS unit, the vehicle includes four wide coverage digital cameras (DCs) that capture video clips facing the front, th e back and the two sides of the vehicle. The

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103 video data, as well as audio data during the drivin g task, are recorded on the HTDR400, and stored at a local hard drive that is located at the trunk of the vehicle. An additional camera facing the driver was installed on the dashboard, t o capture facial reactions of the driver during the experiments. An internal view of the instrumen ted vehicle is shown in Figure 5-1. The data collected directly through the instrumented vehicle include: Instrumented vehicle geographical position, speed, throttle, and left-right turn signal activation. Video clips of the vehicles in front, behind and ad jacent to the instrumented vehicle. Audio recordings during the driving task. A laptop was connected to the system which allows f or reviewing the display of all four cameras, through the HTRD BusView software. All vi deo clips were downloaded from the hard drive to the laptop shown in Figure 5-1 for further analysis. Figure 5-1. Inside view of the TRC instrumented ve hicle. Driving Routes The exact routes that the participants followed for both AM and PM peak periods are illustrated in Appendix B. Each participant would c onduct two loops during the AM routes and three during the PM routes.

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104 These routes were developed after selecting the app ropriate freeway-ramp junctions that meet the following criteria: The ramp junctions experience mild to heavy traffic during AM and/or PM peak periods. The total travel time for the routes does not excee d the expected duration of the in-vehicle experiment, which is approximately one hour, includ ing the required stop for discussion with the participants. The routes are not too complex so that the particip ants would not be confused during their driving. Cameras from the Jacksonville Traffic Operations Ce nter should be available at these ramp junctions. The cameras’ field of view should meet the respective criteria for the concurrent field data collection, as presented in the followin g section. These locations should be free from construction wo rk, as this may affect the driving task of the participants, as well as the data quality ob tained from the detectors. The final routes consist of four consecutive ramp j unctions along I-95. The locations of those junctions are at: (i) I-95 NB @ Phillips Hwy, (ii) I-95 NB @ Baymeadows, (iii) I-95 NB @ WB J.T. Butler, (iv) I-95 SB @ Bowden, and (v) I-95 SB @ J.T. Butler EB. The participants would also drive through the J.T. Butler junction b oth in the SB and NB direction. Geometry of the Freeway Ramp Junctions The selected ramp junctions have different designs, concerning the acceleration lane type and the overall length. Two ramps are tapered and t he remaining four are parallel type. All distances are measured from the gore area until the end of the solid white line, the end of the dashed line and the end of the acceleration lane. T he dimensions of the two tapered ramps at J.T. Butler SB and NB approaches are illustrated in Figu re 5-2.

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105 A B Figure 5-2. Geometric characteristics of tapered e ntrance ramps on I-95 at A) J.T. Butler NBWB approach, and B) J.T. Butler SB-EB approach. Figure 5-3 shows the dimensions of the three parall el ramps. The total length of the acceleration lane ranged from 900 ft to 1,530 ft. A ll locations have three lanes, except the junction at Phillips Highway NB which has four lane s. A Figure 5-3. Geometric characteristics of parallel entrance ramps on I-95 at A) Phillips NB, B) Baymeadows NB, and C) Bowden SB.

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106 B C Figure 5-3. Continued. Selection of Participants The instrumented vehicle experiment was advertized through the internet and local organizations in Jacksonville, FL, and candidates w ere provided a description of the driving routes and a pre-screening questionnaire. The quest ionnaires assembled information on gender, age-group, ethnicity, years of driving experience, occupation, frequency of driving and time of day, and vehicle type, similar to those used for th e focus group experiment. The information was used to select a diverse set of participants. Alth ough the targeted number of participants was sixty, many candidates would fail to appear at the meeting location without earlier notification, resulting in misspent of time and resources at the expense of the experiment. Therefore, only thirty-one participants eventually completed the ex periment. The demographics of the participants are presented in Table 5-1.

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107 Similar to the focus group experiment, the particip ants completed a background survey form, which contained seven multiple-choice questio ns related to their driving habits. These questions solicited the subjects’ desired freeway s peed (assuming good visibility and weather conditions and a 70-mi/h speed limit), lane-changin g habits, how aggressive they consider themselves, how aggressive their friends/family con sider them, when and where they typically merge onto the freeway, how they react if a vehicle merges onto the freeway while they are driving on the right-most lane, and whether they pl an their trips allowing for additional time to mitigate possible delays.

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108 Table 5-1. Demographic characteristics of instrume nted vehicle experiment participants ID Gender Age group Race Experience Occupation Driving frequency Hours per week Peak/ non-peak Vehicle ownership 10 Male 55-65 Caucasian >=10 years Retired Military Everyday 4-8 hrs Peak Pickup/SUV 47 Male 25-35 Caucasian >=10 years Clerk Everyday 8 -14 hrs Peak Sedan/Coupe 49 Male 18-25 Caucasian 3-9 years Full Time Student Everyday <4 hrs Peak Sedan/Coupe 52 Male 25-35 Caucasian >=10 years Professional dri ver Everyday 4-8 hrs Peak Pickup/SUV 63 Male 25-35 Caucasian >=10 years Full Time Studen t Everyday 8-14 hrs Peak Pickup/SUV 65 Male 25-35 Caucasian >=10 years Safety Ranger Ev eryday <4 hrs Peak Sedan/Coupe 69 Female 25-35 Afr/ American >=10 years Full Time Student Everyday 4-8 hrs Peak Pickup/SUV 71 Female 18-25 AsianCaucasian 3-9 years Customer Service Usually 4-8 hrs Peak Sed an/Coupe 72 Male 25-35 Caucasian >=10 years Property Manager Everyday 8-14 hrs Peak Sedan/Coupe 73 Female 45-55 Caucasian >=10 years Office Manager Everyday <4 hrs Peak Sedan/Coupe 76 Male 25-35 Caucasian >=10 years University Staff Never <4 hrs Non-peak Sedan/Coupe 23 Male 45-55 Caucasian >=10 years Military Usually 4-8 hrs Peak Pickup/SUV 27 Male 45-55 Caucasian >=10 years Qual. Assurance Everyday 8-14 hrs Peak Sedan/Coupe 32 Male 55-65 Caucasian >=10 years Pilot Sometimes 4-8 hrs Non-peak Sedan/Coupe 37 Female 45-55 Caucasian >=10 years Housewife Ever yday 4-8 hrs Non-peak Pickup/SUV 51 Female 25-35 Caucasian >=10 years Admin. Assista nt Everyday 4-8 hrs Peak Pickup/SUV 59 Male 18-25 Asian 1-3 years Full Time Student Nev er <4 hrs Non-peak Sedan/Coupe 60 Male 45-55 Caucasian >=10 years Police Officer E veryday 8-14 hrs Peak Sedan/Coupe 61 Male 25-35 Caucasian >=10 years PC Refresh Manag er Everyday 8-14 hrs Peak Sedan/Coupe 67 Male 35-45 Afr/ American >=10 years Cook Everyda y 8-14 hrs Non-peak Sedan/Coupe 68 Female 18-25 Caucasian 1-3 years Full Time Stude nt Everyday 4-8 hrs Peak Sedan/Coupe 74 Female 45-55 Caucasian >=10 years Internet Busin ess Usually 8-14 hrs Peak Sedan/Coupe 17 Female 45-55 Afr/ American >=10 years Secretary Everyday 8-14 hrs Peak Sedan/Coupe 18 Female 35-45 Caucasian >=10 years Officer Everyd ay >14 hrs Peak Sedan/Coupe 19 Female 45-55 Caucasian >=10 years Admin. Assista nt Everyday <4 hrs Peak Pickup/SUV 50 Female 25-35 Caucasian >=10 years Housewife Ever yday 4-8 hrs Peak Pickup/SUV 56 Male 35-45 Afr/ American >=10 years Sales Everyd ay 8-14 hrs Peak Sedan/Coupe 58 Male 18-25 Caucasian 3-9 years Full Time Student Everyday 8-14 hrs Peak Sedan/Coupe 66 Male 35-45 Asian 1-3 years Drafter Everyday <4 h rs Non-peak Pickup/SUV 70 Male 45-55 Caucasian >=10 years Professional Dri ver Everyday >14 hrs Peak Sedan/Coupe 75 Female 55-65 Caucasian >=10 years Sales & Market ing Usually 8-14 hrs Peak Sedan/Coupe

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109 Data Collection Procedures Participants of the instrumented vehicle experiment were requested to drive the vehicle along the pre-selected routes on the Jacksonville a rea, with the presence of the investigator and an assistant. The participants were driving on I-9 5 in the northbound and southbound directions, during near-congested and congested conditions in A M and PM peak periods. Two experiments would run during the morning peak period (7:00-8:00 AM and 8:15-9:15 AM) and three during the evening peak period (3:00-4:00 PM, 4:15-5:15 PM and 5:30-6:30 PM). To examine driver behavior at merging segments, participants were ask ed to enter the freeway from specific onramps and also stay on the mainline, passing throug h other ramp merging sections multiple times. In this way, both behaviors of the “ramp-me rging vehicle” and the “through vehicle” for the same driver were captured. In such behavioral studies it is essential to have feedback from the participants, to record and understand what their stimuli and possible inte ntions or reactions are, during the driving task. However, it is not advantageous to ask the p articipant questions during their driving, because this will not only distract them from the d riving task, but it may also create a feeling of “being observed”, which will contribute to a change in their behavior and thus, result in biased conclusions. To reduce that bias, the investigator and the assistant were sitting at the back seat of the instrumented vehicle, so that the participan t would not feel that he/she is being observed. In addition, participants were asked to drive as th ey normally would, and they were given no guidance with respect to their lane selection. Als o, all questions and discussion regarding the driving of the participants were done after each ro ute is completed, where the vehicle were stopped for five to ten minutes. The completion ti me of all routes was approximately one hour. During the driving task the participants were asked to inform the investigator whenever they have an intention to merge or change lanes, an d to identify the desired gap with respect to

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110 the freeway vehicles, if such issue would emerge. Participants were also asked to report perceived actions of cooperation from the other veh icles primarily during the merging maneuver. After the completion of each route, participants we re asked to explain their thinking process that pertains to specific actions that occurred during t he experiment, if this was not reported while driving. In-Vehicle Data Processing This section describes the methods used for the est imation of the model parameters. The video data collected from the instrumented vehicle mounted cameras were used to estimate parameters related to relative distances and speeds Still images were extracted from both front and rear videos at a 0.5 sec time resolution. When participants were merging into the freeway, the image extraction would start as soon as the veh icle entered the acceleration lane until it had completed the merge. When participants were driving on the freeway, the extraction would start at least 2-3 seconds before they indicated their in tention to react to the merge vehicle. Along with the extracted frames, the instrumented vehicle speed and longitude/latitude data were recovered from the GPS. The following subsections p resent the processing techniques of the collected data. Gaps with adjacent vehicles and gap change rates The gaps between the subject vehicle and its adjac ent vehicles were estimated for each consecutive frame. Appendix C describes the method applied for measuring distances from still images. In addition, the gap change rates were esti mated every 0.5 seconds, throughout the trajectory of the vehicles. The gap change rates re present a measure of the relative speeds and accelerations of the two vehicles. These were evalu ated every o.5 seconds, throughout the entire observed trajectory of the vehicles.

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111 Speeds and accelerations The speeds of either the lag, lead or ramp vehicle s are estimated through consecutive frames using the equations of motion. Average speed s and accelerations are estimated every second. The speeds of the subject vehicle are obtai ned directly from the GPS, whereas the accelerations are calculated as the speeds change r ate, and evaluated at a one-second resolution. Vehicle positions Through the GPS information the exact position of t he subject vehicle is obtained. This position is referenced relative to fixed points in the vicinity of the ramp junction. Usually, the end of the solid white line of each acceleration la ne was used as the reference point. Average density and freeway speed Density was calculated from snapshots of the merge area, taken from the TMC cameras, at the time the instrumented vehicle would enter or dr ive through. Density was measured as the total number of freeway vehicles within a segment t hat ranged from 500 to 1400 ft long depending on the site. The density measures were tr ansformed to equivalent vehicles per mile and then averaged across the travel lanes. The aver age freeway speed of the right-most lane was obtained from the 1-minute RTMS data, at the time t hat the instrumented vehicle was at the subject ramp junction. Data Collection at the Jacksonville TMC Concurrently with the instrumented vehicle experime nt, traffic-related data were collected. More specifically, with the collaboration of the Ja cksonville Traffic Operations Center, the selected traffic monitoring cameras become availabl e during the experiment. The Traffic Operations Center also provided two video feeds to record the video data. An assistant located at the Traffic Operations Center would switch intercha ngeably the connection between the cameras and the communication channels, to capture the inst rumented vehicle at each freeway-ramp

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112 merge location it was going through. In addition, t raffic-related data collected from the remote traffic microwave sensors (RTMSs) were also availab le through the Steward Data Warehouse. The data that are available through the Steward Dat a Warehouse are per lane freeway volume, speed, and occupancy. As shown in Figure 5-4 there are several cameras p laced along I-95 used by the Jacksonville Traffic Operations Center for traffic monitoring. Since the cameras were used for both the selection of the routes for the in-vehicle experiment, and the concurrent field data collection, the following selection criteria were d eveloped: Clear view of the incoming traffic from the freeway and the ramps should be available. Locations should be free of construction work, beca use at those locations the RTMSs are not calibrated, and that would impact the validity of the data. Figure 5-4. Location of available cameras along I95. Figure 5-5 provides video snap-shots of four of the five merging segments used in this study. The TMC cameras face both northbound and so uthbound travel directions.

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113 A B C D Figure 5-5. Camera field of view along I-95 A) Phi llips Hwy (facing NB), B) Baymeadows (facing NB), C) Bowden (facing SB) and D) J.T. Butl er (facing SB). It should be noted that, in the event of an inciden t, the assistant could not have access to the cameras, as these are also operated by the High way Patrol officers. Such instances did occur during the data collection periods, and therefore, the respective videos were not recorded. Also, due to extended congestion resulting from these inc idents, the routes were adjusted to complete the experiment on time. In both cases participants would use the I-95 SB entrance from J.T. Butler WB approach, which is a loop ramp. Of course video recordings from this ramp were not available, since the TMC cameras were not adjusted for that location. TMC Data Processing The merge junctions that experience breakdown event s due to merging operations were evaluated using the RTMSs data. Speed time-series p lots at all detector stations along the freeway segment were constructed, for all days of t he data collection. Visual observations of the

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114 time-series revealed the breakdown locations and ti mes during the AM and the PM peak periods. The breakdown events that were observed during the data collection days occurred at NB junction of I-95 with J.T. Butler Boulevard. Other breakdowns were also observed at the SB offramp at J.T. Butler; however this was due to the of f-ramp queue spilling back on the freeway. Non-recurrent congestion due to an incident was obs erved at the SB junction of I-95 with J.T. Butler. Also, congestion starting from the I-95 NB junction with J.T. Butler would propagate further upstream at the junction with Baymeadows, a nd even reaching the junction with Phillips Highway NB. At the southbound direction, congestion would start sometimes at the on-ramp from J.T. Butler EB approach, and sometimes at the SB exit at J.T. Butler. Breakdowns from those locations would typically propagate congestio n further upstream up to the junction with Bowden Road. n rn n n rn n r n n n n n n A B Figure 5-6. Observed breakdown locations and conge stion propagation along I-95 A) SB direction, and B) NB direction.

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115 Next, the time-series were compared with the times of the TMC video recordings at each location. Depending on the prevailing traffic condi tions, observations were grouped into the following five traffic states: Non congested period (173 observations), Before breakdown on-ramp events at NB or SB J.T.But ler (6 observations), Before breakdown off-ramp events at SB J.T.Butler ( 1 observation), Before congestion starts at the remaining locations (10 observations), Within congested period for all locations (10 obser vations). The video recordings before the breakdown events pr ovide information about the merging maneuvers and the lane changing activity that contr ibuted to the occurrence of the breakdown. These recordings were used to develop the merging t urbulence model, by counting at each minute the number of interacting merging maneuvers (cooperative or forced) and the number of lane changes that caused vehicles to decelerate. Ad ditional causes of decelerations were observed and recorded as well. Sometimes, decelerat ions on the right lane due to merging would cause drivers on the middle lane to decelerate. Als o, decelerations past the merge area and inside the bottleneck were observed, which indicated vehic les’ effort to discharge. Usually, these decelerations became more frequent, forcing the inc oming traffic on the freeway to decelerate as well, thus, creating a wave of decelerations moving upstream. After that, it was clear that merging was not the reason for decelerating – peopl e would still decelerate even if there was no vehicle on the on-ramp. During those intervals, the merging process of the ramp vehicles would become more difficult, and they would start to form queues on the on-ramp. Examination of the speeds during that minute would reveal that the spe ed decrease (i.e., speed-flow breakdown) has initiated.

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116 Field Experiment Results Overview of the Observed Merging Process As part of the field experiment, the participants w ere asked to put into words their thoughts as they were driving on the on-ramp and approaching the merge. Generally, the field observed merging process is quite similar with that identifi ed during the focus group discussions. The following steps summarize the observed merging proc ess: Step 1: Participants start accelerating on the on-r amp and first think about merging when they have a clear view of the freeway traffic. Step 2: Participants evaluate the speed and the flo w of traffic on the freeway, to assess how much they should adjust their own speed. They also account for the presence of other onramp vehicles ahead. If traffic is free-flowing, pa rticipants leave a large gap to use later for acceleration. If the freeway is congested, they do not leave a large gap. Step 3: Participants accelerate to a speed close to the freeway speed as they reach the acceleration lane. They also start looking at poten tial gaps. Step 4: This step includes the gap acceptance and m erging process. In free-flowing conditions participants adjust their speed if neces sary to fit a gap. Tasks such as actuating the turn signal and checking of the mirrors or blin d spots follow. In congested conditions, drivers anticipate cooperation from the freeway veh icles. Step 5: After merging, most of the participants mov e to the middle lane unless they need to exit at the next junction. Distinction of Merging Maneuvers As it was also discussed in Chapter 4, the merging maneuvers are categorized to free, cooperative and forced merges, depending on the deg ree and the type of observed interaction between the ramp vehicle and the freeway lag vehicl e. Generally, a free merge does not involve any interaction between the two vehicles. In a coop erative merge the freeway vehicle decides to yield to the ramp vehicle by either decelerating or changing lanes. In a forced merge, it is the ramp vehicle that initiates the maneuver and the fr eeway vehicle reacts to that by either decelerating or changing lanes.

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117 The distinction of the merging maneuvers when the p articipants were driving on the freeway was done considering their narratives as th ey were approaching the merge area. When the participants were the merging vehicle, there wa s no “inside” information about the freeway drivers’ intended actions. In these cases, the dist inction of the maneuvers was done using the TMC video data and observing the break lights of th e freeway vehicle or its trajectory. However, when drivers decide to provide cooperation (e.g., decelerate) towards the merging vehicle, they will do so well in advance. A s such, their deceleration is not always captured by the TMC cameras, due to limitations of the cameras’ field of view. In this case, the distinction of the maneuver was done by measuring t he gap and its change rate with the lag using the rear in-vehicle camera. If the lag gap was rela tively constant as soon as the ramp vehicle enters the on-ramp and starts to increase, it sugge sts that the two vehicles had similar speeds but the lag vehicle decelerated to increase the gap. If the gap was decreasing, but with a decreasing rate, this suggests that the lag vehicle speed was higher than the ramp vehicle speed, and as soon as it decided to yield the gap was decreasing at a lesser rate. As such, at the time the ramp vehicle is merging, the gap will remain relatively constant; indicating that no further speed adjustment is required (equalized speeds). In force d merging the gap remains constant or it is narrowing as the ramp vehicle is traveling on the o n-ramp, but it starts to increase or to decrease with a diminishing rate as soon as the ramp vehicle initiates the merge. After the maneuver is complete, the gap may continue to increase indicati ng that the lag needs to prolong the deceleration to further adjust its speed. In summary, the definitions of the three types of m erging maneuvers considering vehicle interactions are: Free merge: there is no apparent interaction betwee n the ramp vehicle and the freeway lead or lag.

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118 Cooperative merge: the lag decelerates or changes l anes to allow the ramp vehicle to enter. If the lag decides to cooperate by decelerating, th e gap between the lag and the ramp vehicle will be increasing or decreasing with a dim inishing rate as soon as the ramp vehicle enters the on-ramp and it remains relatively consta nt as the ramp vehicle is merging. Forced merge: the ramp vehicle initiates the mergin g maneuver and the lag responds by either decelerating or changing lanes. In this case the gap between the lead and lag is either constant or narrowing (lag maintains speed or accel erates) before the initiation of the merge, and starts to increase or decrease with a di minishing rate as the ramp vehicle enters. After the merge the gap continues to increase. The total number of merging maneuvers that the part icipants performed as the ramp vehicle was 273 and 109 as the through vehicle. The se maneuvers refer to non-congested conditions. Table 5-2 summarizes the types of mergi ng maneuvers that the participants encountered as both the ramp merging and the freewa y through vehicle at each merge junction. It also provides the percent of decelerations or lane changes performed due to vehicle interactions. Table 5-2. Merging maneuver categories Ramp Junction Free Cooperative Forced Ramp merging vehicle Baymeadows NB 59 22 5 Bowden SB 43 34 6 JTButler NB 9 6 2 JTButler SB 56 7 3 Phillips NB 13 4 4 Total 180 73 20 % decelerations 70% 100% % lane changes 30% 0% Freeway through vehicle Baymeadows SB 19 0 0 JTButler NB 50 28 0 JTButler SB 18 2 0 Total 87 30 0 % decelerations 30.4% % lane changes 69.6% Table 5-2 shows that the participants performed all types of merging maneuvers, the majority of which were free maneuvers. When partici pants received cooperation, usually it was through deceleration rather than lane changing. How ever, it is possible that cooperative lane

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119 changing maneuvers were not captured, neither from the TMC cameras nor from the in-vehicle cameras, given that these maneuvers typically occur further upstream of the merge area. In this case, these would be categorized as free merging ma neuvers. When the participants performed forced merging maneuvers, the reaction of the freew ay vehicles was to decelerate in all cases. Table 5-2 also shows that there were observations w here participants provided cooperation towards ramp vehicles. Usually, participants would move to the inside lane to accommodate the ramp vehicles, and less frequently they would decel erate. This finding is also consistent with the results from the focus group discussions, presented in Chapter 4. Lastly, the participants did not incur any forced merging maneuver. Driver Behavior Types The data obtained through the in-vehicle experiment allow for investigating differences and similarities between the drivers and examining how the variability in driver behavior affects traffic operations during merging. This section des cribes the identification of driver behavior for each participant involved in the experiment. Three types of driver behavior were considered: aggressive, average and conservative behavior. For this task, the actual observed driver behavior was evaluated considering both qualitative assessme nt based on the focus group analysis, and quantitative factors based on the field observation s. The qualitative assessment applies the criterion of “selfishness” for each participant throughout the entire duration of their driving tas k. Drivers that exhibit high degree of selfishness and consider primarily their own status on the road are regarded as aggressive. For example, aggressive drivers are unwilling to yield to ramp vehicles, and they dislike being cut off; however they are very likely to impose to othe r vehicles by forcing them to decelerate. Drivers that act primarily as a response to the oth er vehicles’ actions are considered to be conservative. Conservative drivers show increased h esitation when merging and they are very

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120 likely to yield to a ramp merging vehicle. Drivers that consider both their own status but also the effect of their actions to the other vehicles are c ategorized as average. Average drivers are equally likely to show cooperation towards a ramp v ehicle depending on the traffic conditions. These drivers also do not exhibit any characteristi cs that could describe them as either aggressive or conservative. The quantitative assessment was based on two criter ia (AAA, 2009): (i) number of discretionary lane changes and (ii) observed speeds when driving under free-flowing and not carfollowing conditions. Given the design of the exper iment (i.e., frequent exits from the freeway), participants had generally limited opportunities fo r performing discretionary lane changes and for driving at the inside (faster) lanes. As such, participants that performed up to two lane changes and/or followed a speed up to 5 mi/h the sp eed limit were considered to be conservative. Participants that performed up to five lane changes and/or drove at a speed up to 10 mi/h over the speed limit were considered to be average. Particip ants that performed at least six lane changes and/or drove at high speeds up to 15 mi/h over the speed limit (or 10 mi/h over the limit under raining conditions) were grouped as aggressive. The driver behavior types are intended to investiga te primarily vehicle interrelations and traffic operations, and this is addressed in both q uantitative and qualitative criteria. Therefore, the definition of aggressive behavior presented her e does not include characteristics such as increased risk to collision or drivers’ noncomplian ce, which are typically used to examine the effects of driver behavior on traffic safety. In summary, the characteristics of the three behavi oral types based on both the quantitative and the qualitative assessment are: Aggressive behavior: participants do not hesitate t o cut somebody off when merging. They have a sense of pressure and eagerness to get in, a nd not run out of space. Participants

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121 perform at least six discretionary lane changes and /or drive at speeds up to 15 mi/h over the speed limit (or up to 10 mi/h in raining condit ions). Average behavior: participants’ driving behavior de pends equally on their own status and the surrounding traffic conditions. They perform up to five discretionary lane changes and/or drive up to 10 mi/h over the speed limit. Conservative behavior: participants will not perfor m a forced merge and they will wait for a large gap to merge without disrupting the traffic They might decelerate significantly to allow a vehicle to merge. They also perform up to t wo discretionary lane changes and/or their speed is up to 5 mi/h over the speed limit. Table 5-3 summarizes the results of the driver beha vior analysis for all participants. This table also includes their background survey respons es on their degree of aggressiveness as this is perceived by themselves and by their friends or fam ily, their stated driving speed and lane changing activity.

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122 Table 5-3. Driver behavior types based on actual o bservations and background survey form Field Observations Background Survey Responses ID DLC Driving speed Driver type Lane changing Driving spe ed Aggressiveness Aggressiveness by others 10 7 77 mi /h Aggressive Very o ften 75 to 80 mi/h Somewhat aggressive Somewhat aggressive 47 5 71 mi/h Aggressive Very often 70 to 75 mi/h So mewhat aggressive Somewhat conservative 49 16 72 mi/h Aggressive Very often 70 to 75 mi/h S omewhat aggressive Somewhat aggressive 52 6 68 mi/h (Rain) Aggressive Very often 70 to 75 mi/h Somewhat aggressive Somewhat aggressive 63 12 78 mi/h Aggressive Sometimes 70 to 75 mi/h So mewhat conservative Very conservative 65 9 79 mi/h Aggressive Very often 75 to 80 mi/h So mewhat aggressive Somewhat aggressive 69 16 67 mi/h (Rain) Aggressive Sometimes 70 to 75 mi/h Somewhat conservative Very conservative 71 7 75 mi/h Aggressive Sometimes 70 to 75 mi/h Som ewhat conservative Somewhat aggressive 72 7 78 mi/h Aggressive Very often 70 to 75 mi/h So mewhat aggressive Somewhat aggressive 73 6 77 mi/h Aggressive Very often >80 mi/h Somewha t aggressive Very aggressive 76 6 79 mi/h Aggressive Very often 75 to 80 mi/h So mewhat aggressive Somewhat conservative 23 4 68 mi/h Average Very often 70 to 75 mi/h Somew hat conservative Very conservative 27 5 68 mi/h Average Sometimes 75 to 80 mi/h Somewh at aggressive Somewhat aggressive 32 4 71 mi/h Average Sometimes 75 to 80 mi/h Somewh at aggressive Somewhat conservative 37 4 71 mi/h Average Sometimes 70 to 75 mi/h Somewh at aggressive Somewhat aggressive 51 4 75 mi/h Average Very often 75 to 80 mi/h Somew hat conservative Somewhat aggressive 59 5 68 mi/h Average Sometimes 70 to 75 mi/h Somewh at aggressive Very aggressive 60 4 71 mi/h Average Very often 70 to 75 mi/h Somew hat aggressive Somewhat aggressive 61 5 74 mi/h Average Very often 75 to 80 mi/h Somew hat aggressive Somewhat aggressive 67 4 73 mi/h Average Sometimes 75 to 80 mi/h Somewh at conservative Somewhat aggressive 68 4 70 mi/h Average Very often 70 to 75 mi/h Somew hat conservative Somewhat aggressive 74 4 72 mi/h Average Sometimes 70 to 75 mi/h Somewh at conservative Somewhat conservative 17 0 60 mi/h Conservative Sometimes < 65 mi/h Very conservative Very conservative 18 2 70 mi/h Conservative Sometimes 70 to 75 mi/h S omewhat conservative Somewhat conservative 19 2 65 mi/h Conservative Sometimes 70 to 75 mi/h S omewhat conservative Somewhat conservative 50 2 71 mi/h Conservative Very often 70 to 75 mi/h Very conservative Somewhat conservative 56 2 67 mi/h Conservative Sometimes 70 to 75 mi/h Somewhat conservative conservative Somewhat aggressive 58 2 71 mi/h Conservative Sometimes 70 to 75 mi/h Somewhat conservative conservative Somewhat conservative 66 0 68 mi/h Conservative Sometimes 70 to 75 mi/h S omewhat conservative Somewhat conservative 70 2 69 mi/h Conservative Very often 70 to 75 mi/h Somewhat aggressive Very aggressive 75 1 70 mi/h Conservative Sometimes 70 to 75 mi/h S omewhat conservative Somewhat conservative

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123 In summary, the field observations of driver behavi or come in agreement with the quantitative criteria applied for the driver type d istinction. The resulting categorization of drivers also provided a uniform allocation of all three typ es. However, there were differences between the field observed driver types and those stated at the background survey forms by the participants. For instance, some participants that regard themselves as conservative were found to be rather aggressive (e.g., participant #63, Tab le 5-3), whereas others that consider themselves aggressive, showed the exact opposite behavior (e.g ., participant #70, Table 5-3). This inconsistency may be due to the fact that when aske d about their perceived aggressiveness (or their friends/family perceived aggressiveness), peo ple will respond by comparing themselves with their peers, thus their responses will not nec essarily be objective. Although the sample is not large enough to perform quantitative analysis on the driver type profiles, several qualitative conclusions can be dr awn, by comparing this sample’s demographics with the assigned driver type (Table 5-4). Table 5-4. Demographic characteristics by driver b ehavior type Driver Type Male Female Average age group Age group range Aggressive 8 (73%) 3 (27%) 25-35 18-65 Average 7 (64%) 4 (36%) 35-45 18-65 Conservative 4 (44%) 5 (56%) 35-45 18-65 All 19 (61%) 12 (39%) 35-45 18-65 The average age group for the entire sample falls b etween 35 and 45 years old. The aggressive drivers are on the 25-35 years old group whereas average and conservative drivers are on the older group (35-45). Also, the majority of men fall into the aggressive and average driver types, and women are more often found on the conservative driver type category.

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124 Driver Decision-Making Process The extraction of drivers’ thinking process through the in-vehicle experiments is quite challenging, since drivers do not explicitly state their rationale behind their course of actions. However, some conclusions were drawn regarding thei r cooperation towards the merging vehicles. Based on the in-vehicle observations, dri vers’ decision-making is not necessarily a twolevel process, where they decide first whether to p rovide cooperation or not, and then select the preferred action of cooperation. It was found that they would evaluate the situation considering all three alternatives (or two alternatives if lane changing was not an option) at the same level. Summary and Conclusions In this chapter the field data collection effort wa s discussed. The data obtained in this study contain concurrent observations of the behavior of thirty-one participants at ramp merge areas (both as the ramp and the freeway vehicle) and macr oscopic observations of the traffic stream. Procedures for processing the raw data for further analysis are also presented in this chapter. The following conclusions are offered based on the field observations: The steps involved in the observed merging process are found to be quite similar with that identified during the focus group discussions (Chap ter 4), for both congested and noncongested conditions. When participants were on the freeway they were inv olved only in free and cooperative merging maneuvers, and not in forced merges. Partic ipants would show cooperation through lane changing more often than through decel erating. This indicates drivers’ preference to change lanes if a gap is available. T his finding is consistent with the relevant discussion from the focus groups. When the participants were the merging vehicle the majority of observed merging maneuvers were free. Cooperative and forced maneuve rs were observed as well. When drivers’ received cooperation from the freeway vehi cles, usually this was through deceleration rather than lane changing. However, it is possible that cooperative lane changes were not captured by the cameras since thes e would occur considerably upstream of the merge area. In this case they would be obser ved and characterized as free maneuvers.

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125 The participants’ behavior was categorized as aggre ssive, average and conservative. Participants were categorized based on the criterio n of “selfishness” as this was introduced in Chapter 4, and quantitative information about th eir speed and discretionary lane changing activity. Both assessments are consistent and come in agreement. There were few differences between the resulting dr iver type categorization and the participants’ perceived aggressiveness. This incons istency is most likely because participants responses may not be objective as will respond by comparing themselves with their peers. The resulting behavioral categorization showed that aggressive drivers belong to younger average age group category, compared to the other t wo types. Also, men were most likely to be aggressive than women. The field of view of the TMC cameras was very impor tant for this study, as they dictate whether the locations of interest (e.g., bottleneck s) can be considered for data collection. However, there is a trade-off between the cameras f ield of view and the required zoom of the merge area to identify potential vehicle intera ctions and reactions. If more cameras were available, it would be possible to use multipl e and capture the field of view with acceptable resolution upstream, at the merge and do wnstream of the merge area. The participation of actual drivers was probably th e most challenging task of the data collection. This was primarily because several time s drivers would fail to appear for the experiments, without any prior notification. In add ition to that, obtaining drivers’ thinking process was also challenging since drivers do not e xplicitly state their rationale behind their course of actions.

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126 CHAPTER 6 MODEL DEVELOPMENT This chapter presents the data analysis and estimat ion results that pertain to the models that describe ramp vehicles’ gap acceptance decisions, t hrough vehicles’ deceleration decisions, and the probability of turbulence and breakdown using t he field data. The first section explains the data used to model the ramp vehicle’s gap acceptanc e decisions and presents the estimation specifications of the total accepted gap. The follo wing section presents the model developed to describe the freeway vehicle’s behavior at the ramp merge areas, along with a discussion on the data used to develop this model. The macroscopic mo del that quantifies the observed turbulence due to the merging maneuvers and associates this tu rbulence with the breakdown probability is discussed in the next section. This chapter conclud es with a discussion of the developed models. Development of the Gap Acceptance Model Estimation Dataset for Gap Acceptance Model The estimated parameters used for the merging gap a cceptance model are presented in this section. Descriptive statistics of the estimated pa rameters are given for the entire dataset and also as a function of the merging maneuver type (free, c ooperative, or forced) and the driver behavior type (aggressive, average and conservative). Out of the 273 total observations of merging maneuv ers, several free merges did not involve any freeway lag or lead vehicle therefore t hese were removed from the dataset. Also, the cooperative maneuvers that resulted in the lag vehi cle changing lanes were excluded since these do not provide information about the gap acceptance behavior of the ramp vehicle (i.e., the final selected gaps were free gaps). Lastly, merging mane uvers that occurred under complete congested conditions were not considered as well si nce gap acceptance under those conditions is

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127 different. The final estimation dataset includes 1 42 merging observations across the five freeway-ramp junctions. An illustration of the gaps related to the ramp veh icle and the lead and lag vehicles is provided in Figure 6-1. This figure also shows the positions of the three vehicles with respect to the white solid line and the entire length of the a cceleration lane (parallel type), measured from the gore. Figure 6-1. The ramp, lag and lead vehicle, their related gaps and positions. The ramp vehicle merging speed ranged from 34.0 to 65.7 mi/h with an average of 55.1 mi/h, and its acceleration ranged from 0.0 to 5.9 f t/s2 with an average acceleration of 1.1 ft/ s2. The relative speeds with respect to the lag and lea d vehicles were calculated as the speeds of these vehicles less the speed of the ramp merging v ehicle. The average relative speed with the lag vehicle was found to be -0.2 mi/h, varying from -11.2 mi/h to 18.3 mi/h. The average relative speed with the lead vehicle was 2.6 mi/h, varying f rom -4.5 mi/h to 16.8 mi/h. Histogram of the ramp vehicle speed is presented in Figure 6-2.

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128 nrn Figure 6-2. Distribution of ramp vehicle speed. Traffic conditions such as the average density and the speed in the right-most lane affect the gap acceptance behavior of the ramp vehicle. Th e per-lane average density during the merging maneuvers was 30.8 veh/h/ln and it ranged f rom 10.9 to 52.8 veh/h/ln. The mean freeway speed of the right-most lane was 59.1 mi/h, ranging from 43.0 mi/h to 71.0 mi/h. The gaps with the lag vehicle range from 34.9 ft to 134.8 ft with an average of 75.5 ft. The gaps with the lead vehicle range from 25.2 ft to 140.1 f t, with an average gap of 74.8 ft. Lastly, the total gaps (measured when both lead and lag gaps we re available) range from 84.3 ft to 222.9 ft, with an average total gap of 150.3 ft. The distribu tion of the gaps is shown in Figure 6-3. n A Figure 6-3. Distributions of A) lag gap, B) lead g ap, and C) total gap.

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129 rn B n C Figure 6-3. Continued. The analysis results of the merging position and ac celeration lane usage by ramp design is shown Table 6-1. It was found that, compared to par allel type on-ramps drivers used more length on the tapered on-ramps before merging. On parallel on-ramps the acceleration lane usage averaged to 40.1 percent, however, there were few o bservations where the participants made almost full use of the lane (maximum usage was 83.3 percent). Also, there were few merging maneuvers on parallel on-ramps that were completed prior to the end of the solid white line (minimum position denoted as -50 ft on Table 6-1).

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130 Table 6-1. Statistics of merging position by ramp design Parameter Ramp design Mean St.dev. Minimum Median M aximum Parallel 127.6 116.6 -50.0 99.8 480.0 Position rel. to solid white line (ft) Taper 132.5 72.6 28.5 137.1 246.9 Parallel 40.1% 12.5% 23.9% 37.6% 83.3% Acceleration lane used (%) Taper 65.8% 6.0% 57.3% 66.2% 75.2% On average, the merging position considering both t ypes of ramp design was found to be 129.0 ft downstream of the end of the solid white l ine, and the acceleration lane usage measured from the gore area to the end of the lane (Figure 6 -1) averaged to 48.2 percent. The parameters related to the ramp vehicle were als o grouped based on driver behavior and merging maneuver type. Table 6-2 presents the ramp vehicle speeds, accelerations, gaps, and merging positions associated with the free merging maneuvers. The average density under free merging was 26.6 veh/h/ln and the average speed on the right-most lane was 60.4 mi/h. Table 6-2. Statistics of ramp vehicle gap acceptan ce parameters by driver type for free merges Parameter Driver type Mean St.dev. Minimum Median M aximum Aggressive 58.2 5.6 52.0 58.0 65.7 Average 61.8 2.6 59.0 62.0 64.0 Ramp vehicle speed (mi/h) Conservative 48.5 9.2 42.0 48.5 55.0 Aggressive 1.4 1.9 0.0 0.0 4.9 Average 0.4 0.7 0.0 0.0 1.5 Ramp vehicle acceleration (ft/s2) Conservative 0.0 0.0 0.0 0.0 0.0 Aggressive 92.9 26.1 49.1 95.5 134.8 Average 66.0 22.0 47.9 59.6 97.0 Lag vehicle gap (ft) Conservative 95.1 34.6 70.7 95.1 119.6 Aggressive 75.0 32.9 25.2 66.6 140.1 Average 102.5 32.0 72.6 98.6 139.9 Lead vehicle gap (ft) Conservative 70.7 17.5 58.4 70.7 83.1 Aggressive 168.0 41.5 91.6 178.6 222.9 Average 168.5 25.1 132.7 176.7 187.8 Total gap (ft) Conservative 165.9 17.2 153.7 165.9 178.0 Aggressive 119.8 64.7 28.5 104.5 246.9 Average 139.9 53.1 66.3 153.5 186.0 Position rel. to solid white line (ft) Conservative 163.0 279.0 -34.0 163.0 360.0 Aggressive 51.0% 16.0% 30.6% 46.3% 75.2% Average 59.2% 18.5% 31.5% 67.5% 70.2% Acceleration lane used (%) Conservative 37.8% 18.2% 24.9% 37.8% 50.7%

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131 Table 6-2 shows that the average speeds and acceler ations of the merging vehicle under free merging do not vary significantly by driver ty pe. Also, with respect to the accepted gaps, the data do not reveal any trend based on driver type. This is expected since in free merges the gap selection should be random and independent of drive rs’ interactions. Regarding the merging position the data show that drivers make use of at most 59.2 percent of the acceleration lane, which possibly indicates that they have reached an acceptable speed and acceleration for merging freely. The summary statistics of the ramp vehicle-related parameters in cooperative merging maneuvers are presented in Table 6-3. The average d ensity under this type of merging maneuvers was 32.4 veh/h/ln and the average speed o n the right-most lane was 56.2 mi/h. Table 6-3. Statistics of ramp vehicle gap acceptan ce parameters by driver type for cooperative merges Parameter Driver type Mean St.dev. Minimum Median M aximum Aggressive 48.8 12.0 34.0 50.2 61.0 Average 53.3 5.9 49.0 51.0 60.0 Ramp vehicle speed (mi/h) Conservative 49.0 8.5 41.0 47.0 53.0 Aggressive 1.8 2.1 0.0 1.5 4.2 Average 0.2 0.3 0.0 0.0 0.5 Ramp vehicle acceleration (ft/s2) Conservative 0.0 0.0 0.0 0.0 0.0 Aggressive 47.6 17.1 34.9 41.6 72.5 Average 68.4 27.4 44.6 62.4 98.3 Lag vehicle gap (ft) Conservative 83.8 30.4 62.3 83.8 105.4 Aggressive 67.1 36.6 39.1 56.4 116.6 Average 92.1 47.8 43.1 94.7 138.6 Lead vehicle gap (ft) Conservative 66.8 17.9 54.1 66.8 79.5 Aggressive 114.7 27.5 84.6 111.5 151.4 Average 160.5 35.1 139.2 141.4 201.0 Total gap (ft) Conservative 150.7 12.5 141.8 150.7 159.5 Aggressive 204.1 188.8 75.0 130.6 480.0 Average 176.7 76.2 95.0 189.3 245.9 Position rel. to solid white line (ft) Conservative 73.4 50.3 37.8 73.4 109.0 Aggressive 48.2% 23.5% 33.0% 38.3% 83.3% Average 43.5% 12.6% 33.3% 39.5% 57.6% Acceleration lane used (%) Conservative 46.7% 24.2% 29.6% 46.7% 63.9%

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132 Table 6-3 shows the variation of average speed and acceleration by driver type. Aggressive drivers appear to have the lowest average merging s peeds, however, the observed variability in their speeds was high (12 mi/h). The data also show a distinct trend of the accepted gaps by driver type. Gaps (primarily the lag and total) dec rease as the degree of aggressiveness increases. Also, with respect to the merging position, vehicle s make use of less than 50 percent of the acceleration lane when accepting a gap after the fr eeway vehicle’s cooperation. The summary statistics of the ramp vehicle-related parameters in forced merging maneuvers is presented in Table 6-4. The average d ensity for the observed forced merges was 36.5 veh/h/ln, and the average speed on the right-m ost lane was 59.1 mi/h. Table 6-4. Statistics of ramp vehicle gap acceptan ce parameters by driver type for forced merges Parameter Driver Type Mean St.Dev. Minimum Median M aximum Aggressive 56.1 4.9 49.0 57.8 60.0 Ramp vehicle speed (mi/h) Average 52.0 2.0 50.0 52.0 54.0 Aggressive 2.8 1.8 1.0 1.7 5.9 Ramp vehicle acceleration (ft/s2) Average 2.0 0.8 1.5 1.5 2.9 Aggressive 55.7 18.9 37.2 52.3 81.3 Lag vehicle gap (ft) Average 64.4 21.0 41.5 68.7 82.9 Aggressive 49.9 29.6 31.9 36.8 94.1 Lead vehicle gap (ft) Average 71.0 34.4 31.4 87.8 93.8 Aggressive 105.6 22.5 84.3 103.4 131.3 Total gap (ft) Average 135.4 21.1 114.4 135.3 156.6 Aggressive 46.2 91.3 -50.0 32.5 170.0 Position rel. to solid white line (ft) Average 133.0 91.2 29.1 170.0 200.0 Aggressive 39.0% 13.8% 23.9% 37.4% 57.3% Acceleration lane used (%) Average 45.7% 8.6% 35.9% 48.9% 52.2% None of the conservative drivers was observed to pe rform a forced merge, and this is expected considering the characteristics of this dr iver type, as it was also discussed in Chapter 5. The findings indicate that aggressive drivers merge with higher speeds than average drivers. Also, the speeds and accelerations of both types of drivers are higher than those recorded under cooperative merging (Table 6-3). Aggressive d rivers also accept smaller gaps than average

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133 drivers (lead, lag and total). Lastly, both aggress ive and average drivers have initiated the merge after covering 39.0 and 45.7 percent of the acceler ation lane, respectively. The Gap Acceptance Model The gap acceptance model is based on field observat ions of the total accepted gaps (Figure 6-1). For the model development, the total accepted gaps were assumed to follow a lognormal distribution to ensure their non-negativity. Regres sion was performed considering all types of merging maneuvers. The general form of the total ga p is: X Gap ) ln( (6.1) Or, equivalently, ) exp( X Gap (6.2) Where, a is a constant, X is vector of explanatory variables affecting the t otal gap under the different types of merging maneuvers, T is the corresponding vector of parameters. As it was shown in Table 6-2 through Table 6-4, the accepted gaps vary as a function of the driver type. Although drivers were categorized to three driver types (aggressive, average and conservative), only two types were eventually used in the regression model, namely, the aggressive and the non-aggressive drivers (i.e., av erage and conservative drivers). This was primarily because the differences between the avera ge and the conservative drivers were minimal. The total gap is a function of the maneuver type (f ree, cooperative or forced), the proportion of the acceleration lane used by the ram p vehicle and its acceleration, the average perlane density, and whether the ramp driver is aggres sive. The results of the regression model for the total accepted gaps when merging is shown in Ta ble 6-5.

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134 Table 6-5. Parameter estimates for total accepted gap Parameter Parameter value t-statistic Constant 5.343 33.46 Free Merge 0.141 1.86 Aggressive driver*forced merge -0.324 -2.80 Aggressive driver*cooperative merge -0.262 -2.46 Proportion acceleration lane used -0.445 -2.43 Average density (veh/mi/ln) -0.005 -1.66 Ramp vehicle acceleration (ft/s2) 0.032 1.84 All selected explanatory variables are significant at the 90% confidence level. The R2 of Equation 6.3 is 65.5 percent which indicates the pe rcent of variance in the average total gaps explained by the selected explanatory variables. As expected, gaps under free merging are larger tha n under cooperative or forced merging. Also, the model does not distinguish differences be tween the driver types in gap acceptance decisions under free merges. However, gap acceptance under cooperative or forced merging does depend on the driver type. The model suggests that aggressive drivers me rge at smaller gaps than non-aggressive drivers, when performing cooperative of forced merg ing maneuvers. Also, the gaps under forced merging are smaller than under cooperative merging for aggressive drivers. For non-aggressive drivers, the differences in gap acceptance between forced and cooperative merging maneuvers were not significant. Therefore, the model captures differences in gap acceptance between free and constrained (cooperative or forced) merging man euvers. The model suggests that the total accepted gap decr eases as the vehicle is approaching the end of the acceleration lane. This trend indicates that the urgency to merge increases for all drivers as they approach the end of the lane, and t hey are willing to accept smaller gaps. The trend between the total gap and the proportion of a cceleration lane used, by driver type and

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135 merging maneuver, is shown in Figure 6-4. Average v alues of density and ramp vehicle acceleration were assumed for this graph. 80 100 120 140 160 180 200 220 00.20.40.60.81 Proportion of Acceleration Lane Used Total Gap (ft) All Drivers-Free Aggressive-Coop NonAggressive-Coop/Forced Aggressive-Forced Figure 6-4. Relationship between total gap and pro portion of acceleration lane used by driver type and maneuver type. The total gaps increase with increase in the ramp v ehicles’ acceleration, indicating that the ramp vehicle has accelerated closer to the freeway speed. The relationship between the vehicle’s acceleration depending on their behavior as well as the maneuver type is shown in Figure 6-5. 90 110 130 150 170 190 210 230 250 012345678 Ramp Vehicle Acceleration (ft/s2)Total Gap (ft) All Drivers-Free Aggressive-Coop NonAggressive-Coop/Forced Aggressive-Forced Figure 6-5. Relationship between total gap and ram p vehicle’s acceleration by driver type and maneuver type.

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136 The model suggests that the total gap decreases whe n the average density increases. This is because in dense traffic conditions smaller gaps ar e available for all drivers to accept. Figure 6-6 shows the relationship between the average density and the total gap depending on the maneuver type and driver’s aggressiveness. Average values fo r the proportion of acceleration lane used and the ramp vehicle’s acceleration were applied to dev elop this relationship. 90 110 130 150 170 190 210 230 250 102030405060 Average Density (veh/h/ln)Total Gap (ft) All Drivers-Free Aggressive-Coop NonAggressive-Coop/Forced Aggressive-Forced Figure 6-6. Relationship between total gap and ave rage density by driver type and maneuver type. Development of the Deceleration Model The probability that any freeway vehicle decelerate s when facing a cooperative or forced merging situation is captured by the deceleration p robability model. This model has two components. The first component describes the event that a freeway vehicle will decelerate by providing cooperation, indicating the transition fr om the normal state (no interaction) to the cooperative state. The second component captures th e event that a freeway vehicle will decelerate as a response to a forced merge by the r amp vehicle, given that no cooperation was provided earlier. This assumes the transition of th e freeway vehicle from the normal state (no interaction) to the forced state. These two events are mutually exclusive, i.e., they cannot occur

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137 simultaneously. Therefore, the deceleration probabi lity model can be described by the following expression: Pn(DECt) = Pn(DEC, sn,t = coop/st-1,n = normal) + Pn(DEC, sn,t = forced/st-1,n = normal) (6.3) Where st,n is the state of the freeway vehicle n at time t which can be normal (no interaction), cooperative, or forced. This section describes the dataset and presents the model formulation for both components. Estimation Dataset for Deceleration Model This section describes the datasets used to develop the initiation of cooperation model and the forced merging model. Dataset for initiation of cooperation Observations of the participants while they were dr iving on the freeway passing through a merge junction were used to model their reactions ( deceleration, lane changing or do nothing) towards the merging ramp vehicles. The estimation d ataset for this model includes observations both before, and at the time the participant starts to yield to the ramp vehicle. Typically, participants’ actions would be observed as soon as they could see the (potentially interacting) ramp vehicle entering the acceleration lane, and un til they had expressed their decision to decelerate, change lanes, or driver uninterrupted, by clearly stating so. The sample includes twenty-three observations where the freeway vehicle cooperated by either decelerating or changing lanes (Table 5.2), and thirty-one observations where no cooperation was provided. 13 percent of these obser vations were decelerations, 29.6 percent were lane changes and for the remaining 57.4 percen t the drivers did not cooperate. The ramp vehicle speed ranged from 38 to 67.4 mi/h with an average of 54.4 mi/h, and the freeway vehicle speed ranged from 52 mi/h to 75 mi/ h, with an average speed of 64 mi/h. The relative speed between the freeway vehicle and the ramp vehicle is calculated as the speed of the

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138 freeway vehicle less the speed of the ramp vehicle. Histograms of the relative speed and the freeway vehicle are presented in Figure 6-7. rnr nnA n n nrnB Figure 6-7. Distribution of A) relative speed betw een the freeway vehicle and the ramp vehicle, and B) freeway vehicle speed for initiation of coop eration. The average freeway density was 22.1 veh/mi/ln, and it covers a wide range of values, from 6.6 veh/mi/ln to 40 veh/mi/ln. The average fre eway speed on the right lane was 63.2 mi/h ranging from 46 to 70 mi/h. Histograms of the densi ty and the speed difference between the freeway vehicle and the average speed on the right lane (right lane average speed less the speed of the subject-freeway vehicle) are shown in Figure 6-8.

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139 !"nA r!nnr rnB Figure 6-8. Distribution of A) average density, an d B) speed difference between the freeway vehicle and the average speed on the right lane for initiation of cooperation. The speed difference histogram in Figure 6-8 shows the speed difference covers a wide range suggesting that in many cases the participant s were driving on greater or less speed than their lane average. The average distance between the ramp vehicle and t he freeway vehicle before initiating a cooperative maneuver was found to be 118 ft, rangin g from 39.5 ft to 257 ft. Also, the average position of the ramp vehicle, in terms of proportio n of acceleration lane used was 0.21 (ranging from -0.03 to 0.65). The negative sign of the minim um proportion suggests that the freeway

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140 vehicle reacted before even the ramp vehicle entere d the acceleration lane. The mean ramp vehicles’ position as a function of the remaining d istance to the end of the acceleration lane is 821 ft, and its range is from 211.4 ft to 1675 ft. The average distance between the freeway (subject) vehicle and the ramp vehicle is 118.7 ft ranging from 39.5 ft to 257 ft. Dataset for initiation of forced merging The dataset for the forced merging model contains t wenty-four observations of forced merging maneuvers performed by the participants. A forced merge was assumed to be initiated as soon as the ramp vehicle starts to cross the lin e. The dataset for this model includes the data used f or the gap acceptance under forced merging conditions (Table 6-4). Additional data obt ained before the initiation of the forced maneuver, as well as data where the ramp vehicle di d not initiate a forced merge and the freeway vehicle did not show any cooperation were also used Summary statistics of the data used for the development of the forced merging model are shown i n Table 6-6. Table 6-6. Statistics of dataset for forced mergin g model Parameter Average St.dev. Minimum Median Maximum Ramp vehicle speed (mi/h) 56.00 (50.79) 4.38 (8.41) 49.00 (24.00) 57.50 (51.00) 61.00 (62.50) Ramp vehicle acceleration (ft/s2) 2.57 (0.63) 2.18 (1.05) 0.00 (0.00) 2.20 (0.00) 7.33 (4.40) Lag vehicle relative speed (mi/h) 1.46 (6.72) 4.84 (6.82) -3.27 (-4.61) 0.50 (5.74) 14.41 (27.36) Average right-lane speed (mi/h) 58.67 (58.42) 6.33 (6.75) 50.00 (37.00) 57.50 (58.00) 68.00 (76.00) Cluster size 1.67 (1.82) 0.78 (0.89) 1.00 (1.00) 1.50 (2.00) 3.00 (4.00) Average density (veh/mi/ln) 36.45 (30.12) 12.16 (10.72) 18.21 (12.35) 37.09 (30.80) 52.80 (52.80) Proportion acceleration lane used 46.8% (23.0%) 13.3% (14.0%) 23.9% (5.0%) 46.6% (25.1%) 75.5% (49.4%) Data in parenthesis are for the entire dataset.

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141 Deceleration Model Due to Cooperative Merging The freeway through vehicle is facing three choices when identifying a ramp vehicle which is subject to merge. The freeway vehicle may decide to either provide cooperation to the ramp vehicle by decelerating or by changing lanes, or to continue driving uninterrupted. Based on the focus group discussions and the field observations the decision-making process was modeled as a Multinomial Logit (MNL) Mo del, where the freeway vehicle has three choices: to decelerate, to change lanes, to do noth ing. If gaps are not available, then lane changing is not an option, thus the freeway vehicle s’ choices are to decelerate or not yield to the ramp vehicle. The utilities of the choices for the freeway vehicl e n are: n i n i n iV U, (6.4) i = decelerate, change lanes, no-coop initiation Where, Vi,n are the deterministic components of the utilities of driver n to decelerate, change lanes and to not initiate cooperation. For t he estimation of the deterministic components of the utilities the reference choice was the choic e to decelerate. The utilities for the remaining choices are: n i n i n iX V, ,r (6.5) i = decelerate, change lanes, no-coop initiation Where Xi,n, are the vectors of explanatory variables that aff ect the utilities to change lane, decelerate and do nothing. i,n are the corresponding vectors of the parameters. T he vectors of explanatory variables include only generic variable s. The final model parameters of the MNL model are presented in Table 6-7. The log-likelihoo d function for this model is -39.499 and the adjusted rho-square is 0.216.

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142 Table 6-7. Parameter estimates for MNL model. No cooperation Change lanes Explanatory variables Parameter t-statistic Parameter t-statistic Constant 2.055 1.574 4.179 3.509 Distance to end of acceleration lane 0.002 2.107 0. 002 2.107 Cluster size -0.724 -1.710 Min (0,Vavg-Vn) (non conservative drivers) -0.144 -1.600 Distance to ramp vehicle (conservative drivers) 0.008 1.188 Distance to ramp vehicle (all drivers) -0.018 -2.337 Average density (veh/mi/ln) -0.071 -1.623 Both utilities of do nothing and change lanes depen d on the position of the ramp vehicle with respect to the end of the acceleration lane. A lthough the proportion of acceleration lane used is a parameter more suitable to the data (due to ob servations at ramp junctions with different geometry), the remaining distance was found to be m ore significant, probably because the freeway vehicle is more sensitive to the distance l eft, irrespective of the how far on the acceleration lane the ramp vehicle has traveled. As the ramp vehicle approaches the end of the lane (distance decreases), the utilities of change lanes or do nothing decrease, and therefore, the probability of decelerating increases. Figure 6-9 s hows the probabilities of deceleration, lane changing and no cooperation as a function of the re maining distance and driver type (conservative and non-conservative). Average condit ions were assumed for the development of this graph.

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143 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 02004006008001000120014001600 Distance to end of acceleration lane (ft)Probability P(Dec)-Conservative P(NoCoop)-Conservative P(CL)-Conservative P(Dec) P(NoCoop) P(CL) Figure 6-9. Probability of decelerating, changing lanes or no cooperating as a function of the distance to end of the acceleration lane for conser vative and non-conservative drivers. According to Figure 6-9, the probability of deceler ation is not sensitive to driver types, however non-conservative drivers are more likely to change lanes than conservative drivers. The decision of the freeway vehicle also depends on the number of ramp vehicles present (cluster size). Increased number increases the prob ability that the ramp vehicle will cooperate (Figure 6-10). 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0123456 Cluster sizeProbability P(Dec)-Conservative P(NoCoop)-Conservative P(CL)-Conservative P(Dec) P(NoCoop) P(CL) Figure 6-10. Probability of decelerating, changing lanes or no cooperating as a function of the cluster size for conservative and non-conservative drivers.

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144 When the number of vehicles on the ramp is small, d rivers are less likely to show any cooperation. Figure 6-10 also shows that conservati ve drivers are less likely to change lanes, however, the probability of decelerating is almost the same for all drivers. As the distance between the ramp vehicle decreases, all drivers are more likely to change lanes, and less likely to decelerate. Figure 6-11 s hows the effect of the distance to the ramp vehicle on the freeway vehicle decisions by driver type. 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 050100150200250 Distance to ramp vehicle (ft)Probability P(Dec)-Conservative P(NoCoop)-Conservative P(CL)-Conservative P(Dec) P(NoCoop) P(CL) Figure 6-11. Probability of decelerating, changing lanes or no cooperating as a function of distance to the ramp vehicle for conservative and n on-conservative drivers. Figure 6-11also shows that when the distance betwee n the two vehicles is large, conservative drivers are more likely not to provide cooperation, whereas non-conservative drivers have increased probability of initiating co operation compared to conservative drivers. Also, as the distance decreases, conservative drive rs will become more aware and they are more willing to change lanes. The average density also affects the utility of cha nging lanes. Increase of the average density reduces the probability of changing lanes a nd increases the probability of decelerating as well as showing no cooperation. Also, increase of t he negative relative speed between the

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145 freeway vehicle and lane average speed increases th e probability of decelerating or changing lanes. This parameter concerns the non-aggressive d rivers, and it suggests that when the freeway vehicle speed is close to the average speed, the ve hicle is more likely to cooperate. The probability that any freeway vehicle n will select to decelerate is given in Equation 6.6: ) exp( ) exp( ) exp( ) exp( ) / (, ,1 n Coop NO n CL n DEC n DEC n t n t nV V V V normal s coop s DEC P (6.6) Deceleration Model Due to Forced Merging In the dataset, all observations of forced merging lead to decelerations of the freeway vehicles. Therefore, the deceleration model is equi valent to modeling the probability that any ramp vehicle r will initiate a forced merge. Pn(DEC, st,n = forced/st-1,n = normal) = Pr(st,r = forced/st-1,r = normal) (6.7) The ramp vehicle will initiate a forced merge given that the freeway lag vehicle has not shown any cooperation earlier (previous state is no rmal). This model can be expressed as a binary choice model where the two choices of the ra mp vehicle, are to initiate a forced merge or not. The utilities of the two alternatives are: r j r j r jX V. r (6.8) j = initiate forced, do not initiate forced The parameter estimates for the utility to initiate a forced merge with the respective tstatistics are presented in Table 6-8. The log-like lihood function for this model is -11.060 and the adjusted rho-square is 0.619. All parameters are st atistically significant at a 90% confidence level.

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146 Table 6-8. Parameter estimates for utility of init iation forced merge Initiate forced merge Explanatory variables Parameter value t-statistic Constant -15.28 -2.76 Average density (veh/mi/ln) 0.10 1.93 Proportion of acceleration lane used 21.64 2.71 Number of ramp vehicles on ramp (aggressive ramp driver) 1.14 1.61 Ramp acceleration (ft/s2) 0.88 1.64 Based on this model, the probability of initiating a forced merge and therefore the probability that the freeway vehicle will decelerat e is: ) exp( 1 1 ) / (, ,1 r Forced n t n t nV normal s forced s DEC P (6.9) As it was also concluded from the focus group exper iment, aggressive drivers are more likely to initiate a forced merge than average driv ers. Conservative drivers did not show any indication of initiating a forced merge. This was a lso confirmed from the instrumented vehicle experiment, since none of the conservative drivers performed a forced merging maneuver. Ramp drivers’ aggressiveness is captured through a dummy variable related to the number of ramp vehicles ahead of the subject ramp vehicle. Aggress ive ramp drivers become more eager to enter the freeway if there are other vehicles in front of them waiting to merge. Due to their aggressive nature, they might seek a gap and merge sooner, cau sing the freeway vehicles to decelerate. Increase in average density also reduces the availa bility of gaps, therefore ramp vehicles are more willing to force their way into the freewa y. Assuming average conditions, the relationship between traffic density and the forced merging probability considering drivers’ aggressiveness is shown in Figure 6-12.

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147 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1020304050607080 Average Density (veh/mi/ln)Probability of forced merging Aggressive Average Figure 6-12. Forced merging probability as a funct ion of average density and driver’s aggressiveness. In addition, the probability of initiating a forced merge increases as the ramp vehicle travels on the acceleration lane. Figure 6-13 shows the relationship between the forced merge probability and the proportion of acceleration lane used by the ramp driver as a function of its aggressiveness. 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0.000.100.200.300.400.500.600.700.800.90 Proportion of acceleration lane usedProbability of forced merging Aggressive Average Figure 6-13. Forced merging probability as a funct ion of proportion of acceleration lane used and driver’s aggressiveness. Increased acceleration also suggests increase in th e probability of performing a forced merge. This is probably because of the ramp vehicle s’ effort to increase rapidly their speed on the acceleration lane in order to decrease the spee d difference with the lag vehicle and merge.

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148 Figure 6-14 shows the relationship between ramp veh icle’s acceleration and the probability of initiating a forced merge. As expected, aggressive drivers are more likely to perform a forced merge than average drivers. 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 012345678 Ramp vehicle acceleration (ft/s2)Probability of forced merging Aggressive Average Figure 6-14. Forced merging probability as a funct ion of the ramp vehicle acceleration and driver’s aggressiveness. The Deceleration Probability Model Considering the equations 6.3, 6.6, and 6.9, the mo del that describes the probability that the freeway vehicle will decelerate at the merge ar ea is summarized in the following equation: ) exp( 1 1 ) exp( ) exp( ) exp( ) exp( ) (, , r Forced n Coop NO n CL n DEC n DEC t nV V V V V DEC P (6.10) The Merging Turbulence Model The merging turbulence model transfers the decelera tion probability model to the macroscopic level. The merging turbulence model des cribes the probability (frequency) that N freeway vehicles will decelerate due to the merging ramp flow over time. N n nDec P te RampFlowRa bulence MergingTur P1) ( 1 ) ( (6.11) The data for the merging turbulence model were obta ined through video observations of two breakdown events at the J.T. Butler NB on-ramp. The first occurred during the morning peak

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149 period and the second during the afternoon peak per iod. Vehicle decelerations due to merging, lane changing, and also due to other reasons not ea sily identifiable through the videos were recorded. The prevailing ramp and freeway flow was also obtained. Typically, the decelerations became more frequent w hen the breakdown was imminent. A speed threshold criterion was applied for identifyi ng the breakdown events, since this criterion is typically applied in capacity analysis studies. The breakdown events were identified when the average freeway speed at the merging area would dro p below the 60 mi/h threshold (posted speed limit is 65 mi/h) for at least five minutes. Time-series plots of speed were overlaid with the t ime-series of observed decelerations to compare the identified times to breakdown of the tw o methods. Figure 6-15 shows an example of the two time-series plots for one breakdown event. 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 3:39:00 PM3:44:00 PM3:49:00 PM3:54:00 PM3:59:00 PM TimeAverage Speed (mi/h)0 0.1 0.2 0.3 0.4 0.5 0.6 0.7Turbulence Average Speed Right Lane Speed Total Turbulence Merging Turbulence Figure 6-15. Time-series of speed and number of de celerations on October 9th, 2008. Breakdown 3:48 PM

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150 Figure 6-15 shows an increasing trend of merging de celerations and total decelerations along with decrease in average speeds in all lanes. Based on the applied definition of breakdown, the breakdown is identified at 3:48 PM. Before the breakdown interval, the total decelerations include mostly decelerations due to merging and few decelerations due to lane changing. No decelerations are observed downstream of the merge. Two to three minutes before the breakdown (starting at 3:45) the merging turbulence increases abruptly. The total turbulence also increases slightly, indicating that most of the tur bulence increase is due to merging decelerations. The number of lane changes also increases, however, these were not observed to cause any turbulence. The maximum merging turbulence observed before the breakdown exceeds 0.5, indicating that more than 50 percent of the merging maneuvers caused decelerations. During the breakdown minute, the total turbulence i ncreases even more, and exceeds 0.4. The proportion of vehicles decelerating due to merg ing remains high and over 0.5. Decelerations downstream of the merge start to appear. After that minute, the decelerations are more frequent, and some vehicles even stop at the middle and right lane for few seconds. The average speed has dropped at 50 mi/h and all incoming traffic is redu cing speed to join the queues. Figure 6-16 shows the relationship between the tota l freeway and ramp flow, and the merging turbulence probability for the same breakdo wn event. Generally, as the total flow increases, the merging turbulence probability incre ases as there are more opportunities for vehicle interactions. The highest merging turbulenc e observed one minute before the breakdown (3:47PM) exceeded 0.5. After the breakdown, the mer ging turbulence remains at high levels, however, the volume is decreasing. Several observat ions also resulted in zero merging turbulence probability and these observations. These were obse rved approximately twenty minutes earlier than the breakdown event.

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151 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 020406080100120 Total Freeway and Ramp Volume (veh/min)Merging Turbulence Pre-breakdown Post-breakdown At breakdown Figure 6-16. Relationship between total freeway an d ramp flow and probability of merging turbulence. Based on the field observations during the breakdow n event it was found that there is a correlation between the merging turbulence and the speed reduction associated with the breakdown event. From Figure 6-15 it can be conclud ed that the total turbulence and the merging turbulence can serve as a precursor-indicator of th e breakdown events, and could predict that the breakdown is imminent one to three minutes before t he speed decrease is recorded on the detectors. Additional data are required to verify t his conclusion. The Breakdown Probability Model This section discusses the proposed application of the merging turbulence model for developing the breakdown probability model. For the development of the breakdown probability model, field observations of merging maneuvers and the resulting merging turbulence frequency are required. A large sample size is also necessary (e.g., breakdowns over a six-month period). For the model development the breakdown intervals a re identified considering the merging 3:47 PM

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152 turbulence criterion (e.g., when the turbulence exc eeds 0.5). The Kaplan-Meier method could be used, as this was also applied in Brilon (2005). According to the Kaplan-Meier method, the distribut ion function of the breakdown volume F(q) is: B i k k q Fq q i i ii ; 1 1 ) (: (6.12) Where, q is the total freeway volume (veh/h), qi is the total freeway volume (veh/h) during the breakdown interval i (i.e., breakdown flow), ki is the number of intervals with a total freeway volume of q qi and { B } is the set of breakdown intervals (1-minute obser vations). An illustration of the breakdown probability model is shown in Figure 6-17. The curve was developed by applying the typical breakdown definit ion, where the speed drops below the 60mi/h threshold. The breakdown observations were dur ing the am peak period and cover six months of data. 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 020406080100120140160 Freeway and Ramp volume (veh/min)Breakdown Probability0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00Merging Turbulence Breakdown Probability AM-At breakdown 17.2% 55.0% Figure 6-17. Breakdown probability model and mergi ng turbulence.

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153 Figure 6-17 also displays the merging turbulence fo r one breakdown event, based on the field data collection. The merging turbulence durin g the breakdown interval was 0.55 and it corresponds to breakdown probability of 17.2%. Addi tional breakdown-related data were not available, however, this graph shows the transferab ility of the breakdown probability model considering the two breakdown definitions. Future r esearch direction should be towards the development of the breakdown probability model usin g the merging turbulence probability as the breakdown identification criterion. Summary and Conclusions This chapter presented a gap acceptance model under different merging conditions and a driver behavioral model that predicts freeway vehic les’ interactions with the merging vehicles. Driver characteristics (aggressiveness) and their v ariation based on traffic conditions have been incorporated into both models. This chapter also pr esented the merging turbulence model which evaluates the effect of vehicle interactions at the merge area on the freeway flow. Field observations of one breakdown event showed that the merging turbulence increases before the breakdown and it could serve as an indicator for id entification of the breakdown events. The final conclusions with respect to the data anal ysis and the model development are offered here: The ramp design affects the merging position of the ramp vehicles. It was found that compared to parallel type on-ramps drivers used mor e length on the tapered on-ramps before merging. It was also found that the merging position on parallel on-ramps varies significantly, ranging from almost the end of the a cceleration lane to even before the end of the solid white line. The gap acceptance model considers variations on th e accepted gaps based on drivers’ aggressiveness as well as the type of the merging m aneuver. Drivers were grouped to aggressive and non-aggressive (average and conserva tive). It was found that aggressive drivers accept smaller gaps than non-aggressive, un der cooperative and forced maneuvers. It was also found that the gap acceptance depends o n the position of the ramp vehicle and its acceleration, and the traffic density.

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154 The freeway vehicle’s decision to decelerate, chang e lanes or not provide any cooperation to the ramp vehicle was modeled as an MNL model. It was found that the freeway vehicles’ decisions depend on the ramp vehicle’s po sition on the acceleration lane, the distance with the ramp vehicle, the freeway density and the number of vehicles on the ramp. The driver behavior types were grouped to con servative and non-conservative (aggressive and average). It was found that conservative drivers are more sen sitive to their distance with the ramp vehicle than non-conservative drivers. Although the y are less likely to cooperate compared to non-conservative drivers when the distance is la rge, they become increasingly concerned and try to change lanes when the distance decreases to avoid conflict with the merging vehicle. The forced merging assumes that all freeway vehicle s will decelerate subject to the initiation of a forced maneuver. Aggressive and ave rage driver types are included in this model since conservative drivers were not observed to perform forced merging maneuvers. The initiation of a forced maneuver depends on the ramp vehicle’s aggressiveness and acceleration, its position on the acceleration lane the number of ramp vehicles merging ahead and the freeway density. Although three driver types were initially consider ed, these were grouped into two categories for the model development. Also, for the models that describe the ramp vehicle’s behavior drivers were grouped to aggressi ve and non-aggressive, whereas for the model that describes through drivers’ behavior driv ers were grouped to conservative and non-conservative. This may indicate that driver beh avior changes depending on whether they are on the freeway or the on-ramp. This findin g supports the focus group result, where it was found that drivers’ aggressiveness depends o n their task. Evaluation of the merging turbulence model suggests its correlation with the time to breakdown, as it was found to increase when the bre akdown event was imminent, one to three minutes before the breakdown event (i.e., bef ore a speed drop is recorded on the detectors). The following recommendations are offered: The vehicle interactions and how these differ by dr iver type should be considered in developing or refining existing analytical or simul ation models for freeway operations. The variation of driver types depending on their ta sk should be incorporated to simulation models. This would also assist in developing more r ealistic tools for simulating the freeway flow breakdown. The merging turbulence model needs to be verified w ith additional breakdown observations. It is further recommended to use this measure for identifying and even predicting the time to breakdown.

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155 CHAPTER 7 CONCLUSIONS This chapter summarizes the research conducted in t his thesis and presents the most important findings. Recommendations for future rese arch are also offered. Research Summary A freeway-ramp merging model that considers vehicle interactions and their contribution to the beginning of congestion was presented. Focus group discussions were conducted to attain knowledge about drivers’ thinking process when merg ing. There are three types of merging maneuvers (free, cooperative, and forced), based on the degree of interaction between the freeway and the ramp merging vehicle. Field data co llection using an instrumented vehicle experiment was performed to observe drivers’ mergin g process. Behavioral characteristics of the participants were also evaluated. The collected dat a were used for calibrating driver behavior models that pertain to their decisions to decelerat e, change lanes or not interact subject to the ramp merging traffic, considering their behavioral attributes. A merging turbulence model was developed that captures the triggers for vehicle de celerations at the merging areas. The merging turbulence model due to vehicle interactions was ev aluated through macroscopic observations at near-congested conditions. It was shown that the me rging turbulence increases before the breakdown and it could be used as an indicator of t he breakdown events. Research Conclusions The objective of this research was to develop a mod el that can capture vehicle interactions and determine the probability of breakdown on the f reeway given the behavior of both mainline and ramp merging vehicles. The research conclusions based on the focus group discussions: Participants’ responses were uniform with respect t o the steps involved in merging, both for non-congested and congested conditions.

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156 Ramp design appears to affect drivers’ merging proc ess. Most of the participants indicated they would speed up and be more aggressive on taper ramps, compared to parallel design. Regarding gap acceptance, the participants would li kely react differently, depending on which factors each one considers. Some drivers indi cated that they might choose any gap (adjacent, upstream, or downstream), depending on t he traffic conditions, while others would be less flexible. This searching and targetin g of the surrounding gaps has also been described in Toledo (2003). Variables that affect g ap acceptance have also been identified. Discussion on vehicle interactions showed that, if participants are on the freeway, their preference is to change lanes and avoid deceleratin g. If this cannot be accomplished, they will cooperate, depending on the speed/acceleration of the ramp vehicle, and its size/type. If the ramp vehicle attempts to force its way in, t hey will consider their distance to the upstream vehicle and the relative speed with the ad jacent lane to decide whether to decelerate of change lanes. Ramp vehicle’s decision to initiate a forced merge depends mostly on traffic-related factors, such as freeway speed, congestion and gap availability. Although the discussions captured a significant var iability among participants’, it is likely that their reported actions are different than thei r actual actions, depending on the values of each individual. For example, someone who values ag gressiveness might respond as if he/she is aggressive. The stated driver actions were analyzed to identify differences in driver behavior. The criterion of “selfishness” was used to develop thre e behavioral categories: aggressive, average and conservative. Given this definition, th e degree of aggressiveness of each driver varies as a function of their task and the traffic conditions. In congested conditions, driver behavior displays l ess variability; therefore, it may be more predictable. This is consistent with findings (Pers aud and Hurdle, 1991; Cassidy and Bertini, 1999) indicating that the mean queue disch arge flow displays smaller variability than other capacity-related measures, and remains c onsistent from day to day. The following conclusions are offered based on the field data collection effort: The steps involved in the observed merging process are found to be quite similar with that identified during the focus group discussions (Chap ter 4), for both congested and noncongested conditions. When participants were on the freeway they were inv olved only in free and cooperative merging maneuvers, and not in forced merges. Partic ipants would show cooperation through lane changing more often than through decel erating. This indicates drivers’ preference to change lanes if a gap is available. T his finding is consistent with the relevant discussion from the focus groups. When the participants were the merging vehicle the majority of observed merging maneuvers were free. Cooperative and forced maneuve rs were observed as well. When drivers’ received cooperation from the freeway vehi cles, usually this was through

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157 deceleration rather than lane changing. However, it is possible that cooperative lane changes were not captured by the cameras since thes e would occur considerably upstream of the merge area. In this case they would be obser ved and characterized as free maneuvers. The participants’ behavior was categorized as aggre ssive, average and conservative. Participants were categorized based on the criterio n of “selfishness” as this was introduced in Chapter 4, and quantitative information about th eir speed and discretionary lane changing activity. Both assessments are consistent and come in agreement. There were few differences between the resulting dr iver type categorization and the participants’ perceived aggressiveness. This incons istency is most likely because participants responses may not be objective as will respond by comparing themselves with their peers. The resulting behavioral categorization showed that aggressive drivers belong to younger average age group category, compared to the other t wo types. Also, men were most likely to be aggressive than women. The field of view of the TMC cameras was very impor tant for this study, as they dictate whether the locations of interest (e.g., bottleneck s) can be considered for data collection. However, there is a trade-off between the cameras f ield of view and the required zoom of the merge area to identify potential vehicle intera ctions and reactions. If more cameras were available, it would be possible to use multipl e and capture the field of view with acceptable resolution upstream, at the merge and do wnstream of the merge area. The participation of actual drivers was a very chal lenging task of the data collection. This was primarily because several times drivers would f ail to appear for the experiments, without any prior notification. In addition to that obtaining drivers’ thinking process was also challenging since drivers do not explicitly st ate their rationale behind their course of actions. The conclusions related to the model development ar e summarized here: The ramp design affects the merging position of the ramp vehicles. It was found that compared to parallel type on-ramps drivers used mor e length on the tapered on-ramps before merging. It was also found that the merging position on parallel on-ramps varies significantly, ranging from almost the end of the a cceleration lane to even before the end of the solid white line. The gap acceptance model considers variations on th e accepted gaps based on drivers’ aggressiveness as well as the type of the merging m aneuver. Drivers were grouped to aggressive and non-aggressive (average and conserva tive). It was found that aggressive drivers accept smaller gaps than non-aggressive, un der cooperative and forced maneuvers. It was also found that the gap acceptance depends o n the position of the ramp vehicle and its acceleration, and the traffic density.

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158 The freeway vehicle’s decision to decelerate, chang e lanes or not provide any cooperation to the ramp vehicle was modeled as an MNL model. It was found that the freeway vehicles’ decisions depend on the ramp vehicle’s po sition on the acceleration lane, the distance with the ramp vehicle, the freeway density and the number of vehicles on the ramp. The driver behavior types were grouped to con servative and non-conservative (aggressive and average). It was found that conservative drivers are more sen sitive to their distance with the ramp vehicle than non-conservative drivers. Although the y are less likely to cooperate compared to non-conservative drivers when the distance is la rge, they become increasingly concerned and try to change lanes when the distance decreases to avoid conflict with the merging vehicle. The forced merging assumes that all freeway vehicle s will decelerate subject to the initiation of a forced maneuver. Aggressive and ave rage driver types are included in this model since conservative drivers were not observed to perform forced merging maneuvers. The initiation of a forced maneuver depends on the ramp vehicle’s aggressiveness and acceleration, its position on the acceleration lane the number of ramp vehicles merging ahead and the freeway density. Although three driver types were initially consider ed, these were grouped into two categories for the model development. Also, for the models that describe the ramp vehicle’s behavior drivers were grouped to aggressi ve and non-aggressive, whereas for the model that describes through drivers’ behavior driv ers were grouped to conservative and non-conservative. This may indicate that driver beh avior changes depending on whether they are on the freeway or the on-ramp. This findin g supports the focus group result, where it was found that drivers’ aggressiveness depends o n their task. Evaluation of the merging turbulence model suggests its correlation with the time to breakdown, as it was found to increase when the bre akdown event was imminent, one to three minutes before the breakdown event (i.e., bef ore a speed drop is recorded on the detectors). Future Research The following recommendations and directions for fu ture research are offered: The merging process from the driver’s perspective a s well as the vehicle interactions and how these differ by driver type should be considere d in developing or refining existing analytical or simulation models for freeway operati ons. The variation of driver types depending on their ta sk should be incorporated to simulation models. This would also assist in developing more r ealistic tools for simulating the freeway flow breakdown. Differences in attitudes and driver behavior betwee n non-congested and congested conditions should be explicitly incorporated in tra ffic operational models.

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159 The merging turbulence model needs to be verified w ith additional breakdown observations. It is further recommended to use this measure for identifying and even predicting the time to breakdown.

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160 APPENDIX A PRESCREENING QUESTIONNAIRES Focus Group Questionnaire Transportation Research Center Prescreening Questionnaire for Merging Behavior Res earch To Participants: This questionnaire is used to select a diverse poo l of drivers to participate in the focus group experiment. Information collected in this form will be used fo r traffic engineering research only. All responses will be he ld in complete confidential and exempted from public disclosure by law. In accordance with t he Confidential Information Protection and Statistical Efficiency Act of 2002 (Title 5 of Publ ic Law 107-347) and other applicable Federal laws, your responses will not be disclosed in ident ifiable form without your consent. Since drivers’ diversities are highly encouraged, only th e most fitful responders will be chosen. Please answer as many as possible. Return Address: By Email : azk133@ufl.edu By Mail : Alexandra Kondyli, 518C Weil Hall, PO Box 116580, Gainesville, FL 3260 1 1) What is your gender? Male Female 2) What is your age range? < 20 20 to 29 years 30 to 39 years 30 to 39 years 50 to 59 years >= 60 years 3) Which of the following groups do you most identify yourself as? Caucasian Native American African American Hispanic Asian Pancific Islander Other (please specify) 4) Where did you begin your driving practice and obtai ned your driver’s license? North America Latin America Asia Europe Australia Other (please specify)

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161 5) How long have you been driving in the U.S.? < 1 year 1 to 3 years 3 to 9 years >= 10 years 6) Do you have a valid U.S. driver’s license? Yes No 7) What is your occupation? Full time student University faculty/staff Professional driver Other (please specify) 8) How often do you drive to work/school? Everyday Usually Sometimes Never 9) How much time do you spend driving per week? < 4hr 4 to 8 hr 8 to 14 hr > 14hr 10) What time of the day do you usually drive? Am/pm peak hour (6 am 10 am; 4 pm 7 pm) during work days Non-peak hours (including holiday and weekend) 11) What type of vehicle do you usually drive? Sedan/Coupe Pickup/SUV Jeep Truck 12) What time are you typically available for participa ting in the focus group experiments? Please check as many as possible. Monday morning (9:00 am to 12:00 pm) Tuesday morning (9:00 am to 12:00 pm) Monday afternoon (1:00 pm to 4:00 pm) Tuesday afternoon (1:00 pm to 4:00 pm) Monday evening (4:00 pm to 7:00 pm) Tuesday evening (4:00 pm to 7:00 pm) Wednesday morning (9:00 am to 12:00 pm) Thursday morning (9:00 am to 12:00 pm) Wednesday afternoon (1:00 pm to 4:00 pm) Thursday afternoon (1:00 pm to 4:00 pm) Wednesday evening (4:00 pm to 7:00 pm) Thursday evening (4:00 pm to 7:00 pm) Friday morning (9:00 am to 12:00 pm) Saturday morning (9:00 am to 12:00 pm) Friday afternoon (1:00 pm to 4:00 pm) Saturday afternoon (1:00 pm to 4:00 pm) Friday evening (4:00 pm to 7:00 pm) Saturday evening (4:00 pm to 7:00 pm) Sunday morning (9:00 am to 12:00 pm) Sunday afternoon (1:00 pm to 4:00 pm) Sunday evening (4:00 pm to 7:00 pm) Any time by appointment

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162 13) Participant’s contact information (at least 1 from phone/email/mail) Name: ____________________ (Required) Phone: ____ ______________ Email: ____________________ Date: ______________ Mail Address: _________________________________

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163 Instrumented Vehicle Questionnaire Transportation Research Center Prescreening Questionnaire for Merging Behavior Res earch To Participants: This questionnaire is used to select a diverse poo l of drivers to participate in the ‘in-vehicle’ data collection experiment. Information collected in this form will be used fo r traffic engineering research only. All responses wi ll be held in complete confidential and exempted from public disclosure by law. In accordan ce with the Confidential Information Protection and Statistical Efficiency Act of 2002 ( Title 5 of Public Law 107-347) and other applicable Federal laws, your responses will not be disclosed in identifiable form without your consent. Since drivers’ diversities are highly enco uraged, only the most fitful responders will be chosen. Please answer as many as possible. Return Address: By Email : azk133@ufl.edu By Mail : Alexandra Kondyli, 518C Weil Hall, PO Box 116580, Gainesville, FL 3260 1 14) What is your gender? Male Female 15) What is your age range? < 20 20 to 29 years 30 to 39 years 30 to 39 years 50 to 59 years >= 60 years 16) Which of the following groups do you most identify yourself as? Caucasian Native American African American Hispanic Asian Pancific Islander Other (please specify) 17) Where did you begin your driving practice and obtai ned your driver’s license? North America Latin America Asia Europe Australia Other (please specify) 18) How long have you been driving in the U.S.?

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164 < 1 year 1 to 3 years 3 to 9 years >= 10 years 19) Do you have a valid U.S. driver’s license? Yes No 20) What is your occupation? Full time student University faculty/staff Professional driver Other (please specify) 21) How often do you drive to work/school? Everyday Usually Sometimes Never 22) How much time do you spend driving per week? < 4hr 4 to 8 hr 8 to 14 hr > 14hr 23) What time of the day do you usually drive? Am/pm peak hour (6 am 10 am; 4 pm 7 pm) during work days Non-peak hours (including holiday and weekend) 24) What type of vehicle do you usually drive? Sedan/Coupe Pickup/SUV Jeep Truck 25) What time are you typically available for participa ting in these experiments? Please check as many as possible. Monday morning (6:00 am to 7:00 am) Monday evening (4:00 pm to 5:00 pm) Tuesday morning (6:00 am to 7:00 am) Tuesday evening (4:00 pm to 5:00 pm) Wednesday morning (6:00 am to 7:00 am) Wednesday evening (4:00 pm to 5:00 pm) Thursday morning (6:00 am to 7:00 am) Thursday evening (4:00 pm to 5:00 pm) Friday morning (6:00 am to 7:00 am) Friday evening (4:00 pm to 5:00 pm) Any time by appointment 26) Participant’s contact information (at least 1 from phone/email/mail) Name: ____________________ (Required) Phone: ____ ______________ Email: ____________________ Date: ______________ Mail Address: _________________________________

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165 Participants Background Survey Transportation Research Center Participants’ Background Survey Form Participant’s Name: _________________________ Dat e: _________________ Note: Information collected in this form will be us ed for traffic engineering research only. All responses will be held in complete confidential and exempt from public disclosure by law. In accordance with the Confidential Information Protec tion and Statistical Efficiency Act of 2002 (Title 5 of Public Law 107-347) and other applicabl e Federal laws, your responses will not be disclosed in identifiable form without your consent By law, every interviewer, as well as every agent, is subject to a jail term, a fine, or both i f he or she makes public ANY identifiable information you reported. 27) If the speed limit on the freeway is 70 mph, what s peed are you likely to drive (assuming good visibility and good weather conditions)? <65 mph 65 to 70 mph 70 to 75 mph 75 to 80 mph > 80 mph 28) How often do you change lanes if the vehicle in fro nt of you is slower? Very often Sometimes Seldom 29) What type of driver do you consider your self? Very aggressive Somewhat aggressive Somewhat conservative !Very conservative 30) What type of driver do your friends and family consider you? Very aggressive Somewhat aggressive Somewhat conservative !Very conservative 31) When planning your driving trip, do you allow addit ional time for possible delays due to congestion, construction, or bad weather? Yes, always Sometimes Never 32) You are approaching the acceleration lane from an e ntrance ramp, and traffic has already started to appear on the freeway. When do you typic ally merge onto the freeway? Right after you enter the acceleration lane As soon as you see an appropriate gap on the freew ay Just before you reach the end of the acceleration lane

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166 33) You are driving in the right-most lane of a three-l ane freeway and you are approaching an entrance ramp merge area. You can see that there ar e several vehicles entering the freeway from the entrance ramp. The vehicle in front of you changes lanes to avoid conflict with the merging vehicles. What do you do? Do the same – change lanes to avoid any interactio n with the merging vehicles Remain in your lane, but accelerate and close the gap between you and the vehicle further ahead, to discourage merging vehicles from cutting in front of you Do nothing, and maintain your current speed Slow down so that the vehicles from the entrance r amp can merge

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167 APPENDIX B ROUTES FOR INSTRUMENTED VEHICLE EXPERIMENT AM Route

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168 PM Route

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169 APPENDIX C MEASURING LENGTHS ON DIGITAL IMAGES The derivation of the correct scale for measuring l engths and distances from uncalibrated moving cameras is a difficult task, because the geo metry of the road is constantly changing as the vehicle is traveling on the freeway segment. T o address this issue, the method developed by Psarianos et al. (2001) is adopted. This method has been developed for measuring lane widths but it was modified to account for lengths along th e road axis. This basic geometry is described in Figure C-1, in which O is the perspective center and M is the image center. A B Figure C-1. Image geometry with A) horizontal came ra axis and B) measurements on the digital image. (Source: Psarianos et al., 2001). In Figure C-1 the camera constant is c, yB is the y image coordinate of points B and B on the road surface. If Yo is the camera height measured above ground level, then the scale of the image at a distance ZB is: B B B BX x Y y Z c 0 (C-1) Where XB is the lane width BB’ and xB is the corresponding length measured in the image. Equation C-1 was used first to estimate the camera height Yo from known widths (range

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170 from 6 to 20 ft) measured with a tape. The camera h eight for the front camera is estimated as 3.96 ft 0.30 ft. The camera height for the rear c amera is estimated as 6.65 ft 0.50 ft. Next, the camera constant c was estimated for both cameras given known lane widths XB and distances ZB according to Equation C-2. 0Y y Z X x Z cB B B B B (C-2) Then, the constant c of the cameras was used for es timating the length ZX from any point of the road X, by using the extracted images from the came ras.

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177 BIOGRAPHICAL SKETCH Ms. Alexandra Kondyli is a research assistant at th e Transportation Research Center of the University of Florida, at the Department of Civil A nd Coastal Engineering. Ms. Kondyli received her master’s degree from the Department of Civil an d Coastal Engineering from University of Florida in December 2005. Ms. Kondyli also received her graduate diploma from the Department of Rural and Surveying Engineering of the National Technical University of Athens, Greece, in June 2003.