
Citation 
 Permanent Link:
 http://ufdc.ufl.edu/AA00004713/00001
Material Information
 Title:
 Development of a trafficactuated signal timing prediction model
 Creator:
 Lin, PeiSung, 1964
 Publication Date:
 1995
 Language:
 English
 Physical Description:
 xiii, 171 leaves : ill. ; 29 cm.
Subjects
 Subjects / Keywords:
 Analytical models ( jstor )
Headway ( jstor ) Intersections ( jstor ) Left turns ( jstor ) Modeling ( jstor ) Propagation delay ( jstor ) Signals ( jstor ) Simulations ( jstor ) Traffic delay ( jstor ) Traffic estimation ( jstor ) City of Gainesville ( local )
 Genre:
 bibliography ( marcgt )
theses ( marcgt ) nonfiction ( marcgt )
Notes
 Thesis:
 Thesis (Ph. D.)University of Florida, 1995.
 Bibliography:
 Includes bibliographical references (leaves 164169).
 General Note:
 Typescript.
 General Note:
 Vita.
 Statement of Responsibility:
 by PeiSung Lin.
Record Information
 Source Institution:
 University of Florida
 Holding Location:
 University of Florida
 Rights Management:
 Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for nonprofit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
 Resource Identifier:
 002070305 ( ALEPH )
AKQ8570 ( NOTIS ) 34360604 ( OCLC )

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DEVELOPMENT OF A TRAFFICACTUATED
SIGNAL TIMING PREDICTION MODEL
By
PEISUNG LIN
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENT FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1995
UNIVERSITY OF FLORIDA LIBRARIES
ACKNOWLEDGMENTS
This dissertation cannot be accomplished without the assistance of many people. I
wish to express my sincerest thanks to my supervisory committee, dear friends and lovely
family who helped make it possible.
First, I would like to express my extreme gratitude to professor Kenneth G. Courage,
chairman of my supervisory committee, for giving me the opportunity to pursue my graduate
studies under his enthusiastic guidance. He not only provided me the financial assistance but
also gave me many levels of support. Every time when I face any difficulty in research, he has
always inspired me with his ingenious idea. His lofty standard has always been a source of
motivation to me. I will never forget what he has done for me during my studies.
Dr. Charles E. Wallace is the Director of Transportation Research Center. Under his
leadership, I felt very warm in my mind when I was in this big family. Although Dr. Wallace
was very busy, he always made time for me. He has provided his professional guidance to
my research and lofty standard to my dissertation. I deeply believe his comments on my
dissertation will be beneficial for my professional career. For this, I am eternally grateful.
Dr. Joseph A Wattleworth served as one of my committee member. Although he has
been retired, his assistance and personal support are sincerely appreciated.
Dr. Sherman X. Bai has been a source of inspiration and motivation. His technical
support and personal caring were really invaluable to the success of this research. He has
helped me far more than being a member of the committee. He has become a good friend of
me. I want to thank him for his professional support and true friendship.
Dr. Mang Tia served as one of my supervisory committee member after Dr. Joseph
A Wattleworth retired. His assistance in this matter is really appreciated. Without his help,
the requirement for my dissertation cannot be completed.
Dr. Anne WyattBrown served as the outside member. She has been of great help
with her assistance on the improvement of my technical writing. In addition, her patient
instruction, sincere encouragement are highly appreciated.
I am indebted to Dr. Gary Long for his guidance and encouragement during my
studies although he is not on my supervisory committee. Special thanks go to William M.
Sampson, manager of McTrans Center, and Janet D. Degner, Manager of Technology
Transfer Center, for providing me financial assistance and the personal supports.
I would also like to express my gratitude to my colleagues for their assistance. I like
to thank ShiowMin Lin, YuJeh Cheng, ChengTin Gan, JerWei Wu, MinTang Li, Chian
Chi Jiang and Randy Showers for their encouragements. I also like to extend my thanks to
David Allen, David Hale, Jim Harriott and James Kreminski for their proofreading.
Finally, I want to express my deep appreciation to my family. My parents, Chang
Lang Lin and LiChen Hsu, continually supply me their unwavering love, sincere inspiration
and selfless support throughout my life. My brother, PeiYi Lin, and my sister, LiLing Lin,
continually give me their encouragements and supports. My wife and best friend, HuiMin
Wen, is willing to share every good time and bad mood with me. Her patience and love give
me the warmest feeling and the best support to complete my research.
TABLE OF CONTENTS
ACKNOWLEDGEMENTS
LIST OF TABLES
LIST OF FIGURES ......
ABSTRACT ........
CHAPTER 1. INTRODUCTION .
Problem Statement. .
Objectives ..
Organization .
CHAPTER 2. BACKGROUND .
Introduction .
Literature Review ..
Preliminary Model Development
Simulation Models .
Arterial Considerations .
CHAPTER 3. MODEL DEVELOPMENT
Introduction. ...
Determination of Arrival Rates
Permitted Left Turn Phasing
Compound Left Turn Protection
Applications. ...
. 1
S2
4
5
S6
6
6
S.29
S.54
.57
. .63
. 63
. 66
. 76
. .78
CHAPTER 4. MODEL IMPLEMENTATION
Introduction .
Structure and Logic of the ACT348 Program .
Extension of the Development of Coordinated Operations .
CHAPTER 5. MODEL TESTING AND EVALUATION .
Introduction .
Fullyactuated Operation .
Coordinated Actuated Operation .
Further Evaluation of the Analytical Model .
CHAPTER 6. EXTENDED REFINEMENT OF THE ANALYTICAL MODEL
Introduction .
Refinement of the Analytical Model for Volumedensity Operation
Refinement of the Analytical Model to Incorporate "Free Queue" Parameter
Incorporation of the Analytical Model into the HCM Chapter 9 Procedure .
CHAPTER 7. CONCLUSIONS AND RECOMMENDATIONS .
Conclusions .
Recommendations .
APPENDIX
UNIFORM DELAY FORMULAS .
BIBLIOGRAPHY
BIOGRAPHICAL SKETCH .
.80
.81
.91
.94
.94
.94
105
108
122
122
123
131
143
146
146
149
170
LIST OF TABLES
Table
21 The iteration results and its convergence for the illustrated example.
61 Throughcar equivalents, EL, for permitted left turns in a shared lane
with one free queue. .......
62 Throughcar equivalents, EL1, for permitted left turns in a shared lane
with two free queues .. ......
Page
. .52
135
136
LIST OF FIGURES
Figure Page
21 The operation of an actuated phase under significant demand .35
22 Dualring concurrent phasing scheme with assigned movements 38
23 The relationship among the components in the phase time .39
24 Queue accumulation polygon for a single protected phase .. 42
25 The intersection used as an example for circular dependency illustration 50
26 Queue accumulation polygon in the first iteration of the illustrated example .51
27 Iterative loops in the phase time and cycle time computation procedure 53
28 Phase time comparison between EVIPAS and NETSIM 56
29 Conceptual relationship between major street g/C and minor street demand .58
210 The location of studied intersection .. 59
211 Prediction of the major street g/C ratio based on a power model for minor
street traffic volume. ....... .61
212 Prediction of the major street g/C ratio based on a logarithmic model for minor
street detector occupancy .. 62
31 Arrival rate over a full cycle with coordinated operation 64
32 Queue accumulation for a single protected phase 67
33 Queue accumulation polygon for a permitted left turn from an exclusive lane
with opposing lane number greater than one 69
34 Queue accumulation polygon for a permitted left turn from an exclusive lane
with opposing lane number equal to one .. 70
35 Queue accumulation polygon for a permitted left turn from an exclusive lane
with sneakers .72
36 Queue accumulation polygon for a permitted left turn from a shared lane
(g g ). .75
37 Queue accumulation polygon for a permitted left turn from a shared lane
(g
38 Queue Accumulation polygon for protected plus permitted LT phasing with
an exclusive LT Lane ........77
39 Queue Accumulation polygon for permitted plus protected LT phasing with
an exclusive LT Lane 78
41 Major structure of the ACT348 program .. 82
42 Case 1: Phase sequence for simple permitted turns .. 83
43 Case 2: Phase sequence for leading green .. 84
44 Case 3: Phase sequence for lagging green .. 84
45 Case 4: Phase sequence for leading and lagging green .. 84
46 Case 5: Phase sequence for LT phasing with leading green 85
47 Case 6: Phase sequence for leading dual left turns 85
48 Case 7: Phase sequence for lagging dual left turns .. 85
49 Case 8: Phase sequence for leading and lagging with dual left turns .. .86
51 Cycle length comparison for a 1.5sec allowable gap setting 96
52 Cycle length comparison for a 3.0sec allowable gap setting 97
53 Cycle length comparison for a 4.5sec allowable gap setting 97
54 Composite cycle length computations with all gap settings .. 98
55 Percent of phase terminated by maximum green time for each gap setting .99
56 Phase time comparison between the Appendix H method and NETSIM. .101
57 Phase time comparison between the proposed model and NETSIM 101
58 Intersection configuration of Museum Road and Northsouth Drive on the
campus of the University of Florida 102
59 Phase time comparison between the analytical model and field data 104
510 Phase time comparison between NETSIM and field data 104
511 Phase time comparison between arterial street and cross street 106
512 Relationship of estimated phase times between NONACT and NETSIM 108
513 NETSIM arrival distributions for a singlelink of 100ft length 111
514 NETSIM arrival distributions for a singlelink of 1000ft length 111
515 NETSIM arrival distributions for a singlelink of 2000ft length 112
516 NETSIM arrival distributions for a singlelink of 3000ft length 112
517 Comparison of analytical and simulation model arrival distribution for
singlelane, 100vph flow 114
518 Comparison of analytical and simulation model arrival distribution for
singlelane, 300vph flow 114
519 Comparison of analytical and simulation model arrival distribution for
singlelane, 500vph flow 115
520 Comparison of analytical and simulation model arrival distribution for
singlelane, 700vph flow 115
521 Comparison of analytical and simulation model arrival distribution for
singlelane, 900vph flow 116
522 Optimal NETSIM singlelane link length for various phase termination
headway settings 116
523 Comparison of analytical and simulation model arrival distributions for
twolane, 200vph flow 118
524 Comparison of analytical and simulation model arrival distributions for
twolane, 600vph flow 118
525 Comparison of analytical and simulation model arrival distributions for
twolane, 1000vph flow 119
526 Comparison of analytical and simulation model arrival distributions for
twolane, 1800vph flow 119
61 Variable initial feature for volumedensity operation 124
62 Gap reduction feature for volumedensity operation 125
63 Phase time comparison for volumedensity operation with a zero detector
setback 130
64 Phase time comparison for volumedensity operation with a 150ft detector
setback 130
65 Phase time comparison for volumedensity operation with a 300ft detector
setback 131
66 Phase prediction for single shared lane with free queues 142
Ai Uniform delay formula for ingle protected phase 154
A2 Uniform delay for permitted left turns from an exclusive lane (n >1) 155
A3 Uniform delay for permitted left turns from an exclusive lane (n,=1) .156
A4 Uniform delay for permitted left turns from a shared lane (gq>gf) 157
A5 Uniform delay for permitted left turns from a shared lane (gg,) 158
A6 Uniform delay for compound left turn protection: HCM Chapter 9 Case 1 .159
A7 Uniform delay for compound left turn protection: HCM Chapter 9 Case 2 160
A8 Uniform delay for compound left turn protection: HCM Chapter 9 Case 3 .161
A9 Uniform delay for compound left turn protection: HCM Chapter 9 Case 4 .162
A10 Uniform delay for compound left turn protection: HCM Chapter 9 Case 5 163
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
DEVELOPMENT OF A TRAFFICACTUATED
SIGNAL TIMING PREDICTION MODEL
By
PeiSung Lin
December, 1995
Chairman: Kenneth G. Courage
Major Department: Civil Engineering
The Highway Capacity Manual (HCM) provides a methodology in Chapter 9 to
estimate the capacity and level of service at a signalized intersection as a function of the traffic
characteristics and the signal timing. At trafficactuated intersections, the signal timing
changes from cycle to cycle in response to traffic demand. An accurate prediction of average
phase times and cycle length is required to assess the performance of intersections controlled
by trafficactuated signals. The current technique in Appendix II of HCM Chapter 9 for this
purpose has not been well accepted.
This dissertation describes a more comprehensive methodology and a more
satisfactory analytical model to predict trafficactuated signal timing for both isolated and
coordinated modes. The proposed methodology and model have been verified by simulation
augmented by limited field studies. The results are very encouraging with respect to their
general reliability and their compatibility with the current HCM Chapter 9 structure. The
techniques developed in this study would provide an important contribution to the
methodology of traffic engineering for trafficactuated signal timing prediction and improve
the analytical treatment of trafficactuated control in the HCM Chapter 9.
CHAPTER 1
INTRODUCTION
The concepts of capacity and level of service (LOS) are central to the analysis of a
signalized intersection. Level of service is expressed as a letter grade from A through F that
describes the quality ofperformance of a signalized intersection from the driver's perspective.
It is evaluated based on the average stopped delay per vehicle for various movements within
the intersection. The 1985 Highway Capacity Manual (HCM) [1] prescribes a methodology
in Chapter 9 (Signalized Intersections) to estimate the LOS as a function of the traffic
characteristics and the signal timing.
Intersection traffic control is characterized as "pretimed" if a predetermined timing
plan is repeated cyclically or "trafficactuated" if the operation varies from cycle to cycle in
response to information from traffic detectors on the roadway. Pretimed control is usually
appropriate for constant traffic demand, while trafficactuated control is better suited to
variable traffic demand. Pretimed control is much easier to analyze, but trafficactuated
control offers more in the way of performance to the motorist.
Whether an isolated actuated controlled intersection or a set of coordinated actuated
intersections, the operational performance largely depends on traffic patterns and the actuated
controller parameters to be discussed in this dissertation. A welldesigned actuated control
plan that responds appropriately to traffic demand can significantly reduce delay and fuel
2
consumption. More advanced forms of adaptive traffic control strategies were introduced
recently, but the trafficactuated control concepts still play a very important role today.
Because of its superiority, trafficactuated control has become the predominant mode
throughout the U.S.A. in spite of its analytical complexity.
Many trafficrelated measures at a signalized intersection, such as intersection
capacity, vehicle delay and queue length, are determined by the phase times and cycle length.
For trafficactuated control, the phase times and corresponding cycle length vary from cycle
to cycle in response to the traffic demand. Therefore, it becomes desirable to predict the
average phase times and cycle length for trafficactuated control which are the main inputs
in the procedure contained in the HCM Chapter 9 for the computation of intersection capacity
and vehicle delay.
Improvement of the analytical treatment of trafficactuated control presented in the
HCM Chapter 9 is the subject of this dissertation. An enhanced analytical model will be
proposed and tested.
Problem Statement
Capacity and delay are two major measures of effectiveness for the analysis of a
signalized intersection. The procedure contained in Chapter 9 of the HCM is used almost as
a standard to estimate the intersection capacity and vehicle delay. For trafficactuated
operation, accurate estimates of intersection capacity and vehicle delay must rely on accurate
estimates of the signal timing. However, the primary technique, presented in an appendix to
HCM Chapter 9, to predict the signal timing for trafficactuated operation has been the
subject of much criticism in the literature [2, 3, 4, 5, 6].
3
This technique is based on the simple assumption that a trafficactuated controller will
maintain a high degree of saturation (95% in the HCM Chapter 9 procedure) on the critical
approach to each phase. It does not consider any controller parameter that influences the
signal timing in field. This has created many questions in the literature regarding the validity
of the assumption and the simplistic nature of the technique. Therefore, the main deficiency
of the technique in the appendix to HCM Chapter 9 comes from improper analytical treatment
of trafficactuated control
Some analytical work has been done on estimating individual phase lengths for traffic
actuated operation [2, 6, 7, 8, 9, 10], but a method for treating the entire phase sequence,
given a specified set of traffic volumes, controller parameters and detector placements, does
not exist. Simulation is currently the most reliable method for determining the signal timing.
Simulation is a powerful tool, but its application is best suited to situations that do not lend
themselves to analytical treatment. Furthermore, the signal timing prediction based on
simulation is time consuming.
Therefore, the development of a practical analytical technique to predict traffic
actuated signal timing is very desirable. Such a technique would provide an important
contribution to the methodology of traffic engineering and improve the analytical treatment
oftrafficactuated control in the HCM Chapter 9.
In this case, there are three major questions with the development of the traffic
actuated signal timing prediction model The first question is whether the model can improve
the analytical treatment oftrafficactuated control in the HCM Chapter 9 procedure on signal
timing prediction. The proposed methodology must be in a form that can be incorporated
4
into the HCM Chapter 9 procedure. The second one is whether the model can treat the entire
phase sequence for a specified set of traffic volumes, actuated controller parameters,
intersection configuration and detector placements. The third question is whether the model
can accurately and quickly predict the signal timing for trafficactuated operation.
Objectives
The signal timing of a trafficactuated signal will vary from cycle to cycle in response
to traffic demand. The goal of this research is to develop an analytical model to accurately
predict the average signal timing for trafficactuated intersection for both isolated and
coordinated modes. Although performance measures (delay, stops, queue length, fuel
consumption, etc.) are sensitive to actuated controller parameters, it is necessary to note that
this study does not include the development of an optimization methodology of the actuated
controller parameters. The specific objectives of the research are stated as follows:
1. Review the literature that deals with the subject of trafficactuated control,
particularly related to signal timing prediction and vehicle delay estimation.
2. Develop a model to improve the analytical treatment of trafficactuated control
in the HCM Chapter 9 on signal timing prediction and present the methodology
in a form that may be incorporated into the HCM Chapter 9 procedure.
3. Assure that the developed analytical model can predict the average phase times
and corresponding cycle length for a specified set of traffic volumes, controller
settings, intersection configuration and detector placements.
4. Test and evaluate the analytical model using simulation and limited field data to
assess its accuracy and feasibility of implementation.
Organization
This dissertation includes seven chapters that are devoted to developing an analytical
model to predict the signal timing for trafficactuated control The first chapter provides a
general introduction to the dissertation topic, problem statement and research objectives.
The next two chapters describe the development of the proposed analytical model
Chapter 2 presents the background knowledge required for the analytical model development
and a preliminary model that deals with protected movements from exclusive lanes only.
Chapter 3 extends the methodology developed in Chapter 2 to include shared lanes, permitted
left turns and compound left turn protections (permitted plus protected phasing and protected
plus permitted phasing).
The implementation of the proposed analytical model and procedure in a computer
program to predict trafficactuated signal timing is addressed in Chapter 4. The
computational process of this program is also presented.
The comparisons of predicted phase times between the proposed analytical model and
simulation and field data are presented in Chapter 5. An intensive evaluation is also made on
the comparison of vehicular arrivals at the stopline produced by simulation and the proposed
analytical model.
Chapter 6 presents several refinements of the proposed analytical model to achieve
a stronger capability on the phase time prediction. Uniform delay formulations developed in
this study for trafficactuated control are shown in the appendix. The final conclusions and
recommendations are stated in Chapter 7.
CHAPTER 2
BACKGROUND
Introduction
There has been a substantial amount of research conducted on trafficactuated control
which provides essential information for trafficactuated operating characteristics and signal
timing prediction. This chapter first reviews past and current research on the trafficactuated
control followed by the presentation of a preliminary model structure of phase time prediction
for fullyactuated operation. Each traffic control concept or theory that has contributed to
the model development is addressed separately. Next, two simulation models, TRAF
NETSIM (NETSIM) and EVIPAS, which have been adopted by this study as evaluation tools
for the proposed analytical model, are introduced. Finally, a preliminary consideration of
signal timing prediction for semiactuated traffic signal coordination is described. Further
model development and implementation for trafficactuated signal timing prediction will be
mostly based on the background knowledge presented in this chapter.
Literature Review
Trafficactuated control has been used since in the early 1930s. Whether an isolated
actuated controlled intersection or a set of coordinated actuated intersections, the operational
performance is largely determined by the traffic arrival patterns and actuated controller
parameters. The arrival patterns refers to the arrival headway distributions. The basic
7
actuated controller parameters include the minimum green time, maximum green time and
allowable gap settings (vehicle interval or unit extension). A welldesigned actuated control
plan that responds appropriately to traffic demand can significantly reduce delay and fuel
consumption. Therefore, shortly after actuated signal control was first introduced,
researchers began to study the influence of traffic arrival patterns and departure characteristics
at a signalized intersection with trafficactuated control Many researchers also focused on
the optimization of controller settings, detector placement, and the relationship among them.
Recently, some researchers began to develop models to predict trafficactuated signal timing
for the purpose of more accurate capacity computation and delay estimation.
Review of past and current research is an area which definitely merits attention. There
has been a substantial amount of research conducted on trafficactuated control which will
contribute to this dissertation.
The development of a trafficactuated signal timing prediction model is the subject of
this study. Thus, the major emphasis ofthis literature review is on the trafficactuated control
that particularly is related to operation characteristics, vehicle arrival headway distributions
and signal timing prediction models. The procedure contained in the HCM Chapter 9 is used
almost as a standard to analyze signalized intersection capacity and level of service, so the
literature review also covers the methodology for both capacity computation and delay
estimation. One item that needs to be reviewed carefully is a new program called EVIPAS.
The EVIPAS model is an optimization program which is able to analyze and determine the
optimal settings of controller parameters for trafficactuated control The results of the
testing efforts on EVIPAS are report in this chapter.
The main topics of the literature review include
Trafficactuated control definitions;
Warrants for trafficactuated control;
Benefits and operating considerations for trafficactuated control;
Effects of coordination and phaseskipping for trafficactuated control;
Latenight, lowvolume operation of coordinated actuated systems;
Evaluation of trafficactuated control by simulation;
Prediction of phase times and cycle length for trafficactuated control;
Delay models for trafficactuated control;
Signalized intersection capacity models for trafficactuated control; and
Overview and evaluation of "Enhancement of the Value Iteration Program for
Actuated Signals" (EVIPAS).
Trafficactuated Control Definitions
Three basic forms oftraffic control: pretimed, fullyactuated and semiactuated were
mentioned by Orcutt [11] in 1975. He indicated that pretimed control was used primarily in
the Central Business District (CBD) area, especially where a network of signals must be
coordinated. He defined actuated signals in terms of equipment that responds to actual traffic
demand of one or more movements as registered by detectors. If all movements are detected,
the operation is referred to as "fullyactuated." If detectors are installed for some, but not all,
traffic movements, the term "semiactuated" is applied. Orcutt suggested fullyactuated
control should normally be used at isolated intersections.
9
Precise definitions of the basic controller types were described by the National
Electrical Manufacturers Association (NEMA) standards [12] in 1976. According to the
NEMA standards, the basic controllers include pretimed, semiactuated, fulyactuated
without volumedensity features, and fullyactuated with volumedensity features. In the
remainder of this dissertation, fullyactuated without volumedensity features will be just
called fullyactuated control, and fullyactuated with volumedensity features will be called
volumedensity control
Warrants for Trafficactuated Control
Warrants for selecting traffic control modes, which are very useful for practicing
engineers, have been researched since the early 1960s. Studies of delay at actuated signals
have been made for the purpose of evaluating warrants for this type of control on the basis
of the information in the 1961 edition of the Manual on Uniform Traffic Control Devices
(MUTCD). This information was expanded by the Texas Department of Highways and
Public Transportation into a graphical format. The graphical relationships were studied in
1971 by Vodrazka, Lee and Haenel [13], who concluded that they provide good guidelines
for selecting actuated equipment for locations where traffic volumes do not warrant pretimed
signals. The current edition of the MUTCD stops short of numerical warrants for choosing
between pretimed and trafficactuated control, but it does suggest certain qualitative
conditions under which trafficactuated control should be implemented.
Benefits and Operating Considerations for Trafficactuated Control
In 1967, Gerlough and Wagner [14] began to compare pretimed control effectiveness
with volumedensity control. They found that trafficactuated control at higher traffic
10
volumes degraded performance. One of the problems cited for volumedensity control was
that the duration of green for each phase was dependent on the estimated queue length at the
beginning of the phase. Difficulties with queue length estimation made this type of control
less effective.
Longloop presence detection operates by producing a vehicle call for the duration
of time that the vehicle is over the detector. This is as opposed to the mode of smallarea
detector operation in which the detector outputs a pulse of less than 0.1 seconds when the
vehicle is first detected. This latter mode of operation is known as passage, pulse or count
detection. The longloop presence detector with fullyactuated controllers in a mode known
as laneoccupancy control or loopoccupancy control (LOC). LOC operation occurs when
the controller is programmed for an initial green interval of zero. Extensions are set either
to zero or to a very low value. There is no need for a nonzero initial interval or minimum
green time because the long loops continuously register the presence of any vehicles that are
waiting, causing the controller to extend the green until the entire queue is discharged. The
result is a signal operation that responds rapidly to changes in traffic flow.
In 1970, Bang and Nilsson [15] compared LOC operation with small area detector
(pulse detector) operation. They concluded that delay was reduced 10 percent and stops by
6 percent under the same traffic conditions with LOC. In 1975, Cribbins and Meyer [16]
compared pulse and presence detectors. They concluded that the longer the length of the
presence detector on the major approach to the intersection, the longer the delay. They also
concluded that the highest intersection travel time values occurred when either longloop
presence or pulse detectors were used on both major and minor approaches. The intersection
11
travel time was defined here as the average time it takes a vehicle to pass through an
intersection, whether it is stopped or slowed.
Numerous theoretical studies on traffic signal timing were conducted between 1958
and 1970. The theoretical work on pretimed control by Webster [17] in 1958 and Miller [18]
in 1963 has been applied to the computation of optimum cycle lengths as a function of vehicle
arrival rates. It has also been used for evaluating vehicle delay, intersection capacity,
probability of stops and so on. These results were also well validated through the comparison
of field data. In 1969, Newell [19] and Newell and Osuma [20] expanded the body of theory
by developing relationships for mean vehicle delay with both pretimed and actuated control
at intersections of oneway streets and intersections of twoway streets, respectively. Newell
[19] demonstrated that the average delay per vehicle for an actuated signal is less than that
of a pretimed signal by a factor of about three for intersections of oneway streets. Osuma
[20] considered intersections oftwoway streets without turning vehicles. For the particular
trafficactuated policy which holds the green until the queue has been discharged, the traffic
actuated control will not perform as well as pretimed control under the following two
conditions: 1) flows are nearly equal on both approaches of a given phase and 2) the
intersection is nearly saturated.
In 1976, Staunton [21] summarized the work of numerous signal control researchers.
In his paper, the comparisons of delay produced by pretimed control and actuated control,
as a function of vehicle volumes, were presented. Staunton demonstrated that fullyactuated
control with 2.5sec extensions will always be better than the best form of pretimed operation,
given optimum settings for all volumes. Longer values for the extensions can easily degrade
12
actuated control performance. His conclusions were based on simulation, but the details of
the detector configuration were not specified. In view of the 2.5sec extension time, short
or passage detectors were probably used in his study. The performance estimates from
Staunton were supported by Bang [22].
In 1981, Tarnoffand Parsonson [23] compiled an extensive literature review on the
selection of the most appropriate form of traffic control for an individual intersection. Three
complementary approaches were used to evaluate controller effectiveness: 1) field data
collection using observers to manually measure vehicle volumes, stops and delay; 2)
simulation using the NETSIM model developed by the Federal Highway Administration
(FHWA) to evaluate control system performance; and 3) analytical techniques developed by
the research team and other agencies. The general conclusions from their extensive literature
review were as follows:
1. Pretimed controllers operate most effectively when the shortest possible cycle
length is used subject to the constraints ofproviding adequate intersection capacity
and minimum green times for pedestrians and vehicle clearance intervals.
2. The delay produced by fullyactuated controllers is extremely sensitive to the value
of the extension that is used. In general, shorter extensions reduce vehicle delay.
3. For small area detectors (motion or pulse detectors), at low and moderate volumes
when extensions of two or three seconds are employed, the use of the filly
actuated controllers will reduce delays and stops over those which can be achieved
using pretimed controllers. When high traffic volumes occur both on the main
street and on the side street causing the controller to extend the green time to the
13
maximum on all phases, the fullyactuated controller will perform as a pretimed
controller, producing comparable measures of vehicle flow.
4. The relative effectiveness of the various control alternatives depends on the quality
of the signal timing employed. A poorly timed actuated controller will degrade
traffic performance to as great an extent as a poorly timed pretimed controller.
Through the detailed evaluation of controller performance, the conclusions by Taroff
and Parsonson [23] are described as follows: semiactuated controllers produce a higher level
of stops and delays for all traffic conditions than either the fullyactuated or pretimed
controllers. However, for side street traffic volumes that are less than 20 percent of main
street volumes, there is an insignificant difference between semiactuated and fullyactuated
controller effectiveness. Fullyactuated controllers produce significant benefits when used in
an eightphase and dualring configuration over that which would be possible with a four
phase pretimed controller.
From the simulation results on small area detectors for fullyactuated control, the
location of 150 ft produced a level of performance far superior for a 3sec vehicle interval to
that of closer detectors for the approach speed of 35 mph. Tarnoff and Parsonson concluded
that it is appropriate to locate the detector such that the travel time is equal to the extension
time. It was also concluded that for volumes in excess of 450 vehicles per hour per lane,
additional improvement can be realized through the use ofthe added initial feature of volume
density controller for an approach of 35 mph or higher.
They indicated that further modest gains in performance for fullyactuated control
were possible with the use of long loops and short (or zero) initial and extension settings.
14
This application was found to produce a performance similar to a 2sec extension time with
a short loop. From the simulation results, they concluded that LOC was more effective than
pulse detection over a wide range of traffic volumes. LOC offered the further advantage not
reflected by the simulation results of screening out false calls caused by vehicles approaching
but not traveling through the intersection.
Volumedensity controllers provide the greatest benefit at intersections with high
approach speeds where a detector setback in excess of 125 ft from the intersection requires
a variable initial green time. Tarnoff and Parsonson found that the variable initial and gap
reduction options of the volumedensity control did not improve the controller's performance
over that of a fillyactuated controller unless the option is used to reduce the vehicle
extension to a value that is less than the one used for the fillyactuated controller. Thus, if
the volumedensity controller is timed to provide a 3sec passage time and a 2sec minimum
allowable gap, its performance will be superior to that of a fillyactuated controller with a
constant 3sec allowable gap. Noted that the above simulation results given by Tarnoffand
Parsonson do not properly account for the problem of premature termination of green due to
the variation in queue discharge headways that occur under normal operating conditions.
In 1985, Lin [24] studied the optimal timing settings and detector lengths for filly
actuated signals operating in presence mode using the RAPID simulation model He
suggested the optimal maximum green for hourly flow patterns with a peaking hour factor of
1.0 was about 10 seconds longer than the corresponding optimal greens with a peaking hour
factor of 0.85, and the optimal maximum green was approximately 80 percent longer than the
corresponding optimal greens. This result was similar to the 1.5 times pretimed split
15
suggested by Kell and Fullerton [25]. Lin indicated that optimal vehicle intervals were a
function of detector length and flow rate. For detectors 30,50 and 80 ft long, the use of 2
sec, 1sec and 0sec vehicle intervals can lead to the best signal performance over a wide
range of operating conditions, respectively. The use of vehicle intervals greater than zero
second for detectors 80 ft or longer is not desirable unless the combined critical flow at an
intersection exceeds 1,400 vph.
In order to improve the VIPAS model, a new optimization algorithm and a new
intersection simulation were designed and programmed. The original VIPAS traffic
characteristics and vehicle generation routines were combined with these new models to
create the enhanced version called EVIPAS. In 1987, Bullen, Hummon, Bryer and Nekmat
[26] developed EVIPAS, a computer model for the optimal design ofa trafficactuated signal
The EVIPAS model was designed to analyze and optimize a wide range of intersection,
phasing, and controller characteristics of an isolated, fdllyactuated traffic signal It can
evaluate almost any phasing combination available in a two to eightphase NEMA type
controller and similar phasing structures for a Type 170 controller. The model has been field
tested and validated.
In 1987, Messer and Chang [27] conducted field studies to evaluate four types of
basic fullyactuated signal control systems operating at three diamond interchanges. Two
signal phasing strategies were tested: a) threephase and b) fourphase with two overlap.
Two smallloop (point) detection patterns (single and multipoint) were evaluated for each
type ofphasing. They concluded that 1) singlepoint detection was the most costeffective
threephase design; and 2) multipoint detection was the more delayeffective fourphase
16
configuration. Fourphase control characteristically operates a longer cycle length than the
threephase for a given traffic volume. This feature may produce higher average delays unless
the cycle increase is controlled to the extent that the internal progression features of four
phase control can overcome this deficiency.
In 1989, Courage and Luh [28] developed guidelines for determining the traffic
actuated signal control parameters which would produce the optimal operation identified by
SOAP84. They also evaluated the existing signal control parameters on an individual traffic
actuated signal The significant conclusions are summarized as follows:
Under low volumes, the maximum green settings have little or no effect on the
performance of actuated signal controllers. Under moderate volumes, shorter maximum
greens increase the average delay considerably. Longer maximum greens, however, have no
significant effect on delay. Under high volumes, the maximum green settings become more
important. There is a setting which minimizes average delay. Other settings with longer or
shorter maximum greens will produce more average delays. The optimal maximum green
setting can be achieved by running SOAP under actuated control with an optimal saturation
level set in the BEGIN card. They indicated that the settings that are optimal at some time
may not be appropriate in other times of day.
The value of 0.95, which is the default value used in SOAP actuated control, was
suggested for multiphase operation and a slightly higher saturation level may be desirable for
twophase operation. For approaches with a reasonably even distribution of traffic volume
by lane, settings of 4.0, 2.0 and 1.4 seconds were recommended by the study for one, two and
three lanes as the best values for unit extension, respectively.
17
In the same year, Bullen [29] used the EVIPAS simulation and optimization model
to analyze trafficactuated traffic signals. The variables studied were detector type, detector
placement, minimum green time and vehicle interval. The evaluation criterion was minimum
average vehicle delay. The study showed that the optimum design of a trafficactuated signal
was specific for some variables but relatively unaffected by others. The design was critical
only for high traffic volumes. At low volumes, vehicle delay is relatively unaffected by the
design parameters studied in his paper. The most critical variable Bullen found was vehicle
interval, particularly for passage detectors, where it should be at least 4.0 seconds regardless
of detector placement and approach speed. This conclusion somewhat contradicts previous
study results. However, it should be noted that the EVIPAS model used by Bullen considered
variable queue discharge headways.
Detector configuration is essential to the success of actuated control Kell and
Fullerton [30] in their second edition ofthe Manual of Traffic Signal Design in 1991 indicated
the small area detector might ideally be located three or four seconds of travel time back from
the intersection, with the allowable gap set accordingly. Similar principles were proposed in
previous research by Tarnoffand Parsonson. Kell and Fullerton also indicated that, in some
states, the detectors setback were determined on the safe stopping distance. The main
purpose is to avoid the dilemma zone in which a vehicle can neither pass through the
intersection nor stop before the stopline. For long loop detectors, they indicated the concept
of loop occupancy can provide good operation when vehicle platoons are well formed. The
use of several smaller loops instead of one long loop was suggested to solve the problem of
random vehicles causing excessive green.
18
In 1993, Bonneson and McCoy [31] proposed a methodology for evaluating traffic
detector designs. They indicated that the safety and efficiency of a traffic detector design can
be determined by the probability ofmaxout and the amount of time spent waiting for gapout
and the subsequent phase change. The stopline detector and advance loop detector with
presence and pulse mode were discussed, respectively. The methodology presented by
Bonneson and McCoy determined the optimal combination of design elements in terms of
safety (via infrequent maxout) and operations (via a short waiting time for phase change).
The design elements included detector location, detector length, vehicle speed, passage time
settings, and call extension setting). They concluded a large maximum allowable headway
will have an adverse effect on performance by increasing the maxout probability and the
length of wait for phase change.
Effects of Coordination and Phase Skipping for Trafficactuated Control
In 1986, Jovanis and Gregor [32] studied the coordination of actuated arterial traffic
signal systems. In the past, all optimization methods required that each actuated signal be
converted to its nearest equivalent pretimed unit. Using bandwidth maximization as a starting
point, a new procedure was developed by Jovanis and Gregor that specifically accounts for
actuated timing flexibility. Yield points and force offs at noncritical signals are adjusted so
they just touch the edges of the throughband while critical signals are unmodified. This
method was applied to a data set describing midday traffic conditions on an urban arterial
system of six signals in central Illinois. Simulation was used to evaluate these signal timings
and compare them with corresponding pretimed alternatives. They were surprised to find out
that pretimed, coordinated control appeared superior in general to actuated coordinated
19
control in this experiment. They also concluded that the level of service of side streets was
much more important for pretimed than actuated strategies.
In 1989, Courage and Wallace [33] developed the guidelines for implementing
computerized timing designs from computer programs such as PASSER I, TRANSYT7F
and AAP in arterial traffic control systems. The coordination of a group oftrafficactuated
signals must be provided by some form of supervision which is synchronized to a background
cycle length with splits and offsets superimposed. Both external and internal coordination of
the local controllers were addressed.
This report focused on the external coordination of traffic signal controllers.
Permissive periods were introduced to indicate the time interval following the yield point
during which the controller is allowed to yield to cross street demand. If the computed splits
are longer than the minimum phase times, it might be possible to establish a permissive period
without further sacrifice or compromise on the rest of the sequence. The methodology of
computing permissive periods was introduced. The effect of phaseskipping due to lack of
traffic demand was also presented. The Timing Implementation Method for Actuated
Coordinated Systems (TIMACS) program was developed to perform the computations of
permissive periods.
Since most previous studies were more specific to certain geometric and phasing
combinations, the qualitative and quantitative evaluation methodology for coordinated
actuated control needed to be fully investigated. In 1994, Chang and Koothrappally [34]
designed a field study to demonstrate the operational effectiveness of using coordinated,
actuated control They concluded 1) there was significant improvement, based on both delay
20
and number of stops, between the semiactuated control, fullyactuated, and pretimed
coordinated timing during the study; 2) there were no significant differences in performance
among all the semiactuated operations as long as the progressionbased signal coordination
timing was developed correctly; and 3) the use of longer background cycle lengths generally
caused fewer arterial stops. However, it would generate much higher overall system delays.
Latenight, Lowvolume Operation of Coordinated Actuated Systems
Coordinating the timing of adjacent signals to promote progressive traffic movement
was recognized as one of the most effective means for reducing vehicular stops, delay, fuel
consumption and exhaust emissions. Early efforts on the subject of signal control always
indicated the need to interconnect signals into a single system and to work toward maimizing
progressive movement during peak periods.
In 1990, Luh and Courage [35] evaluated the latenight traffic signal control strategies
for arterial systems. They stated that latenight, lowvolume arterial signal control involved
a tradeoff between the motorists on the artery and those on the cross street. The
conventional measures of effectiveness such as stops, delay, and fuel consumption were not
appropriate for evaluating this tradeoff Luh and Courage proposed a methodology to
choose between coordination and free operation on arterial roadways controlled by semi
actuated signals when traffic is light. The choice was made on the basis of a disutility function
that was a combination of the number of stops on the artery and the average crossstreet
waiting time. The results indicated that this method provides a promising tool for latenight
arterial signal control
Evaluation of Trafficactuated Control by Simulation
Simulation modeling has become an extremely important approach to analyzing
complex systems. After 1980, more and more simulation modeling was used in traffic
operations. In 1984, Lin and Percy [36] investigated the interactions between queuing
vehicles and detectors for actuated controls, which govern the initiation, extension, and
termination of a green duration. They emphasized that a model used in the simulation analysis
should be calibrated in terms of observed characteristics such as queue discharge headway,
arrival headway, the relationship between the arrival time of a queuing vehicle and the
departure time of its leading vehicle, the number of queuing vehicles in a defined area at the
onset of a green duration, and the dwell time of a vehicle on the detection area. They also
indicated, under a presence control, the chance for premature termination of a green duration
increases when detector lengths are shortened and a detector length of longer than 80 ft can
effectively eliminate the premature termination. Using long detectors, however, results in
longer dwell times and may reduce control efficiency.
Lin and Shen [37] also indicated that the modeling of the vehicledetector interactions
should take into account the stochastic aspects of queuing in relation to detectors. The use
of average characteristics of departure headway could result in underestimates or
overestimates of the probabilities of premature termination of the green.
Later, Lin [38] evaluated the queue dissipation simulation models for analysis of
presencemode fullyactuated signal control The queue dissipation models used in the
NETSIM program and the VIPAS program were evaluated. He indicated that both models
were capable of producing realistic departures of queuing vehicles from the detector area.
22
The models were rather weak, however, in representing other aspects of vehicledetector
interactions. A major weakness of the model in NETSIM was that the simulated movements
of queuing vehicles have little to do with the discharge times generated separately from a
probability distribution. The weakness of VIPAS was that the Pitt carfollowing model used
in VIPAS did not provide a flexible model structure for calibration. Therefore, the outputs
of the model could not be made to conform easily and simultaneously with observed
departure, arrival and dwell characteristics of queuing vehicles.
In 1988, Chang and Williams [39] investigated the assumption that independent
vehicle arrivals at traffic signals, such as in the Poisson distribution, have been widely used
for modeling delay at urban intersections. The study introduced an effective yet economic
approach to estimate the degree of correlation among arriving vehicles under given conditions
and geometric characteristics. With the proposed technique, traffic professionals can easily
determine if the existing delay formulas and other traffic simulation models based on the
Poisson distribution are applicable.
The presence of high variability in traffic simulation results often leads to concern
about their reliability, and consequently precludes a rigorous evaluation of the target traffic
system's performance under various control strategies. In 1990, Chang and Kanaan [40]
presented the variability assessment for NETSIM. The batchmeans method, which allows
the user to assess the variability of parameters, such as the average delay per vehicle, through
a single relative long run, was introduced. This study provided a good contribution to traffic
simulation users, given the large expenditures on computer simulation.
Prediction of Phase Times and Cycle Length for Trafficactuated Control
Trafficrelated phenomena at a signalized intersection, such as lane capacity, delay and
queue length are influenced by the green times (or phase times) and cycle length. For traffic
actuated control, green split and cycle length fluctuate with respect to the traffic demand.
Consequently, it becomes desirable to predict the average phases times and cycle length. The
phase time is equal to the green time displayed plus intergreen time (clearance interval or
duration of yellow plus allred).
In 1982, Lin [7] began to develop a model to estimate the average phase duration for
fullyactuated signals. The model was developed primarily on the basis of probabilistic
interactions between traffic flows and the control He assumed the arrival at the upstream
side of an intersection would be at random, so the arrival pattern in each lane was represented
by a Poisson distribution. Later, Lin and Mazdeyasna [8] developed delay models for semi
actuated and fullyactuated controls that employ motion detectors and sequential phasing.
These models were based on a modified version of Webster's formula. The modifications
included the use of average cycle length, average green time, and two coefficients of
sensitivity reflecting the degree of delay sensitivity to a given combination of traffic and
control conditions. In 1992, Lin [2] proposed an improved method for estimating average
cycle lengths and green intervals for semiactuated signal operations as mentioned before.
In 1994, Ak9elik [9, 10] proposed an analytical methodology for the estimation of
green times and cycle length for trafficactuated signals based on the bunched exponential
distribution of arrival headway. The discussions in his papers were limited to the operation
of a basic actuated controller that used passage detectors and a fixed allowable gap setting.
24
Both fullyactuated and semiactuated control cases were studied. A discussion of arrival
headway distributions was presented since the estimation of arrival headways is fundamental
to the modeling of actuated signal timings. The formulae were derived to estimate the green
times and cycle length based on the bunched exponential distribution of arrival headway.
The bunched arrival model was proposed by Cowan [41] and used extensively by
Troutbeck [42, 43, 44, 45, 46, 47] for estimating capacity and performance of roundabouts
and other unsignalized intersections. The bunched arrival model considers that the bunched
relationship between vehicles increases when the flow arrival rate increases. Since the
bunched arrival model appears to be more representative of reallife arrival patterns in
general, Akgelik used this arrival model for deriving various formulae for the analysis of
trafficactuated signal operations. The random arrival model which uses negative exponential
or shift negative exponential distribution of arrival headway can be derived as a special case
of the bunched arrival model through simplifying assumptions about bunching characteristics
of the arrival stream. The methods given in his papers provide essential information (average
green times and cycle length) for predicting the performance characteristics (capacity, degree
of saturation, delay, queue length and stopped rate) of intersections.
Delay Models for Trafficactuated Control
With the increase of computer software, the comparison of different traffic programs
for pretimed and actuated controls became intuitively appealing. In 1974, Nemeth and
Mekemson [48] compared the delay and fuel consumption between deterministic Signal
Operations Analysis Package (SOAP79) and the microscope and stochastic NETSIM
simulation for pretimed and actuated controls. They indicated that in terms of delay
25
prediction, SOAP79 and NETSIM were found to be entirely compatible except for the
difference in delay definitions.
In 1988, Akcelik [49] evaluated the 1985 HCM [1] delay formula for signalized
intersections. He stated that the HCM formula predicted higher delays for oversaturated
conditions. An alternative equation to the HCM formula was proposed. This formula gave
values close to the HCM formula for degrees of saturation less than 1.0, and at the same time,
was similar to the Australian, Canadian and TRANSYT formulas in producing a delay curve
asymptotic to the deterministic delay line for a degree of saturation greater than 1.0.
The signalized intersection methodology presented in the 1985 HCM [1] introduced
a new delay model Lin [3] evaluated the delay estimated by the HCM with field observed
delay in 1989. Some inconsistency existed in the delay estimation between the HCM results
and field observation. He suggested improving the progression adjustment in the HCM
procedure and using a reliable method to estimate average cycle lengths and green durations
for trafficactuated signal operations.
In 1989, Hagen and Courage [50] compared the HCM [1] delay computations with
those performed by the SOAP84 and TRANSYT7F Release 5. The paper focused on the
effect of the degree of saturation, the peakhour factor, the period length on delay
computations and the treatment of left turns opposed by oncoming traffic. They indicated
that all of the models agreed closely at volume level below the saturation point. When
conditions became oversaturated, the models diverged; however, they could be made to agree
by the proper choice of parameters. The computed saturation flow rates for left turns
opposed by oncoming traffic also agreed closely. However, the treatment of protected plus
26
permitted left turns produced substantial differences. It was concluded that neither SOAP nor
HCM treats this case adequately.
A delay model was recommended in the HCM [1] for levelofservice analysis at
signalized intersections. The use of this model for the evaluation of trafficactuated signal
operations required the knowledge of the average green times and cycle length associated
with the signal operation being analyzed. Since the method suggested in the HCM to estimate
delay of trafficactuated signal operations was not reliable, Lin [2] proposed an improved
method for estimating average green times and cycle length in 1990. The method was
appropriate for semiactuated signal operations. Lin stated that the method was sufficiently
simple and reliable. Realistic examples were used to illustrate the application of the method.
In 1993, Li, Rouphail and Akcelik [4] presented an approach for estimating overflow
delays for lane groups under trafficactuated control using the 1985 HCM [1] delay model
format. The signal timing used in the delay model was from a cyclebycycle simulation
model This study was limited, however, to twophase singlelane conditions. The results
indicated that the signal timings are much related to the controller settings, with longer
extension times producing higher cycle length. It was found that overflow delay increases
with longer extension times. Further, by applying the 1985 HCM delay formula to the
simulated signal settings, the resultant delays were much higher. This implies the need for
calibration of the second delay term to account for the actuated control effects.
Signalized Intersection Capacity Models for Trafficactuated Control
Intersection capacity analysis is essential for measurements of most traffic control
effectiveness. The first U.S. Highway Capacity Manual (HCM) in 1950 contained a chapter
27
for estimating the capacities of signalized intersections. Numerous studies were undertaken
to evaluate the different aspects of signalized intersections, and many capacity methods were
developed. In 1983, May, Gedizlioglu and Tai [51] began the evaluation of eight available
methods for capacity and trafficperformance analysis at signalized intersections including
pretimed and actuated controls. The eight methods included the U.S. Highway Capacity
Manual method (1965), British method (1966), Swedish method (1977), Transportation
Research Board (TRB) Circular 212 planning method (1980), TRB Circular 212 operations
and design method (1980), Australian method (1981), National Cooperative Highway
Research Program (NCHRP) planning method (1982), and NCHRP operations method
(1982). They concluded that the NCHRP operations method and the Australian method were
found to be the most costeffective.
In 1991, Prevedouros [5] studied the traffic measurements and capacity analysis for
actuated signal operations. He verified that the methodology in Chapter 9 of the 1985 HCM
[1] was not appropriate to treat the pretimed and actuated controls identically, especially
concerning the estimation of capacity and performance of existing intersections. The main
sources of error and their potential impacts were presented. He developed a comprehensive
data collection and analysis methodology to complement the procedure in the 1985 HCM.
Overview and Evaluation of EVIPAS
EVIPAS [52] is an optimization and simulation model for actuated, isolated
intersections. It is capable of analyzing and determining the optimal settings of controller
parameters for a wide range of geometric configurations, detector layouts, and almost any
phasing pattern available in a single or dualring NEMA and Type 170 controllers. It will
28
generate the optimized timing settings for controllers ranging from pretimed to volume
density actuated controllers. The optimum settings of timing parameters include minimum
green time, maximum green time, unit extension, minimum gap, time before reduction, time
to reduce, variable (added) initial and maximum initial for each phase.
The value of optimal timing is defined as the timing setting which results in the
minimum "total cost." The model allows the user to define "total cost: to include a variety
of measures of effectiveness, such as delay, fuel consumption, depreciation, other vehicle
costs and emissions. The EVIPAS model allows for two modes of operation. In its
optimization mode, the model is used to obtain optimal timing settings by a multivariate
gradient search optimization module and an eventbased intersection microscopic simulation.
In the simulation mode, EVIPAS allows the evaluation of a prespecified signal plan just by
microscopic simulation.
For the capacity and level of service of trafficactuated control, the performance
outputs are primarily concerned, which includes the summary of delays and signal
performance. The summary of delay table provides delay statistics for the intersection and
for each approach and lane. The summary of signal performance table shows the average
phase length and average cycle length. All above delay measures, average phase length, and
average cycle length are based on the microscopic simulation results.
Since both EVIPAS and TRAFNETSIM are microscopic simulation models, the
phase time comparison between these two models becomes necessary. The phase times
estimated from the EVIPAS simulation model will be compared with those from NETSIM
simulation model later in this chapter.
Preliminary Model Development
The purpose of this study is to accurately predict the average phase times and
corresponding cycle length for actuated operations. The preliminary model developed in this
study is limited to through movements and left turns with "protected only" phasing from an
exclusive lane. However, this preliminary model is very useful for later development of a
complete and comprehensive model.
It is important to note that the proposed preliminary model is mainly based on the
methodology proposed by Courage and Akcelik [6] for evaluating the operation of a traffic
actuated controller in their working paper NCHRP 3481 for National Cooperative Highway
Research Program (NCHRP) project 348, "Capacity Analysis of Trafficactuated Signals."
The proposed analytical model for predicting average phase times and corresponding
cycle length applies several traffic engineering concepts and theories. They include traffic
actuated operation logic, dualring control concept, average phase time prediction for traffic
actuated signals, queue accumulation polygon (QAP) concept, vehicle arrival headway
distribution, circular dependency relationship and sequential process. These concepts and
theories are used for both preliminary and comprehensive model development, and their
model implementation.
In the discussion of the preliminary model, the method in the Appendix I to HCM
Chapter 9 will initially be reviewed following the model development issues. Then, each
concept and theory used in the model development will be presented. Finally, the
computational framework proposed by Courage and Akelik [6] for modeling trafficactuated
controller operations will be summarized.
Review of the Appendix II Method to HCM Chapter 9
In the HCM [1] Chapter 9 Appendix I methodology, an actuated signal is assumed
to be extremely efficient in its use ofthe available green time. Thus, the average cycle length
is estimated using a high critical volume over capacity ratio (v/c) which is approximately equal
to 0.95. In other words, the controller can be effective in its objective of keeping the critical
approach nearly saturated. The formula for the average cycle length may be stated as
C = L/(1Y/X,) (21)
where
C, = the average cycle length;
L = the total lost time per cycle, ie., the sum of the lost times associated with the
starting and stopping of each critical lane group in the phase sequence;
Y = the critical flow ratio, determined as the sum of the flow ratios (v/s) for the
individual lane groups that are critical in each phase. The flow ratio for each
lane group is defined as the ratio of the traffic volume (v) to the saturation
flow rate (s); and
X, = the target degree of saturation (volume/capacity ratio or v/c ratio). A value
of 0.95 is suggested in Appendix II for trafficactuated control
After the average cycle length has been computed, the average effective green time
(g) for each lane group I can be determined by dividing the average cycle length (C,) among
lane groups in proportion to their individual flow ratios ( (v/s) ) over target degree of
saturation (X,). The formula of average effective green time for each lane group may be
stated as
31
= C, [ (v/s) / X ] (22)
The effective green time, rather than the signal displayed green time, is usually used in signal
timing computation which is the signal displayed green time plus the intergreen time (change
interval or yellow plus allred clearance) minus the lost time in the phase.
As mentioned before, the Appendix II method for estimating the signal timing for
actuated operation has been questioned in the literature. There are three major problems with
the Appendix I methodology:
1. The assumption that a trafficactuated controller will maintain 95% saturation on
the critical approach to each phase has not well been accepted. Several studies
have indicated that a somewhat lower degree of saturation often results.
2. The effects of actuated design parameters such as minimum green time, maximum
green time, unit extension and detector configuration are not reflected in the
formula for average cycle length, so it is not sensitive to the above parameters.
3. The simplistic nature of this model does not provide for realworld complications
such as minimum or maximum green time setting, sharedlane permitted left turns,
left turns that are allowed to proceed on both permitted and protected phases,
phase skipping due to lack of demand, constraints imposed by coordination, etc.
In their working paper, Courage and Akgelik [6] indicated that the limitations of
Appendix I technique can be overcome, but not without adding considerable complexity to
the computational procedures. The HCM has traditionally dealt with "single pass" analytical
models that may be described in manual worksheets. The updated version (1994) of HCM
Chapter 9 worksheets are analytically much more complicated, however, they have retained,
32
with one minor exception, their "single pass" characteristics. Therefore, Courage and Ak9elik
proposed a model with a sequential process of multiple iterations to improve the model
addressed in Appendix II with "single pass."
Model Development Issues
Since the entire Chapter 9 methodology has reached the limits of singlepass
procedures, the limitations of Appendix II, as mentioned before, cannot be addressed without
resorting to complex iterative procedures. Because the limitation of the Appendix II
technique is a result of the primitive treatment of actuated control, it may only be overcome
by improving the actuated control model Thus, the model to be developed in this study must
be able to perform effective comparisons between the pretimed and trafficactuated control
modes. The model must also be functionally capable of providing reasonable estimate of
operating characteristics (timing and performance measures) of trafficactuated controllers
under the normal range of practical design configurations. It must be sensitive to common
variations in design parameters. The design parameters include
Actuated controller settings (minimum green time, maximum green time and
allowable gap);
Conventional actuated vs. volumedensity control strategies;
Detector configurations (length and setback);
Pedestrian timings (Walk and Flashing Don't Walk, FDW);
Left turn treatments (permitted, protected, permitted and protected, and not
opposed); and
Left turn phase positions (leading and lagging).
33
Additional input data are needed to improve the accuracy of the analysis methodology.
The information that is already required by the Chapter 9 procedure will naturally be used to
the fullest extent possible to avoid the need for new data. Most of the additional data items
are related to the operation itself The proposed model will be based on the standard eight
phase dualring control concept that is more or less universally applied in the U. S. A. In this
study, a standard assignment of movements to phase is adopted. It can greatly simplify the
development and illustration of all modeling procedures without affecting the generality of
the capacity and level of service results.
It is difficult to analytically deal with the very low volume operation that typically
occurs late at night. Under this condition, the repetitive cyclical operation upon which the
analysis is based no longer applies. The effort required to develop a model for dealing
accurately with delays of a few seconds per vehicle (i.e., level of service A) is difficult to
justify. An approximation of the operating characteristics for very low volumes will generally
be acceptable from a capacity and level of service perspective.
In the literature, many analytical studies on trafficactuated operation assume that
passage detectors are used, whereas in actual practice, presence detectors are much more
common. Passage detectors transmit a short pulse to the controller upon the arrival of each
vehicle. Presence detectors transmit a continuous signal to the controller as long as the
vehicle remains in the detection zone. For purpose of this study, variable length presence
detectors will be assumed. The operation of using passage detectors to detect vehicles may
be approximated by using short length presence detectors.
Trafficactuated Operation Logic
Actuated operation is one kind of traffic control which uses the information collected
by detectors to determine the signal timing of an intersection. The detector type can be either
passage or presence. The main advantage of trafficactuated control is that the traffic signal
can properly display the green times according to traffic demand. There are three types of
actuated controllers. They are semiactuated, fullyactuated and volumedensity.
The operation of the semiactuated signal is based on the ability of the controller to
vary the length of the different phases to meet the demand on the minor approach. Maximum
and minirmm green times are set only for the minor street. Detectors are also placed only on
the minor street. On the other hand, fullyactuated controllers are suitable for an intersection
at which large fluctuations of traffic volumes exist on all approaches during the day.
Maximum and minimum green times are set for each approach. Detectors are also installed
on each approach. The volumedensity control is one kind of actuated control with added
features which 1) can keep track of the number of arrivals, and 2) reduce the allowable gap
according to several rules. It is usually used at intersections with high speed approaches. For
illustration purposes on actuated control logic, a passage detector will first be assumed
because it is simple. Some basic term definitions are addressed as follows:
Initial interval is the first portion of the green phase that an actuated controller has
timed out for vehicles waiting between the detector and stopline during the green
time to go through the intersection.
Vehicle interval, also called "unit extension" or "allowable gap" is the time that the
green time is extended for each detector actuation.
Maximum green time is simply the total green time allowed to the phase.
Minimum green time is the shortest green time that can be displayed.
To avoid vehicles being trapped between the detector and stopline, it is necessary that the
vehicle interval be at least the "passage time" of a vehicle from the detector to the stopline.
Maximum Green Time
Minimum Green Ti Extension Period
trial Int.Ie. It.
Time *
t^
Detector actuation on phase with rightofway
SUnexpired portions of vehicle intervals
Figure 21. The operation of an actuated phase under significant demand.
Figure 21 shows the operation of an actuated phase under significant demand. Prior
to the beginning of the figure, a "call" for green had been put in by the arrival on the studied
approach. Then, the phase with rightofway on this approach will first display the initial
interval plus one unit extension for the arrival The sum of initial interval and one unit
extension is usually called minimum green time. During the minimum green time, if an
36
additional vehicle arrives, as shown in Figure 21, a new unit extension is begun from the time
of detector actuation. The unexpired portion of the old vehicle interval with the shaded area
shown in the figure is wiped out and superseded. If vehicle actuation continues, the green
time will also be extended with the same process until the maximum green time is reached.
The total extension time after the minimum green time is referred to as the extension period.
If the traffic volume is less intense, the extension period will not reach the maximum
green time. When a vehicle interval expires without an arrival of a new vehicle (indicated by
an asterisk [*]), the green time will be terminated and the signal light will turn to yellow plus
red clearance if there is a vehicle waiting for the next subsequent phase. Since in this
illustrated example significant demand is assumed, the maximum green time is reached.
Dualring Control Concept
In a pretimed controller, the controller operates under a single ring sequential timing
process. Each phase is taken as an interval of time in which specified traffic movements are
serviced. Of course, it is possible to have a given movement served on more than one phase
of the sequence, and it is expected that a combination of two nonconflicting movements (two
through, two left turns or a left turn plus through) will be serviced on any one phase.
However, the vast majority of modem traffic control systems use NEMA standard
trafficactuated controllers which employ a dualring concurrent timing process. By keeping
the nonconflicting phases in separate rings, it is capable of displaying them simultaneously
to optimize the combinations of movements which are displayed on each cycle. Since the
standard eightphase dualring operation is more or less universally applied in the U. S. A.,
and in this study a standard assignment oftraffic movements is also based on the dualring
37
NEMA phase configuration, it is essential to be familiar with the dualring concurrent phasing
scheme with assigned movements. The dualring phasing scheme and operation logic will
be presented next.
The standard dualring concurrent phasing scheme using NEMA phase definition is
shown in Figure 22. In Figure 22 phases 1, 2, 3 and 4 are belong to ring 1, while phases 5,
6, 7 and 8 are belong to ring 2. A specific traffic movement is assigned to each NEMA phase
as shown at the corer of each phase box. For example, NEMA phase 2 is an eastbound
through movement and NEMA phase 7 is the southbound left turn. In a standard dualring
concurrent phasing scheme, eastwest movements are assigned to the left side of barrier
(phases 1, 2, 5, 6), whereas northsouth movements are assigned to the right side of barrier
(phases 3, 4, 7, 8). The barrier can be reversed to assign northsouth movements to the left
side and eastwest movements to the right side if needed.
Traffic movements for phases 1 and 2 conflict with each other. It is also true for
phases 3 & 4, 5 & 6, and 7 & 8. Since the conflicting phases on each ring are sequential, on
the side of the barrier, none of the phases within ring 1 will conflict with any of the phases
within ring 2. In such a way, nonconflicting phases can be displayed simultaneously to
optimize the combinations of movements.
An example of the dualring concurrent phasing scheme based on the eastwest
movement in Figure 22 is presented as follows. The phase sequence begins with the non
conflicting combination ofNEMA phases 1 and 5. The next phase sequence can be either the
combination of NEMA phases 1 and 6 or NEMA phases 2 and 5 according to the traffic
demand. If the demand for eastbound left turns is heavier than that of westbound left turns,
38
in general, the combination of phases 2 and 5 will display most of the time. Finally, NEMA
phases 2 and 6 will display.
It is a standard convention to assign the odd number to the left turn in any phase pair
(12, 34, 56, 78), and the even number to the through movement. This reflects the
popularity of leading left turn protection. When the lagging left turn protection is to be
implemented, the phase assignment may be reversed (ie., even number to the left turn).
Although any phase may be theoretically designated as the coordinated phase in each ring, it
is common to designate the phase with through movement on the left side of the barrier as
the coordinated phase. It is necessary to note that the above phasing assignments conform
to those used by the PASSER II arterial signal timing. It has also been adopted by the
WHICH program for mapping data into NETSIM.
Barrier
Ring 1
Ring 2
Left Side of Barrier
( EW Movements )
Right Side of Barrier
( NS Movements)
Barrier
Figure 22. Dualring concurrent phasing scheme with assigned movements.
Average Phase Time Prediction for Trafficactuated Signals
The main objective of this study is to accurately predict the average phase times for
trafficactuated signals. The average phase time includes two major portions of timing. One
is the queue service (clearance) time and the other is the extension time after queue service.
Therefore, accurate phase time predictions are mainly dependent on the accurate predictions
of both queue service times and extension times after queue service.
Before the illustration of the methodology to predict average phase times and cycle
length, some key term definitions need to be addressed first. The phase time is the signal
displayed green time (controller green time) plus the intergreen time. In the signal timing
analysis, the effective green time and the effective red time are frequently used. Therefore,
appropriate conversion of the displayed green time to an effective value is required before the
signal timing analysis.
SR G I
r g
Sgqst e
Phase Time 
Figure 23. The relationships among the components in the phase time.
40
The relationship among phase time (PT), displayed green time (G) and effective green
time (g) shown in Figure 23 is expressed as follows:
PT = G+I = t, +g = t, +gst+g, (23)
subject to PTm < PT < PT,=
In more detail, Equation 23 can be expressed as follows:
PT = t, +Go+EI = t= t+gqt+eg+I = t +g + s+ + t (24)
subject to PT, < PT < PT,
where
I = intergreen time (yellow plus allred);
ti = lost time, which is the sum of startup lost time, t., and end lost time, td;
gq,, G, = the queue service time (saturated portion of green), where gq, = G= ;
e., E. = the green extension time by gap change after queue service, where eg =
EI, and the total extension time, EXT, is defined as (ei+I) or (Eg+I);
ge = the effective extension time by gap change after the queue service period,
where g = e + I td; (25)
PTn, = the minimum phase time, PTm, = G. + I, where G. is minimum green
time; and
PT. = the maximum phase time, PT,= G + I, where G. is maximum green
time.
Queue Accumulation Poygon (OAP) Concept
The analysis of queue accumulation polygon (QAP) is an effective way to predict the
queue service time, gq, (= G.). The QAP is a plot of the number of vehicles queued at the
41
stopline over the cycle. For a single protected phase which could be the through phase or the
protected left turn phase, when traffic volume does not exceed its capacity, QAP is just a
single triangle as shown in Figure 24. In Figure 24, g, stands for actual queue service time
(in this case, gq~ = g), while g, is the effective extension time after queue service. More
complex polygons occur when a movement proceeds on more than one phase.
Based on the vehicle arrival rate q, during effective red time, the accumulated queue
(Qr) before the effective green time can be estimated. The time taken to discharge the
accumulated queue can be computed simply by dividing the accumulated queue of Qr with the
net departure rate (s q) which is equal to the departure rate (s) minus the vehicle arrival rate
(q) during the effective green time. For this simple protected phase, the departure rate s is
equal to the saturation flow rate. The target v/c ratio may be considered in the peak hour
analysis. However, it must be set to 1.0 to determine the actual queue service time. In order
to determine the critical queue service time (gq) of different lane groups within the same
phase, a lane utilization factor is considered in the computation of actual queue service time
(g). In general, g, can be estimated from the following formula:
g = fu q (26)
s(qIXT)
where
fq = a queue length calibration factor [7] proposed by Ak9elik to allow for
variations in queue service time, where
= 1.08 0.1 (G/ G )2 (27)
42
f = a lane utilization factor for unbalance lane usage based on the HCM Table
94;
q, qs = q, is red arrival rate and q. (veh/sec) is green arrival rate (veh/sec);
XT = a specified target volume/capacity (v/c) ratio; and
r, s = r is red time (sec) and s is saturation flow (veh/sec).
In multilane cases, the saturated portion of green time should represent the time to
clear the queue in the critical lane (i.e. the longest queue for any lane) considering all lanes
of an approach in the signal phase. More complex polygons occur when a movement
proceeds on more than one phase. The computation for queue service time is mainly based
on the QAP concept.
o
0
0
oa
.a/
Time (seconds)
Figure 24. Queue accumulation polygon for a single protected phase.
Vehicle Arrival Headway Distributions
Arrival headway distributions play a fundamental role in the estimation of green
extension time, eg (or E), at actuated signals. The bunched exponential distribution of arrival
headways was proposed by Cowan [36], which considers that the bunched relationship
increases among the arriving vehicles when the traffic volume increases. The free
(unbunched) vehicles are those with headways greater than the minimum headway (A), and
the proportion of free vehicles (p) represents the unbunched vehicles with randomly
distributed headways. Thus, the measurement of the proportion of free vehicles (p) depends
on the choice of minimum headway (A). The proportion of bunched vehicles in the arrival
stream is (1p). In this arrival model, all bunched vehicles are assumed to have the same
intrabunched headway (A). The cumulative distribution function, F(t), for this bunched
negative exponential distribution of arrival headways, representing the probability of a
headway less than t seconds, is
F(t) = 1 ype A) for t >A (28)
= 0 fort
where
A = minimum arrival (intrabunch) headway (seconds);
(p = proportion of free (unbunched) vehicles; and
X = a parameter calculated as
SIAq (29)
subject to q < 0.98/A
where
q = total equivalent through arrival flow (vehicles/second) for all
lane groups that actuate the phase under consideration.
A detailed discussion of the application of this model on actuated control and the
results of its calibration using reallife data for singlelane and multilane cases are given in
Akelik and Chung [53]. The more commonly used simple negative exponential and shifted
negative exponential models of arrival headways are special cases of the bunched exponential
model Therefore, in this study, the bunched arrival model is used to estimate the extension
time after queue clearance.
The method for estimating the green extension time, e, for an actuated controller that
uses a passage detector and a fixed gap time (unit extension) setting (e.) was described by
Akqelik [34]. In this study, presence detectors are assumed. The headway (h) between two
consecutive vehicles is equal to the sum of the gap time (e) and the detector occupancy time
(to). Therefore, the headway, hk, that corresponds to the allowable gap time setting, e,, is
h= e. + to (210)
where to is the detector occupancy time given by
to = (Ld +L )/v (211)
where
Ld = effective detector length (ft);
L = vehicle length (ft); and
v = vehicle speed (ft/sec).
There is no need for the estimation of an extension time if the actual queue service
time, g, is less than the minimum effective green time, gn, or g, is greater than the maximum
effective green time, g Ifg, < g< then g willbe set to gan and ifg &> gn then g is equal
to g,. Detection of each additional vehicle between gnn and g in general, extends the
green period by an amount that is, in effect, equal to the headway time, h.. The green period
terminates when the following two conditions are satisfied.
1. the headway between two successive vehicle actuations exceeds the headway that
corresponds to the gap time setting, h > ho (gap change); or
2. the total green extension time after the expiration of minimum green time equals
the maximum extension setting. It is equivalent that g is equal to g..
During a gap change, the green period terminates after the expiration of the gap time.
Assuming that the termination time at gap change is the headway corresponding to the gap
time setting (ho = e. + to), the green extension time, eg, by gap change can be estimated from
the following formula [6, 9, 10] based on the bunched exponential headway distribution.
e 1
eg= pqq (212)
Once the green extension time, e, is obtained, the effective extension time, g&, is just equal
to the sum ofeg and the intergreen, I, minus the end lost time, td, as shown in Equation 25.
46
As mentioned before, the more commonly used simple negative exponential and
shifted negative exponential models of arrival headways are special cases of the bunched
exponential model. For simple negative exponential model, use
A= 0 and (p =1
(therefore X = q)
and for the shifted negative exponential model (normally used for singlelane traffic only), use
P = 1 (therefore X = q / (1 Aq)) (214)
These two models unrealistically assume no bunching ((p =1) for all levels of arrival flows.
The bunched model can be used either with a known (measured) value of (p, or more
generally, with a value of
relationship suggested by Akqelik and Chung [53] can be used for estimating the proportion
ofunbunched vehicles in the traffic stream ((p)
p = e b (215)
The recommended parameter values based on the calibration of the bunched
model by Akqelik and Chung [53] are:
exponential
Singlelane case:
A = 1.5 seconds and b = 0.6
Multilane case (number of lanes =2): A = 0.5 seconds and b = 0.5
Multilane case (number of lanes > 2): A = 0.5 seconds and b = 0.8
(216a)
(216b)
(216c)
(213)
Effect of Phase Skip
The minimum phase time requires more attention when the phase may be skipped due
to low traffic volume. The minimum phase time would only be valid if the controller was set
to recall each phase to the minimum time regardless of demand. On the other hand, the real
significance of the minimum phase time in an actuated controller is that a phase must be
displayed for the minimum time unless it is skipped due to lack of demand. This situation may
be addressed analytically by determining the probability of zero arrivals on the previous red
phase. Assuming a bunched arrival headway distribution, this may be computed by using the
following equation:
POV = p e A) (217)
where
POv = probability of zero arrivals during the previous red phase; and
R = previous red phase time.
So, assuming that the phase will be displayed for the minimum time, except when no vehicles
have arrived on the red, the adjusted vehicle minimum time then becomes
AVM = MnV(1 Po) (218)
where
AVM = the adjusted vehicle minimum time; and
MnV = the nominal minimum vehicle time.
The similar concept for adjusted vehicle minimum time may also be applied to compute an
adjusted pedestrian minimum time.
48
If the phase may be skipped due to lack of demand, the adjusted minimum phase time
is the maximum of adjusted vehicle minimum time and adjusted pedestrian minimum time.
It will be used as lower bound of the predicted phase time. When the Pov for a phase is not
zero, the estimated phase time must also be modified by multiplying the (1Pov) factor to the
original total extension time. Therefore, the predicted phase time becomes
PT = tj +Gqs +(1 Pov) (Eg +I) (219)
Circular Dependency Relationship and Sequential Process
The determination of required green time using the Appendix II method is relatively
straight forward when the cycle length is given. However, trafficactuated controllers do not
work on this principle. Instead, they determine, by a mechanical analogy, the required green
time or phase time given only the length of the previous red interval The green time or phase
time required for each phase is dependent on the green time or phase time required by the
other phases. Thus, a circular dependency relationship exists between actuated phase times.
There are two way to resolve this type of circular dependency. The first one is
simultaneous solutions of multiple equations. The second one is a sequential process
involving repeated iterations that converge toward a unique solution. Either method could
be applied to solve this dependency problem. Since the simultaneous solution will not lend
itself to the complications that must be introduced to solve the more general problem,
Courage and Akgelik [6] proposed and set up an iterative procedure that will apply to the
general problem. This iterative procedure is adopted in this study to predict the average
phase time for general cases, not just limited to the protected phases.
49
An initial set of values for all phase times must be established before the iterative
procedure may begin. With each iteration, the phase time required by each phase, given all
of the other phase times, may be determined. If the minimum phase times turn out to be
adequate for all phases, the cycle length will simply be the sum of the minimum phase times
of the critical phases. If a particular phase demands more than its minimum time, then a
longer red time will be imposed on all the other phases. This, in turn, will increase the phase
time required for the subject phase. Through a series of repeated iterations, the circular
dependency will come to an equilibrium and converge to a unique solution. When the
convergence of cycle length is reached, the final cycle length and phase times are determined.
This convergence may be demonstrated easily by using an simple example. Consider
the intersection shown in Figure 25. This is a trivial intersection with four identical single
lane approaches carrying the through volume of 400 vph. A saturation flow rate of 1900
vphgpl is assumed. Each phase has assigned the following constant parameters:
Detector: 30 feet long, placed at the stopline
Intergreen time (I): 4 seconds
Lost time (t,) 3 seconds per phase
Startup lost time (td): 2 seconds per phase
Minimum phase time: 15 seconds
Allowable gap: 3 seconds
Maximum phase time: 50 seconds
No pedestrian timing features.
No volumedensity features.
N FHE1NS SB
t t
HE1NS NB
Figure 25. The intersection used as an example for circular dependency illustration.
The QAP for the first iteration in this example is shown in Figure 26. Initially, the
"trial time" is the nominal minimum vehicle time (15 seconds in this case) for each phase.
Although this operation has four through phases, it can actually be treated as a twophase
operation because the northbound through phase is identical to the southbound through phase
and the eastbound through phase is the same as the westbound through phase.
Hence, the trial cycle length is equal to 15 x 2 = 30 seconds. This initial timing would
result in an effective red time of 18 seconds for each phase. The traffic volume for each
approach is 400 vehicles per hour. In other words, the arrival rate is equal to 400/3600 =
0.11 vehicles per second. Therefore, during the effective red time, the accumulated queue
can be computed as the product of arrival rate and effective red time, which is equal to 0.11
x 18 = 2 vehicles.
Required phase time
o 3 i
13+5.16+8.3 16.46 see I
S13 15.16 sec 8.3 see
g Isecl I
.11 x 18 2.00 veh I
2
P 0.11 vps 0153 0.11
o* 1  0'42 vps
z 15 + 3 18 sec
effective red r tl gg ge
0 10 20 30
Time (seconds)
Figure 26. Queue accumulation polygon in the first iteration of the illustrated example.
The departure rate is the saturation flow rate (1900 vehicles per hour), so the phase
can discharge (1900/3600)= 0.53 vehicles per second. Therefore, the net service rate is equal
to (0.53 0.11) = 0.42 vehicle per second. Since f is about 1.07 and f, equals 1.0, the actual
queue service time, g, taken to discharge the queue will be (1.07 2) / 0.42 = 5.16 seconds.
The extended green time, e., is 5.3 seconds and intergreen time, I, is 4 seconds. Thus, the
total extension time, EXT (= es + I), is 9.3 seconds (= 5.3 + 4) and the effective extension
time, g equals 8.3 seconds (= 5.3 + 4 1). By using Equation 23, the phase time, PT,
equals the sum of the lost time, tz, the queue service time, gq,, (= g, in this example) and the
effective extension time, g& which is about 16.46 seconds (= 3 + 5.16 + 8.3). By using
Equation 24, PT is equal to the sum oft,, gq,, (= g in this example) and EXT which is also
about 16.46 seconds (= 2 + 5.16 + 9.3). The new phase times produce a new cycle length
52
of (16.46 x 2) = 32.92 seconds. This will generate another version of Figure 26 with
different dimensions. By repeating these calculations with a new cycle length each time, the
computed cycle length will converge to within 0.1 second. Convergence for this example is
especially rapid. The process is very reliable. Table 21 shows the iteration result and
convergence for this trivial example.
Table 21. The iteration results and its convergence for the illustrated example.
Itera Cycle Old Acc. Total Total New New Differ
tion phase queue service time ext. time phase cycle ence
time (= t + g) (= e + I) time
(sec) (sec) (sec) (sec) (sec) (sec) (sec)
1 30.0 15.0 2.00 7.16 9.3 16.5 32.9 2.9
2 32.9 16.5 2.16 7.57 9.3 16.9 33.7 0.8
3 33.7 16.9 2.21 7.68 9.3 17.0 33.9 0.2
4 33.9 17.0 2.22 7.71 9.3 17.0 34.0 0.1
Computational Process
The computation framework with five worksheets proposed by Courage and Ak9elik
[6] for modeling trafficactuated controller operations for simple through and protected left
turn phases is adopted by this study as the basis for more complicated and general model
development. This computation process will be introduced here. The worksheets play a very
important part in overcoming the "black box" image of a complex model such as the one in
this study. They provide a structure for presenting the results of intermediate computations
in a common form that is compatible with their proposed techniques.
53
Worksheet 1 is "Trafficactuated Control Data Input". "Lane Group Data" is shown
in Worksheet 2. Worksheet 3 is "Trafficactuated Timing Computation" and Worksheet 4
is "Required Phase Times". The last worksheet, worksheet 5, is "Extension Times Based on
Allowed Gaps". The worksheet format offered a clear and concise way to document the
information. This format is also consistent with the current HCM. While the worksheets
themselves are quite simple, the overall procedure contains iterative loops. In this research,
the worksheets proposed by Courage and Akgelik will be modified and enhanced for the
computation of more general and complicated scenarios, not just limited to simple protected
scenarios. The complete procedure involving the five worksheets is illustrated in Figure 27.
This figure shows the five worksheets, the main information flow path and two iterative
loops indicated as "Loop A" and "Loop B".
1. Data 2. Lane
A Adjustments SYMBOLS
S^..* Main
Information
Flow
** Worksheets
5. Phase W
Extension n 
Times : Iterative Loops
Fu s
Figure 27. Iterative loops in the phase time and cycle *..... computation procedure.
Figure 27. Iterative loops in the phase time and cycle time computation procedure.
54
Loop A. Required Time Cycle Time Adjustment: This is an external iteration
between Worksheets 3 and 4. It is required to make the phase times converge
to a stable cycle length. Worksheet 4 must also refer to Worksheet 5 if phase
time extensions are required to compute the required phase times.
Loop B. Phase Extension Time: This is an internal iteration within Worksheet 5.
It is only required when gap reduction is employed. When the allowable gap is a
function of the phase time, the phase time cannot be computed without iteration.
Simulation Models
Simulation is one of the most powerful analysis tools available to those responsible
for the design and operation of complex process and systems. Simulation might have more
credibility because its behavior has been compared to that of a real system, or because it has
required fewer simplifying assumptions and thereby has captured more of the true
characteristics of the real system.
NETSIM, a popular and powerful microscopic traffic simulation model, has been
continually developed by the Federal Highway Administration (FHWA) for many years.
NETSIM is able to model an eightphase, dualring controller explicitly, recognizing all of the
phasespecific parameters. EVIPAS is an optimization and simulation model for actuated
controlled, isolated intersections. In the simulation mode, it is also capable of providing
simulated phase times for a wide range of actuated parameter settings. Thus, both the
NETSIM and EVIPAS simulation models could be used as tools to verify the phase time
estimation from the proposed analytical model
Comparison between NETSIM and EVIPAS Simulation Results
Since both NETSIM and EVIPAS are simulationbased models, it becomes necessary
to compare the simulation results between EVIPAS and NETSIM. The current version of
NETSIM (P version 5.0) produces very detailed tables of several performance measures. It
does not, however, provide sufficient information on the operation of the controller itself in
the standard output tables. To obtain this information, it was necessary to develop a
postprocessor to extract the operational data from special files used to support the animated
graphics features ofNETSIM.
The actuatedcontroller data for each second of operation are recorded and stored in
a text file that is given a file name with extension of ".F45" by NETSIM. The format of
".F45" files is hard to read. After it is properly converted, a readable text file can be produced
with extension of".X45". Then, a postprocessor was developed to read the .X45 file and
produce a summary ofthe operation. Both conversion and postprocessor were combined into
a program called "NETCOP" for "NETSIM Controller Operation Postprocessor." It provides
phasespecific information such as percent skipped, percent gapout, percent maxout, average
cycle length, average phase time, adjusted cycle length and adjusted average phase time. The
"adjusted cycle length" is computed by subtracting the number of seconds of dwell (ie., the
time during which no demand was registered on any phase) from the total number of seconds
simulated before dividing by the number of cycles. The adjusted phase time is computed
according to the adjusted cycle length. Since the adjusted phase time from NETSIM can
represent the effective use of phase time, it is adopted for later phase time comparison.
56
Although the simulation techniques used in EVIPAS and NETSIM may differ in some
degree, theoretically, the phase time estimates for the same traffic conditions, geometric
configurations and actuated timing settings should be close. Thus, an evaluation has been
made by comparing the simulated phase times from both NETSIM and EVIPAS based on 9
hypothetical examples with trafficactuated operations. These examples cover both two
phase and multiphase actuated operations. The comparison result is shown in the Figure 28.
In a simple regression analysis between the above two simulated phase times, a 0.96
coefficient of determination, R2, was achieved. As expected, the simulated phase times from
EVIPAS are very close to those from NETSIM simulation, which demonstrates that the
EVIPAS model has the similar effectiveness on phase time estimation as NETSIM.
70
I R2 = 0.96
S50 2
S.......... ...............NETSIM S..... simulated Pha e Ti e ( ec) 
< u a
EM Sate) 
0 10 20 30 40 50 60 70
NETSIM Simulated Phase Time (aec)
Figure 28. Phase time comparison between EVIPAS and NETSIM.
Arterial Considerations
As urban roadways become more congested, and resources available for building new
facilities become more limited, transportation professionals are exploring all possible
alternatives to improve the existing transportation systems. Fullyactuated traffic signals are
powerful for isolated intersections, but not proper for coordinated intersections. One major
area that holds great potential in reducing urban congestion is the implementation of
coordinated semiactuated traffic signals on arterial streets. Unlike pretimed signals, semi
actuated signals are intrinsically more intelligent and complex to implement and they provide
a better coordination than pretimed signals [34].
In semiactuated operation, detectors are placed only on the minor street and
exclusive left turn lanes on the major street. No detectors are installed for the through
movements on the major street. Under this operation, once there is no detection on the minor
movements, the green will always come back to the through (coordinated) movements on the
major street. Therefore, the major benefit of using semiactuated control is to assign unused
minor street green to the major street. This concept is fundamental to the signal timing
prediction for coordinated semiactuated operation.
In pretimed control, the phase time of each movement is fixed, so the effective green
over cycle length ratio (g/C) for each movement is a constant. Unlike pretimed signals, the
phase time of each lane group for actuated signals does not stay constant but fluctuates from
cycle to cycle, so the g/C ratio for each movement fluctuates. Therefore, the major difference
between pretimed and trafficactuated intersections lies in the g/C. The g/C ratio is important
because it is required for the capacity and delay computation. It is necessary to note that the
58
coordination for actuated signals must be provided by some form of supervision which is
synchronized to a background cycle length. Since coordinated semiactuated control is
frequently used at intersections along an artery, the g/C ratio of the critical throughlane
group on the major street is especially important.
The true g/C ratio of each movement is difficult to access in current practice directly
from a traffic controller. Therefore, an alternative for obtaining the g/C ratio is needed. It
is found, in general, that the g/C ratio on a major street is high when the demand on minor
streets is low, and vice versa. This observation suggests the potential for using minor street
traffic demand measures to predict the major street g/C ratio. To verify the concept of the
assignment of unused minor street green to the major street, attempts have been made to
quantify the relationship between the major street g/C ratio and minor street traffic demand.
100
S0 Low Medium High
0
'a
0C
Minor Street Demand, x
Figure 29. Conceptual relationship between major street g/C and minor street demand.
59
Since traffic volume and detector occupancy are easy to measure with reasonable
accuracy for minor street demand, a conceptual model focusing on these two variables was
developed to predict the major street g/C ratio. As the minor street demand, x, increases
from zero, the major street g/C ratio, y, should start as a sharply decreasing function. The
rate of decrease should attenuate as x increases. The conceptual relationship between y and
x is shown in Figure 29.
Data Acquisition
Data from a closed loop signal system were used for the calibration of the candidate
models. The data set includes 98 intersection records generated from four coordinated semi
actuated intersections during seven time periods along SW 34th St. in Gainesville, Florida.
A layout of the arterial system is shown in Figure 210. The SW 34th St. artery is a major
street, and Radio Rd., Hull Rd., SW 20th Ave. and Windmeadows are four minor streets.
Protected left turn signals exist on the major street at all four intersections.
N
1 Radio Rd.
2 Hull Rd.
SW 20th Ave. 3
Archer Rd.
Windmeadows
SW 34th St.
Figure 210. The location of four studied intersection.
60
The Traffic Actuated Controller Monitor/Analyzer (TACMAN) computer package
[54] uses information collected by a microcomputerbased control system, the Signalized
Intersection Monitor (SIMON) [54], to produce hourly phasespecific descriptive information
and performance measures. The descriptive information includes traffic volume, detector
occupancy, etc., and performance measures include stops, delay and fuel consumption. The
measures used in the study pertain to the critical movements.
Model Calibration
Statistical Analysis System (SAS) [55] programs were applied to perform correlation
and regression analyses. Regression techniques were used to calibrate the parameters of the
conceptual models. Regression results show that either the minor street volume or detector
occupancy can explain most of the variation in the major street g/C. Furthermore, the F and
t values indicate that both candidate models are overall significant and the coefficients in each
model are also individually statistically significant. The power model (volume model)
produced the highest adjusted R2 using the traffic volume data, while the logarithmic model
(occupancy model) was better for detector occupancy data. These two models can be
expressed as follows:
MAJG = 100(1 + 0.01 VOLUME) 3045 Adj. R2= 0.88 (220)
MAJG = 100 12.0954 LN(1 + OCCUPANCY) Adj. R2 = 0.91 (221)
where
MAJG = g/C ratio (%) for the major street critical through movement;
VOLUME = hourly volume for the minor street critical movement; and
OCCUPANCY = hourly detector occupancy for the minor street critical movement.
61
The curves for these two minor street demand measures are shown in Figures 211
and 212, respectively. As expected, the shape of both curves conforms to the described
conceptual model Although the occupancy model might be slightly better than the volume
model, the volume model may frequently be used because minor street volumes are often
known, estimated or forecast when no information is available about detector occupancy.
Based on the concept that the unused minor street green time is assigned to the major
street in coordinated semiactuated operation, the relationship between the g/C ratio of the
critical throughlane group on a major street (major street g/C ratio) and the traffic demand
of the critical movement on minor streets (minor street demand) was quantified by the above
volume model and occupancy model In the further study, this concept will continue to be
implemented in the phase time estimation for coordinated semiactuated operation.
S100
o 90
0 80
S70'
S60
50 Ii  ,
0 100 200 300 400 500
Minor Street Traffic Volume (vph)
Figure 211. Prediction of the major street g/C ratio based on a power model for
minor street traffic volume.
0 5 10 15 20 25 30
Minor Street Detector Occupancy (%)
Figure 212. Prediction of the major street g/C ratio based on a logarithmic model for
minor street detector occupancy.
CHAPTER 3
MODEL DEVELOPMENT
Introduction
The scope of the preliminary model development presented in chapter 2 was limited
to basic through movements and protected left turn movements from an exclusive lane. This
chapter continually explores the analytical basis for extensions of the preliminary methodology
to cover permitted left turns in both shared and exclusive lanes and the complicated
compound left turn protection (Le., protected plus permitted phasing or permitted plus
protected phasing).
Determination of Arrival Rates
In the previous analytical work, the arrival and departure rates were constant
parameters determined externally. The arrival rates were determined by the specified traffic
volumes and the departure rates were determined by the saturation flow rates. Neither
depended on the signal timing. In fullyactuated operation which is very often used at an
isolated intersection, the progression effect is not considered, therefore, the arrival type 3
(green arrival rate = red arrival rate) is appropriate. For coordinated semiactuated operation,
since the progression effect is an important consideration, the use of different arrival types to
represent progression quality is required. The derivation of arrival rate is presented first in
this chapter for later application on coordinated semiactuated intersections.
64
With arrival type 3, the arrival rate is constant over the whole cycle at q veh/sec. With
other arrival types, two different arrival rates must be computed. q, is the arrival rate on the
green phase, and q, is the arrival rate on the red phase. For a given average arrival rate, the
values of q and q, will depend on the platoon ratio, Rp, associated with the arrival type, and
the green ratio, g/C, which is a part of the timing plan. The HCM defines the platoon ratio
as follows:
Rp = PC/g (31)
where
P = the probability of arrival on the green;
g = the green time for the phase; and
C = the cycle length.
Basic Continuity Relationship: qr + qgg = q(r+g)
o
o q = average arrival rate
r g
A. r
(t:___ O____
Time (seconds)
Figure 31. Arrival rate over a full cycle with coordinated operation.
65
From Equation 31,
P = R g/C
Now, with arrival type 3, R = 1, so P = g/C, and q == q = On the other hand, if Rp 1,
then the arrival rates will be different on the red and green phases, as illustrated in Figure 31.
The problem is to determine q and q given q, Rp, g and C.
From Equation 31:
P(r+g)
g
But, by definition,
p gqg
q(r+g)
Sgqg(r+g)
q(r+g)g
R q
q
Therefore,
qg = qR
(32)
As an extension of this derivation, the red arrival rate may be determined from the continuity
relationship shown on Figure 31.
qrr + qg = q(r+g)
From which,
qrr = q(r+g) (qR)g
Therefore,
q(r+g) (qR)g (33)
r
Permitted Left Turn Phasing
Before beginning the discussion of permitted left turn (LT) phasing, the concept of
green time determination for a protected phase is briefly reviewed first. This concept is based
on the queue accumulation polygon (QAP) shown in Figure 32 which was presented earlier.
It is convenient to be shown here again for the illustration. The QAP shows the number of
vehicles accumulated in a queue on a signalized approach over one cycle of operation. Each
cycle is assumed to repeat the same pattern indefinitely. The number of vehicles accumulated
at any time in the cycle may be determined as the difference between the cumulative arrivals
and departures since the start of the cycle.
The queue accumulation increases throughout the red phase at the rate ofq, veh/sec.
The maximum accumulated queue occurs at the end of the red phase, and is indicated on
Figure 32 as Q. During the green phase, the queue decreases at the net departure rate, (s 
q), until it has been fully serviced. The time required to service the actual queue is indicated
on Figure 32 is g. The green phase will continue until the occurrence of a gap in the arriving
67
traffic of sufficient length to cause the controller to terminate the phase. The effective
extension time is indicated on Figure 32 as g,. Of course, this whole process is subject to
a specified maximum phase time. An analytical model for predicting g,, g& and average phase
time, PT, was presented in the preliminary methodology. In this simple case, the queue
accumulation polygon is just a triangle. In the remainder of the cases to be discussed in this
dissertation, the QAP will assume a more complex shape.
r
!* Qr
Time (seconds)
Figure 32. Queue accumulation polygon for a single protected phase.
Permitted Left Turns from Exclusive Lanes
The basic QAP concept may be extended to cover a slightly difficult case in which
a permitted left turn is from an exclusive lane, yielding to oncoming traffic, instead of a
protected movement. This introduces a couple of important changes in the QAP. Since the
number of opposing lanes, np, may influence the net arrival rate during the period when the
opposing queue is being serviced, it will be considered for the permitted left turns form
opposing queue is being serviced, it will be considered for the permitted left turns form
68
exclusive lanes. Based on the number of opposing lanes, the QAPs for condition 1 (nW, > 1)
and condition 2 (np = 1) shown in Figures 33 and 34 are discussed, respectively.
If the number of opposing lanes is greater than one (see Figure 33), the queue
continues to accumulate throughout the first part of the green with the arrival rate of q, while
the opposing queue is being serviced. The time required to service the opposing queue is
indicated on Figure 33 as gq. There is no chance for a permitted left turner to make a
maneuver during the period ofgq. The maximum queue, indicated on Figure 33 as Qq, can
be computes as follows:
Qq Q +qg *gq (34)
If the number of opposing lane is equal to one (see Figure 34), the left turns from the
opposing lane do create the chance for the left turns from the exclusive left turn lane to make
maneuvers. According to the HCM Chapter 9, the adjusted saturation flow rate, s,, during
the period ofgq can be computed using the following formula:
sq = / EL2 (35)
where
sq = the permitted saturation flow rate during the period of g;
s = the protected saturation flow rate; and
E, = the left turn equivalence as determined from Equation 922 in the HCM.
the queue continues to accumulate throughout the period of g with the net green arrival rate
of (q sq) while the opposing queue is being serviced. The maximum queue, indicated on
Figure 34 as Qq, can be computes as follows:
Qq = Q + (q s,) *gq (36)
69
Thereafter, the LT vehicles will filter through the opposing traffic at a rate determined
by the opposing volume. This is indicated on Figures 33 and 34 as the permitted saturation
flow rate, Sp. The net departure rate is shown as the difference between the permitted
saturation flow rate and the green arrival rate, which is equal to (s, q.). Fortunately, the
HCM Chapter 9 worksheets already provide the means to compute these values. The value
of gq is determined explicitly on the supplemental worksheet for permitted left turns. The
value of permitted saturation flow rate, s,, may be determined as
s, = s / EL (37)
where
s, = the permitted saturation flow rate;
s = the protected saturation flow rate; and
ELI = the left turn equivalence as determined from Figure 97 in the HCM.
0
4 Qq
4)qg
SQ
S.S q8
r
Time (seconds)
Figure 33. Queue accumulation polygon for a permitted left turn from an exclusive
lane with opposing lane number greater than one.
o q
.B Qr q sq5
I I s
s 1 i q8
o qr Iq
Sr
Time (seconds)
Figure 34. Queue accumulation polygon for a permitted left turn from an exclusive
lane with opposing lane number equal to one.
Green Time Extension for Permitted Movements
The model for estimating the effective green time extension, g, assumes that the
arrivals after the queue has been serviced will be freeflowing as they cross the detector. This
will not be the case for permitted left turns. A complex stochastic model would be required
to treat this situation in detail
It should, however, be possible to use the left turn equivalence, ELI, described above
as an approximation in this situation. In other words, the equivalent through volume, VL EL,
would be used in place of the actual left turn volume, VL The green extension time must be
determined using an equivalent through volume of(VT + VLELI) in place of the actual volume
of (VT + V).
Effect of Sneakers
Sneakers are permitted LT vehicles that exit the intersection at the end of the green
phase, usually during the intergreen interval It is common to assume that a maximum of two
vehicles per cycle may be released from the queue. Sneakers are treated implicitly in the
Chapter 9 worksheets by imposing a lower limit of two vehicles per cycle on the capacity of
each exclusive LT lane with permitted movements. For purposes of this analysis, sneakers
must be recognized explicitly in the QAP. This requires the definition of some new terms:
Maximum Sneakers, Sm: The maximum number of LT vehicles released at the end
of the green phase assuming that the LT queue has not already been serviced.
Permitted phase terminal queue, Qp: The number of vehicles accumulated at the
end of the permitted phase before sneakers have been released.
Adjusted permitted phase terminal queue, Qp: The number of vehicles accumulated
at the end of the permitted phase after sneakers have been released.
Actual Sneakers, Sa: The actual number of sneakers released at the end of the green
phase. This is determined as Min (Sm, Qp).
For the purpose of illustration, the effect of sneakers on the QAP for the condition,
np > 1, is shown in Figure 35. This illustrates the case in which the phase is terminated by
the maximum green time before the queue of LT vehicles is completely serviced. If Qp is
greater than zero, then the maximum phase length will be displayed as a pretimed equivalent.
The adjusted permitted phase terminal queue, Qp', is equal to Qp minus Sa. If Qp is greater
than zero, then the v/c ratio for the approach will be exceeded. These parameters will be
involved in a more complex way in the analysis of compound left turn protection.
i Qq
Sqgq
I Qr ... / Spqg
Sr Qp
 S
Time (seconds)
Figure 35. Queue accumulation polygon for a permitted left turn from an exclusive
lane with sneakers.
MultiLane Approaches
IfLT vehicles are accommodated in an exclusive lane, it is reasonable to assume that
there will be additional lanes available to handle the through traffic. It is also expected that
the detectors installed in both the through and left turn lanes will activate and extend the same
phase. Under these conditions, the queue service time, g,, for the through and LT lanes will
be different. The required phase time (RPT) is the sum of lost time (t), effective extension
time (g = g + I t, ) and the maximum value of through queue service time, g, (= g), and
left turn queue service time, gq,(= g + g,):
RPT = Max ( Through gq, Left turn g,) + t, + g (38)
and eg must be determined using an equivalent through volume of(VT + VLEL) in place of the
actual volume of(VT + VL).
Shared Lane Permitted Left Turns
The shared lane permitted left turn case is only slightly more complicated than the
exclusive lane permitted left turn case. The additional complication may be seen in the QAPs
shown in Figures 36 and 37. The concept of free green, g,& must be introduced here. In an
exclusive left turn lane, the first vehicle in the queue will always be an LT vehicle. However,
in a shared lane, the first vehicle could be either a through or LT vehicle. The portion of
effective green blocked by the clearance of an opposing queue is designated as gq. During the
time, an LT vehicle may be stopped by the opposing traffic, but a through vehicle will not.
Until the first leftturning vehicle arrives, however, the shared lane is unaffected by left
turners. The free green represents the average green time from the beginning of green that
will be available to move through vehicles in the shared lane. The Chapter 9 supplemental left
turn worksheets provide a method for computing gq and gf As indicated on Figures 36 and
37, there will be a net discharge rate of(s q) during the free green interval, and the queue
remaining at the end of the interval is represented as Q,
The computation for queue service time, gq, is more complicated for a shared lane
than that for an exclusive left turn lane or through lane. Basically, the gq for a shared lane
can be divided into two parts. One is the green time before the beginning of the actual queue
service time (g&), and the other one is g, itself
In Figure 36, since g, is greater or equal to g,, the gq, is just equal to the sum of g
and g, Note that according to the HCM Chapter 9, Q, can be computed based on the number
of the opposing lanes. The detail description for the computation of Qq is in the HCM
Chapter 9. Figure 37 represents the scenario that gq is less than gf. The accumulated queue,
74
Q, which belongs to through vehicles, will be served at a net service rate of(s qa). Assume
the time to clean all of these accumulated through vehicles is designated as &. Ifgf is less than
g, then gqg, will equal the sum ofgf and g&. On the other hand, ifgr is greater or equal to go
then g just equals g, because g, is zero for this condition. The time to clear all accumulated
through vehicles, g, may be represented by Equation 26. The computation for gq, may be
summarized as the following equations. If g is greater than or equal to g, the queue service
time, gq can be computed as
g& = gq + gs (39)
Ifgq is less than g, the formula for the computation of the queue service time, g, becomes
gst = gf + g when g,<&g (310)
gqst = gt when gf&g& (311)
The remainder of Figures 36 and 37 follows the same process as the exclusive lane
cases shown in Figure 33 and 34. The permitted movement saturation flow rate for the
shared lane must, however, be computed somewhat differently. In an exclusive LT lane, the
left turn equivalence, EL, was applied to all of the vehicles in the LT lane. In a shared lane,
it is only appropriate to apply this factor to the LT vehicles. So, s, should be computed as
s
sp 1 + PL(EL 1) (312)
where
PL = the proportion of left turns in the shared lane, as computed by the supplemental
worksheet for permitted left turns, and all other terms are as defined previously.
75
eg should be computed in the same manner as described for the exclusive LT lane case and
using an equivalent through volume of (V, + V, EI) instead of the actual volume.
o
0
3
.0 I
o qr Qf
z 1
1 s I Pqg
Z7, ^
Time (seconds)
Figure 36. Queue accumulation polygon for a permitted left turn from a shared lane
(gq> g).
Qr
0 0
.9 sqg
i 1
qr ff
Sspqg
Time (seconds)
Figure 37. Queue accumulation polygon for a permitted left turn from a shared lane
(gq <&.
Compound Left Turn Protection
The QAP concept may be extended to cover the case in which an LT movement
proceeds on both permitted and protected phases from an exclusive lane. One important
difference between the simple permitted LT phasing and the compound protected LT phasing
is the assignment of detectors to phases. It is assumed that detectors will be installed in all
LT lanes to ensure that LT vehicles will not face a permanent red signal. The discussion of
simple permitted LT phasing assumes that the detector in the LT lane (either shared or
exclusive) will actuate the same phase as the concurrent through traffic. On the other hand,
it is logical to assume that a protected left turn will have a detector that actuates the protected
left turn phase. This has very important implications for the analysis of compound left turn
protection. It means that LT vehicles will not extend the permitted phase. When they occupy
the detector during the permitted phase, they will simply be placing a call for their own
protected phase. In the analysis of compound left turn protection, it is necessary to make a
strong distinction between protected plus permitted (leading), and permitted plus protected
(lagging) left turn phasings. Each of these cases will be analyzed separately.
Protected Plus Permitted Phasing
The QAP for protected plus permitted phasing is presented in Figure 38. In Figure
38, it is necessary to note that if the number of opposing lanes, n,, is greater than one, s,
will be equal to zero. Keep in mind that the QAP is used for the purpose of determining the
length of the protected phase only. The length of the permitted phase will be determined by
the simple process of its corresponding through phase because there are no permitted left
turns that actuate the detector. The The most important piece of information provided by
77
the QAP in this case is the size of the queue accumulated at the beginning of the green arrow,
Q0. With protected plus permitted phasing, this is equal to the queue at the end of effective
red time, Q, Given %Q, the determination of green time follows the simple procedure for
protected movements.
r
SQr = Qga
Pqr
o4 q
QP S \Isqg
Figure 38. Queue accumulation polygon for protected plus permitted LT phasing with
an exclusive LT lane.
Permitted Plus Protected Phasing
This case is illustrated in Figure 39, which is essentially the same as Figure 38,
except that the order of the phases has been reversed. It is very important to note that the
protected (green arrow) phase must be presented last in both cases, because this is the phase
whose length we are trying to determine.
Again, it is needed to know the number of vehicles accumulated at the beginning of
the green arrow phase, Q., which is equal to Q'in this case. This will raise an interesting
78
question. Suppose that the value of Q9 is zero. This could happen if the permitted phase was
able to accommodate all ofthe left turns. Theoretically, the protected phase should never be
called under these conditions. However, there is a stochastic element which dictates that all
of the phases will be called occasionally. In this scenario, the adjusted minimum phase time
will be used to estimate the phase time for this protected phase.
Q1
o
lf Q, g,..
Spqr
r
Time (seconds)
Figure 39. Queue accumulation polygon for permitted plus protected LT phasing with
an exclusive LT lane.
ATime (selications
The analysis presented in this chapter fills the gaps left in the preliminary
methodology. The complete analytical basis for a practical computational method to predict
traffic actuated signal timing are conducted. This method should be sensitive to a wide range
of actuated controller parameters. The QAP concept is especially attractive because it can
provide a clear picture for estimating the signal timing. Another essential benefit is that it can
79
also provide a direct estimate of the uniform delay that is compatible with the current HCM
Chapter 9 delay model The methodology presented in this chapter will be incorporated into
the computational framework described in the preliminary model structure to develop a
complete model implementation for predicting the signal timing at a trafficactuated signalized
intersection. The model implementation and model evaluation will be presented in the next
two chapters, respectively.
CHAPTER 4
MODEL IMPLEMENTATION
Introduction
A specific analysis program, ACT348, was developed by Courage and Lin in this
study as a tool to implement the developed analytical model and procedure to predict the
trafficactuated signal timing. The original worksheets have also been modified in accordance
to the analytical modelto cover all possible movements described in Chapter 3. The ACT3
48 program can produce intermediate outputs in a format identical to the modified
worksheets. The computer program is required because the iterative nature of the procedure
makes it totally impractical for manual implementation. The program is able to evaluate the
proposed analytical models using a variety of data. In this chapter, the computer program
structure and logic are presented.
The analytical model developed in this study is for isolated mode of actuated
operation. An effective method to predict the phase times for coordinated mode of actuated
operation is to apply the analytical model for isolated mode to predict the phase times of
actuated phases and then properly assign the unused phase times to the nonactuated phases
(arterial through movements). By appropriate implementation of the analytical model for
isolated mode, a procedure has been built to predict the phase times for coordinated mode,
which will also be addressed in this chapter.
Structure and Logic of the ACT348 Program
The major structure of the ACT348 program is shown in Figure 41. It is not
difficult to recognize an iterative loop inside the flow chart. The iterative loop is required to
make the cycle time converge to a stable value. The program structure is divided into six
major parts: 1) Data Input, 2) Lane Group Specification, 3) Accumulated Queue
Computation, 4) Extension Time Computation, 5) Required Phase Time Computation, and
6) Cycle Time Adjustments. These six parts will be addressed separately.
Data Input
The data input for the ACT348 program is from the WHICH program, which not
only has a userfriendly input scheme, but also provides sufficient information for actuated
operations. After the data is input, the ACT348 program can be executed from WHICH to
process these data and compute phase times.
In the "control specification" shown in Figure 41, control treatments are determined
first according to the input data. These treatments include left turn types (protected,
permitted or compound protection), phase swaps and overlaps. In addition, a left turn
equivalence, ELi, is computed. Finally, the phase sequence pattern is recorded.
The phase sequence pattern needs to get more attention because in each iteration, it
is required for the accumulated queue computation and phase time prediction. The
computation of most time elements such as g, r, gf and gq in the QAP are also based on the
phase sequence pattern. The initial phase pattern is from the input of WHICH. Due to the
dualring control logic, the phase sequence pattern may change during the iterative process.
Therefore, possible phase sequence patterns are required to be considered in the program.
Figure 41. Major structure of the ACT348 program.
83
There are eight possible cases of phase sequence patterns in all. For the purpose of
illustration, only the phase sequence patterns in the northsouth direction are shown in figures.
Case 1 is a standard case for permitted turns which is shown in Figure 42. Case 2 is the
phase sequence for leading green which is shown in Figure 43. In contrast to Case 2, Case
3 is the phase sequence for lagging green which is presented in Figure 44. Case 4 shown in
Figure 45 is the phase sequence for leading and lagging green. Case 5 is a left turn phase
with leading green which is shown in Figure 46. Case 6 is leading dual left turns, and Case
7 is lagging dual left turns. Cases 6 and 7 are shown in Figures 47 and 48, respectively. In
Cases 6 and 7, the phases for dual left turns will terminate simultaneously. Finally, Case 8
shown in Figure 49 is leading and lagging with dual left turns. Case 4 and Case 8 are
interchangeable. For example, when the volume of northbound left turn volumes are heavy
and through traffic is light, Case 4 may become Case 8.
3 4
7 8
Figure 42. Case 1: Phase sequence for simple permitted turns.
3 4
7 8
Figure 43. Case 2: Phase sequence for leading green.
3 4
7 8
Figure 44. Case 3: Phase sequence for lagging green.
3 4
7 8
Figure 45. Case 4: Phase sequence for leading and lagging green.
3 4
7 8
Figure 46. Case 5: Phase sequence for LT phase with leading green.
3 4
7 8
Figure 47. Case 6: Phase sequence for leading dual left turns.
3 4
7 8
Figure 48. Case 7: Phase sequence for lagging dual left turns.
3 4
7 8
Figure 49. Case 8: Phase sequence for leading and lagging with dual left turns.
In "actuated parameter specification", the actuated parameters are specified based on
each NEMA phase which was defined in Chapter 2. The actuated parameters consist of
minimum initial, maximum initial, minimum phase time, maximum green time, allowable gap
recall, detector configuration and so on. Based on the control specification and the actuated
parameter specification, Worksheet 1: Trafficactuated Control Input Data can be produced
by the ACT348 program.
Lane Group Specification
In "lane group specification", the ACT348 program will determine the phase
movements for each NEMA phase and the lane group movement within each NEMA phase.
For example, ifa NEMA phase includes all left turns, through traffic and right turns, the phase
movement of this NEMA phase will be specified as "LTR". If a lane group within the NEMA
phase is just for through and right turns, it should be presented as "TR". The purpose for this
specification is to associate each of the lane group with its NEMA phase.
87
The lane group specification is convenient and necessary for later computation. For
example, the phase time computation for permitted left turn movement from an exclusive lane
("L") will be different from that for through and right turn movements ("TR"). In addition,
the ACT348 program will also determine the traffic volume (veh/hr), arrival rate (veh/sec),
saturation flow (veh/hr) and departure rate (veh/sec) for each lane group based on the input
data from WHICH. Worksheet 2: Lane Group Data is then generated.
Accumulated Queue Computation
In a new iteration, the most important step is to create a new queue accumulation
polygon (QAP). With the phase sequence pattern, phase times and other information from
the last iteration, the new QAP can be produced easily for simple through or protected
phases. It becomes more difficult in computation for permitted left turns from either an
exclusive or a shared LT lane and compound left turn protection because more information
is required before accumulated queues can be computed.
In the analytical model for permitted left turns from an exclusive lane, the opposing
queue service time, g, is needed for QAP. For the permitted left turns from a shared LT lane,
both gq and free green, gf are required. In the compound LT protection, an exclusive LT lane
is assumed, so gq must be obtained. Fortunately, the method for estimating g and gf has been
presented in HCM Chapter 9, which is used in this study to compute g and g. In the ACT3
48 program, the computation of gq is based on 1994 version of HCM Chapter 9. Since the
computation of& is based on the length of green time in the latest HCM version which may
cause unreliable convergence of cycle length, the method presented in 1985 HCM Chapter
9 is used instead. Based on the number of opposing lanes, there are two scenarios described

Full Text 
DEVELOPMENT OF A TRAFFICACTUATED
SIGNAL TIMING PREDICTION MODEL
By
PEISUNG LIN
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENT FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1995
UNIVERSITY OF FLORIDA LIBRARIES
ACKNOWLEDGMENTS
This dissertation cannot be accomplished without the assistance of many people. I
wish to express my sheerest thanks to my supervisory committee, dear friends and lovely
family who helped make it possible.
First, I would like to express my extreme gratitude to professor Kenneth G. Courage,
chairman of my supervisory committee, for giving me the opportunity to pursue my graduate
studies under his enthusiastic guidance. He not only provided me the financial assistance but
also gave me many levels of support. Every time when I face any difficulty in research, he has
always inspired me with his ingenious idea. His lofty standard has always been a source of
motivation to me. I will never forget what he has done for me during my studies.
Dr. Charles E. Wallace is the Director of Transportation Research Center. Under his
leadership, I felt very warm in my mind when I was in this big family. Although Dr. Wallace
was very busy, he always made time for me. He has provided his professional guidance to
my research and lofty standard to my dissertation. I deeply believe his comments on my
dissertation will be beneficial for my professional career. For this, I am eternally grateful.
Dr. Joseph A. Wattleworth served as one of my committee member. Although he has
been retired, his assistance and personal support are sincerely appreciated.
Dr. Sherman X. Bai has been a source of inspiration and motivation. His technical
support and personal caring were really invaluable to the success of this research. He has
u
helped me far more than being a member of the committee. He has become a good friend of
me. I want to thank him for his professional support and true friendship.
Dr. Mang Tia served as one of my supervisory committee member after Dr. Joseph
A. Wattleworth retired. His assistance in this matter is really appreciated. Without his help,
the requirement for my dissertation cannot be completed.
Dr. Anne WyattBrown served as the outside member. She has been of great help
with her assistance on the improvement of my technical writing. In addition, her patient
instruction, sincere encouragement are highly appreciated.
I am indebted to Dr. Gary Long for his guidance and encouragement during my
studies although he is not on my supervisory committee. Special thanks go to William M.
Sampson, manager of McTrans Center, and Janet D. Degner, Manager of Technology
Transfer Center, for providing me financial assistances and the personal supports.
I would also like to express my gratitude to my colleagues for their assistances. I like
to thank ShiowMin Lin, YuJeh Cheng, ChengTin Gan, JerWei Wu, MinTang Li, Chian
Chi Jiang and Randy Showers for their encouragements. I also like to extend my thanks to
David Allen, David Hale, Jim Harriott and James Kreminski for their proofreadings.
Finally, I want to express my deep appreciation to my family. My parents, Chang
Lang Lin and LiChen Hsu, continually supply me their unwavering love, sincere inspiration
and selfless support throughout my life. My brother, PeiYi Lin, and my sister, LiLing Lin,
continually give me their encouragements and supports. My wife and best friend, HuiMin
Wen, is willing to share every good time and bad mood with me. Her patience and love give
me the warmest feeling and the best support to complete my research.
TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS Ã¼
LIST OF TABLES vi
LIST OF FIGURES vÃ¼
ABSTRACT xÃ¼
CHAPTER 1. INTRODUCTION 1
Problem Statement 2
Objectives 4
Organization 5
CHAPTER 2. BACKGROUND 6
Introduction 6
Literature Review 6
Preliminary Model Development 29
Simulation Models 54
Arterial Considerations 57
CHAPTER 3. MODEL DEVELOPMENT 63
Introduction 63
Determination of Arrival Rates 63
Permitted Left Turn Phasing 66
Compound Left Turn Protection 76
Applications 78
iv
CHAPTER 4. MODEL IMPLEMENTATION
80
Introduction 80
Structure and Logic of the ACT348 Program 81
Extension of the Development of Coordinated Operations 91
CHAPTER 5. MODEL TESTING AND EVALUATION 94
Introduction 94
Fullyactuated Operation 94
Coordinated Actuated Operation 105
Further Evaluation of the Analytical Model 108
CHAPTER 6. EXTENDED REFINEMENT OF THE ANALYTICAL MODEL 122
Introduction 122
Refinement of the Analytical Model for Volumedensity Operation . 123
Refinement of the Analytical Model to Incorporate "Free Queue" Parameter 131
Incorporation of the Analytical Model into the HCM Chapter 9 Procedure . 143
CHAPTER 7. CONCLUSIONS AND RECOMMENDATIONS 146
Conclusions 146
Recommendations 149
APPENDIX UNIFORM DELAY FORMULAS 152
BIBLIOGRAPHY 164
BIOGRAPHICAL SKETCH 170
v
LIST OF TABLES
Table Page
21 The iteration results and its convergence for the illustrated example . . . .52
61 Throughcar equivalents, Eu, for permitted left turns in a shared lane
with one free queue 135
62 Throughcar equivalents, EL1, for permitted left turns in a shared lane
with two free queues 136
vi
LIST OF FIGURES
Figure Page
21 The operation of an actuated phase under significant demand 35
22 Dualring concurrent phasing scheme with assigned movements .... 38
23 The relationship among the components in the phase time 39
24 Queue accumulation polygon for a single protected phase 42
25 The intersection used as an example for circular dependency illustration .50
26 Queue accumulation polygon in the first iteration of the illustrated example . .51
27 Iterative loops in the phase time and cycle time computation procedure . . .53
28 Phase time comparison between EVEPAS and NETSIM 56
29 Conceptual relationship between major street g/C and minor street demand . .58
210 The location of studied intersection 59
211 Prediction of the major street g/C ratio based on a power model for minor
street traffic volume 61
212 Prediction of the major street g/C ratio based on a logarithmic model for minor
street detector occupancy 62
31 Arrival rate over a lull cycle with coordinated operation 64
32 Queue accumulation for a single protected phase 67
33 Queue accumulation polygon for a permitted left turn from an exclusive lane
with opposing lane number greater than one 69
Vll
34 Queue accumulation polygon for a permitted left turn from an exclusive lane
with opposing lane number equal to one 70
35 Queue accumulation polygon for a permitted left turn from an exclusive lane
with sneakers 72
36 Queue accumulation polygon for a permitted left turn from a shared lane
(gq>gf) 75
37 Queue accumulation polygon for a permitted left turn from a shared lane
(&,<&) 75
38 Queue Accumulation polygon for protected plus permitted LT phasing with
an exclusive LT Lane 77
39 Queue Accumulation polygon for permitted plus protected LT phasing with
an exclusive LT Lane 78
41 Major structure of the ACT348 program 82
42 Case 1: Phase sequence for simple permitted turns 83
43 Case 2: Phase sequence for leading green 84
44 Case 3: Phase sequence for lagging green 84
45 Case 4: Phase sequence for leading and lagging green 84
46 Case 5: Phase sequence for LT phasing with leading green 85
47 Case 6: Phase sequence for leading dual left turns 85
48 Case 7: Phase sequence for lagging dual left turns 85
49 Case 8: Phase sequence for leading and lagging with dual left turns . . . .86
51 Cycle length comparison for a 1.5sec allowable gap setting 96
52 Cycle length comparison for a 3.0sec allowable gap setting 97
53 Cycle length comparison for a 4.5sec allowable gap setting 97
54 Composite cycle length computations with all gap settings 98
viii
55 Percent of phase terminated by maximum green time for each gap setting
56 Phase time comparison between the Appendix II method and NETSIM .
57 Phase time comparison between the proposed model and NETSIM .
58 Intersection configuration of Museum Road and Northsouth Drive on the
campus of the University of Florida
59 Phase time comparison between the analytical model and field data .
510 Phase time comparison between NETSIM and field data ....
511 Phase time comparison between arterial street and cross street .
512 Relationship of estimated phase times between NONACT and NETSIM
513 NETSIM arrival distributions for a singlelink of 100ft length .
514 NETSIM arrival distributions for a singlelink of 1000ftlength .
515 NETSIM arrival distributions for a singlelink of 2000ft length .
516 NETSIM arrival distributions for a singlelink of 3000ft length .
517 Comparison of analytical and simulation model arrival distribution for
singlelane, 100vph flow
518 Comparison of analytical and simulation model arrival distribution for
singlelane, 300vph flow
519 Comparison of analytical and simulation model arrival distribution for
singlelane, 500vph flow
520 Comparison of analytical and simulation model arrival distribution for
singlelane, 700vph flow
521 Comparison of analytical and simulation model arrival distribution for
singlelane, 900vph flow
522 Optimal NETSIM singlelane link length for various phase termination
headway settings
. 99
101
101
102
104
104
106
108
111
111
112
112
114
114
115
115
116
116
IX
523 Comparison of analytical and simulation model arrival distributions for
twolane, 200vph flow 118
524 Comparison of analytical and simulation model arrival distributions for
twolane, 600vph flow 118
525 Comparison of analytical and simulation model arrival distributions for
twolane, 1000vph flow 119
526 Comparison of analytical and simulation model arrival distributions for
twolane, 1800vph flow 119
61 Variable initial feature for volumedensity operation 124
62 Gap reduction feature for volumedensity operation 125
63 Phase time comparison for volumedensity operation with a zero detector
setback 130
64 Phase time comparison for volumedensity operation with a 150ft detector
setback 130
65 Phase time comparison for volumedensity operation with a 300ft detector
setback 131
66 Phase prediction for single shared lane with free queues 142
A1 Uniform delay formula for ingle protected phase 154
A2 Uniform delay for permitted left turns from an exclusive lane (nopp>l) . . 155
A3 Uniform delay for permitted left turns from an exclusive lane (nopp= 1 . 156
A4 Uniform delay for permitted left turns from a shared lane (gq>gf) . . 157
A5 Uniform delay for permitted left turns from a shared lane (gf
A6 Uniform delay for compound left turn protection: HCM Chapter 9 Case 1 . 159
A7 Uniform delay for compound left turn protection: HCM Chapter 9 Case 2 . 160
A8 Uniform delay for compound left turn protection: HCM Chapter 9 Case 3 . 161
x
A9 Uniform delay for compound left turn protection: HCM Chapter 9 Case 4 . 162
A10 Uniform delay for compound left turn protection: HCM Chapter 9 Case 5 . 163
xi
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
DEVELOPMENT OF A TRAFFICACTUATED
SIGNAL TIMING PREDICTION MODEL
By
PeiSung Lin
December, 1995
Chairman: Kenneth G. Courage
Major Department: Civil Engineering
The Highway Capacity Manual (HCM) provides a methodology in Chapter 9 to
estimate the capacity and level of service at a signalized intersection as a function of the traffic
characteristics and the signal timing. At trafficactuated intersections, the signal timing
changes from cycle to cycle in response to traffic demand. An accurate prediction of average
phase times and cycle length is required to assess the performance of intersections controlled
by trafficactuated signals. The current technique in Appendix II of HCM Chapter 9 for this
purpose has not been well accepted.
This dissertation describes a more comprehensive methodology and a more
satisfactory analytical model to predict trafficactuated signal timing for both isolated and
coordinated modes. The proposed methodology and model have been verified by simulation
augmented by limited field studies. The results are very encouraging with respect to their
Xll
general reliability and their compatibility with the current HCM Chapter 9 structure. The
techniques developed in this study would provide an important contribution to the
methodology of traffic engineering for trafficactuated signal timing prediction and improve
the analytical treatment of trafficactuated control in the HCM Chapter 9.
CHAPTER 1
INTRODUCTION
The concepts of capacity and level of service (LOS) are central to the analysis of a
signalized intersection. Level of service is expressed as a letter grade from A through F that
describes the quality of performance of a signalized intersection from the driver's perspective.
It is evaluated based on the average stopped delay per vehicle for various movements within
the intersection. The 1985 Highway Capacity Manual (HCM) [1] prescribes a methodology
in Chapter 9 (Signalized Intersections) to estimate the LOS as a function of the traffic
characteristics and the signal timing.
Intersection traffic control is characterized as "pretimed" if a predetermined timing
plan is repeated cyclically or "trafficactuated" if the operation varies from cycle to cycle in
response to information from traffic detectors on the roadway. Pretimed control is usually
appropriate for constant traffic demand, while trafficactuated control is better suited to
variable traffic demand. Pretimed control is much easier to analyze, but trafficactuated
control offers more in the way of performance to the motorist.
Whether an isolated actuated controlled intersection or a set of coordinated actuated
intersections, the operational performance largely depends on traffic patterns and the actuated
controller parameters to be discussed in this dissertation. A welldesigned actuated control
plan that responds appropriately to traffic demand can significantly reduce delay and fuel
1
2
consumption. More advanced forms of adaptive traffic control strategies were introduced
recently, but the trafficactuated control concepts still play a very important role today.
Because of its superiority, trafficactuated control has become the predominant mode
throughout the U.S.A. in spite of its analytical complexity.
Many trafficrelated measures at a signalized intersection, such as intersection
capacity, vehicle delay and queue length, are determined by the phase times and cycle length.
For trafficactuated control, the phase times and corresponding cycle length vary from cycle
to cycle in response to the traffic demand. Therefore, it becomes desirable to predict the
average phase times and cycle length for trafficactuated control which are the main inputs
in the procedure contained in the HCM Chapter 9 for the computation of intersection capacity
and vehicle delay.
Improvement of the analytical treatment of trafficactuated control presented in the
HCM Chapter 9 is the subject of this dissertation. An enhanced analytical model will be
proposed and tested.
Problem Statement
Capacity and delay are two major measures of effectiveness for the analysis of a
signalized intersection. The procedure contained in Chapter 9 of the HCM is used almost as
a standard to estimate the intersection capacity and vehicle delay. For trafficactuated
operation, accurate estimates of intersection capacity and vehicle delay must rely on accurate
estimates of the signal timing. However, the primary technique, presented in an appendix to
HCM Chapter 9, to predict the signal timing for trafficactuated operation has been the
subject of much criticism in the literature [2, 3, 4, 5, 6],
3
This technique is based on the simple assumption that a trafficactuated controller will
maintain a high degree of saturation (95% in the HCM Chapter 9 procedure) on the critical
approach to each phase. It does not consider any controller parameter that influences the
signal timing in field. This has created many questions in the literature regarding the validity
of the assumption and the simplistic nature of the technique. Therefore, the main deficiency
of the technique in the appendix to HCM Chapter 9 comes from improper analytical treatment
of trafficactuated control.
Some analytical work has been done on estimating individual phase lengths for traffic
actuated operation [2, 6, 7, 8, 9, 10], but a method for treating the entire phase sequence,
given a specified set of traffic volumes, controller parameters and detector placements, does
not exist. Simulation is currently the most reliable method for determining the signal timing.
Simulation is a powerful tool, but its application is best suited to situations that do not lend
themselves to analytical treatment. Furthermore, the signal timing prediction based on
simulation is time consuming.
Therefore, the development of a practical analytical technique to predict traffic
actuated signal timing is very desirable. Such a technique would provide an important
contribution to the methodology of traffic engineering and improve the analytical treatment
of trafficactuated control in the HCM Chapter 9.
In this case, there are three major questions with the development of the traffic
actuated signal timing prediction model The first question is whether the model can improve
the analytical treatment of trafficactuated control in the HCM Chapter 9 procedure on signal
timing prediction. The proposed methodology must be in a form that can be incorporated
4
into the HCM Chapter 9 procedure. The second one is whether the model can treat the entire
phase sequence for a specified set of traffic volumes, actuated controller parameters,
intersection configuration and detector placements. The third question is whether the model
can accurately and quickly predict the signal timing for trafficactuated operation.
Objectives
The signal timing of a trafficactuated signal will vary from cycle to cycle in response
to traffic demand. The goal of this research is to develop an analytical model to accurately
predict the average signal timing for trafficactuated intersection for both isolated and
coordinated modes. Although performance measures (delay, stops, queue length, fuel
consumption, etc.) are sensitive to actuated controller parameters, it is necessary to note that
this study does not include the development of an optimization methodology of the actuated
controller parameters. The specific objectives of the research are stated as follows:
1. Review the literature that deals with the subject of trafficactuated control,
particularly related to signal timing prediction and vehicle delay estimation.
2. Develop a model to improve the analytical treatment of trafficactuated control
in the HCM Chapter 9 on signal timing prediction and present the methodology
in a form that may be incorporated into the HCM Chapter 9 procedure.
3. Assure that the developed analytical model can predict the average phase times
and corresponding cycle length for a specified set of traffic volumes, controller
settings, intersection configuration and detector placements.
4. Test and evaluate the analytical model using simulation and limited field data to
assess its accuracy and feasibility of implementation.
5
Organization
This dissertation includes seven chapters that are devoted to developing an analytical
model to predict the signal timing for trafficactuated control. The first chapter provides a
general introduction to the dissertation topic, problem statement and research objectives.
The next two chapters describe the development of the proposed analytical model.
Chapter 2 presents the background knowledge required for the analytical model development
and a preliminary model that deals with protected movements from exclusive lanes only.
Chapter 3 extends the methodology developed in Chapter 2 to include shared lanes, permitted
left turns and compound left turn protections (permitted plus protected phasing and protected
plus permitted phasing).
The implementation of the proposed analytical model and procedure in a computer
program to predict trafficactuated signal timing is addressed in Chapter 4. The
computational process of this program is also presented.
The comparisons of predicted phase times between the proposed analytical model and
simulation and field data are presented in Chapter 5. An intensive evaluation is also made on
the comparison of vehicular arrivals at the stopline produced by simulation and the proposed
analytical model.
Chapter 6 presents several refinements of the proposed analytical model to achieve
a stronger capability on the phase time prediction. Uniform delay formulations developed in
this study for trafficactuated control are shown in the appendix. The final conclusions and
recommendations are stated in Chapter 7.
CHAPTER 2
BACKGROUND
Introduction
There has been a substantial amount of research conducted on trafficactuated control
which provides essential information for trafficactuated operating characteristics and signal
timing prediction. This chapter first reviews past and current research on the trafficactuated
control followed by the presentation of a preliminary model structure of phase time prediction
for fullyactuated operation. Each traffic control concept or theory that has contributed to
the model development is addressed separately. Next, two simulation models, TRAF
NETSIM (NETSIM) and EVIPAS, which have been adopted by this study as evaluation tools
for the proposed analytical model, are introduced. Finally, a preliminary consideration of
signal timing prediction for semiactuated traffic signal coordination is described. Further
model development and implementation for trafficactuated signal timing prediction will be
mostly based on the background knowledge presented in this chapter.
Literature Review
Trafficactuated control has been used since in the early 1930s. Whether an isolated
actuated controlled intersection or a set of coordinated actuated intersections, the operational
performance is largely determined by the traffic arrival patterns and actuated controller
parameters. The arrival patterns refers to the arrival headway distributions. The basic
6
7
actuated controller parameters include the minimum green time, maximum green time and
allowable gap settings (vehicle interval or unit extension). A welldesigned actuated control
plan that responds appropriately to traffic demand can significantly reduce delay and fuel
consumption. Therefore, shortly after actuated signal control was first introduced,
researchers began to study the influence of traffic arrival patterns and departure characteristics
at a signalized intersection with trafficactuated control. Many researchers also focused on
the optimization of controller settings, detector placement, and the relationship among them
Recently, some researchers began to develop models to predict trafficactuated signal timing
for the purpose of more accurate capacity computation and delay estimation.
Review of past and current research is an area which definitely merits attention. There
has been a substantial amount of research conducted on trafficactuated control which will
contribute to this dissertation.
The development of a trafficactuated signal timing prediction model is the subject of
this study. Thus, the major emphasis of this literature review is on the trafficactuated control
that particularly is related to operation characteristics, vehicle arrival headway distributions
and signal timing prediction models. The procedure contained in the HCM Chapter 9 is used
almost as a standard to analyze signalized intersection capacity and level of service, so the
literature review also covers the methodology for both capacity computation and delay
estimation. One item that needs to be reviewed carefully is a new program called EVIPAS.
The EVIPAS model is an optimization program which is able to analyze and determine the
optimal settings of controller parameters for trafficactuated control. The results of the
testing efforts on EVIPAS are report in this chapter.
8
The main topics of the literature review include
â€¢ Trafficactuated control definitions;
â€¢ Warrants for trafficactuated control;
â€¢ Benefits and operating considerations for trafficactuated control;
â€¢ Effects of coordination and phaseskipping for trafficactuated control;
â€¢ Latenight, lowvolume operation of coordinated actuated systems;
â€¢ Evaluation of trafficactuated control by simulation;
â€¢ Prediction of phase times and cycle length for trafficactuated control;
â€¢ Delay models for trafficactuated control;
â€¢ Signalized intersection capacity models for trafficactuated control; and
â€¢ Overview and evaluation of "Enhancement of the Value Iteration Program for
Actuated Signals" (EVIPAS).
Trafficactuated Control Definitions
Three basic forms of traffic control: pretimed, fullyactuated and semiactuated were
mentioned by Orcutt [11] in 1975. He indicated that pretimed control was used primarily in
the Central Business District (CBD) area, especially where a network of signals must be
coordinated. He defined actuated signals in terms of equipment that responds to actual traffic
demand of one or more movements as registered by detectors. If all movements are detected,
the operation is referred to as "fullyactuated." If detectors are installed for some, but not all,
traffic movements, the term "semiactuated" is applied. Orcutt suggested fullyactuated
control should normally be used at isolated intersections.
9
Precise definitions of the basic controller types were described by the National
Electrical Manufacturers Association (NEMA) standards [12] in 1976. According to the
NEMA standards, the basic controllers include pretimed, semiactuated, fullyactuated
without volumedensity features, and fullyactuated with volumedensity features. In the
remainder of this dissertation, fullyactuated without volumedensity features will be just
called fullyactuated control, and fullyactuated with volumedensity features will be called
volumedensity control.
Warrants for Trafficactuated Control
Warrants for selecting traffic control modes, which are very useful for practicing
engineers, have been researched since the early 1960s. Studies of delay at actuated signals
have been made for the purpose of evaluating warrants for this type of control on the basis
of the information in the 1961 edition of the Manual on Uniform Traffic Control Devices
(MUTCD). This information was expanded by the Texas Department of Highways and
Public Transportation into a graphical format. The graphical relationships were studied in
1971 by Vodrazka, Lee and Haenel [13], who concluded that they provide good guidelines
for selecting actuated equipment for locations where traffic volumes do not warrant pretimed
signals. The current edition of the MUTCD stops short of numerical warrants for choosing
between pretimed and trafficactuated control, but it does suggest certain qualitative
conditions under which trafficactuated control should be implemented.
Benefits and Operating Considerations for Trafficactuated Control
In 1967, Gerlough and Wagner [14] began to compare pretimed control effectiveness
with volumedensity control. They found that trafficactuated control at higher traffic
10
volumes degraded performance. One of the problems cited for volumedensity control was
that the duration of green for each phase was dependent on the estimated queue length at the
beginning of the phase. Difficulties with queue length estimation made this type of control
less effective.
Longloop presence detection operates by producing a vehicle call for the duration
of time that the vehicle is over the detector. This is as opposed to the mode of smallarea
detector operation in which the detector outputs a pulse of less than 0.1 seconds when the
vehicle is first detected. This latter mode of operation is known as passage, pulse or count
detection. The longloop presence detector with fixllyactuated controllers in a mode known
as laneoccupancy control or loopoccupancy control (LOC). LOC operation occurs when
the controller is programmed for an initial green interval of zero. Extensions are set either
to zero or to a very low value. There is no need for a nonzero initial interval or minimum
green time because the long loops continuously register the presence of any vehicles that are
waiting, causing the controller to extend the green until the entire queue is discharged. The
result is a signal operation that responds rapidly to changes in traffic flow.
In 1970, Bang and Nilsson [15] compared LOC operation with small area detector
(pulse detector) operation. They concluded that delay was reduced 10 percent and stops by
6 percent under the same traffic conditions with LOC. In 1975, Cribbins and Meyer [16]
compared pulse and presence detectors. They concluded that the longer the length of the
presence detector on the major approach to the intersection, the longer the delay. They also
concluded that the highest intersection travel time values occurred when either longloop
presence or pulse detectors were used on both major and minor approaches. The intersection
11
travel time was defined here as the average time it takes a vehicle to pass through an
intersection, whether it is stopped or slowed.
Numerous theoretical studies on traffic signal timing were conducted between 1958
and 1970. The theoretical work on pretimed control by Webster [17] in 1958 and Miller [18]
in 1963 has been applied to the computation of optimum cycle lengths as a function of vehicle
arrival rates. It has also been used for evaluating vehicle delay, intersection capacity,
probability of stops and so on. These results were also well validated through the comparison
of field data. In 1969, Newell [19] and Newell and Osuma [20] expanded the body of theory
by developing relationships for mean vehicle delay with both pretimed and actuated control
at intersections of oneway streets and intersections of twoway streets, respectively. Newell
[19] demonstrated that the average delay per vehicle for an actuated signal is less than that
of a pretimed signal by a factor of about three for intersections of oneway streets. Osuma
[20] considered intersections of twoway streets without turning vehicles. For the particular
trafficactuated policy which holds the green until the queue has been discharged, the traffic
actuated control will not perform as well as pretimed control under the following two
conditions: 1) flows are nearly equal on both approaches of a given phase and 2) the
intersection is nearly saturated.
In 1976, Staunton [21] summarized the work of numerous signal control researchers.
In his paper, the comparisons of delay produced by pretimed control and actuated control,
as a function of vehicle volumes, were presented. Staunton demonstrated that fullyactuated
control with 2.5sec extensions will always be better than the best form of pretimed operation,
given optimum settings for all volumes. Longer values for the extensions can easily degrade
12
actuated control performance. His conclusions were based on simulation, but the details of
the detector configuration were not specified. In view of the 2.5sec extension time, short
or passage detectors were probably used in his study. The performance estimates from
Staunton were supported by Bang [22].
In 1981, Tamoff and Parsonson [23] compiled an extensive literature review on the
selection of the most appropriate form of traffic control for an individual intersection. Three
complementary approaches were used to evaluate controller effectiveness: 1) field data
collection using observers to manually measure vehicle volumes, stops and delay; 2)
simulation using the NETSIM model developed by the Federal Highway Administration
(FHWA) to evaluate control system performance; and 3) analytical techniques developed by
the research team and other agencies. The general conclusions from their extensive literature
review were as follows:
1. Pretimed controllers operate most effectively when the shortest possible cycle
length is used subject to the constraints of providing adequate intersection capacity
and minimum green times for pedestrians and vehicle clearance intervals.
2. The delay produced by fullyactuated controllers is extremely sensitive to the value
of the extension that is used. In general, shorter extensions reduce vehicle delay.
3. For small area detectors (motion or pulse detectors), at low and moderate volumes
when extensions of two or three seconds are employed, the use of the fully
actuated controllers will reduce delays and stops over those which can be achieved
using pretimed controllers. When high traffic volumes occur both on the main
street and on the side street causing the controller to extend the green time to the
13
maximum on all phases, the fullyactuated controller will perform as a pretimed
controller, producing comparable measures of vehicle flow.
4. The relative effectiveness of the various control alternatives depends on the quality
of the signal timing employed. A poorly timed actuated controller will degrade
traffic performance to as great an extent as a poorly timed pretimed controller.
Through the detailed evaluation of controller performance, the conclusions by Tamoff
and Parsonson [23] are described as follows: semiactuated controllers produce a higher level
of stops and delays for all traffic conditions than either the fullyactuated or pretimed
controllers. However, for side street traffic volumes that are less than 20 percent of main
street volumes, there is an insignificant difference between semiactuated and fullyactuated
controller effectiveness. Fullyactuated controllers produce significant benefits when used in
an eightphase and dualring configuration over that which would be possible with a four
phase pretimed controller.
From the simulation results on small area detectors for fullyactuated control, the
location of 150 ft produced a level of performance far superior for a 3sec vehicle interval to
that of closer detectors for the approach speed of 35 mph. Tamoff and Parsonson concluded
that it is appropriate to locate the detector such that the travel time is equal to the extension
time. It was also concluded that for volumes in excess of 450 vehicles per hour per lane,
additional improvement can be realized through the use of the added initial feature of volume
density controller for an approach of 35 mph or higher.
They indicated that further modest gains in performance for fullyactuated control
were possible with the use of long loops and short (or zero) initial and extension settings.
14
This application was found to produce a performance similar to a 2sec extension time with
a short loop. From the simulation results, they concluded that LOC was more effective than
pulse detection over a wide range of traffic volumes. LOC offered the further advantage not
reflected by the simulation results of screening out false calls caused by vehicles approaching
but not traveling through the intersection.
Volumedensity controllers provide the greatest benefit at intersections with high
approach speeds where a detector setback in excess of 125 ft from the intersection requires
a variable initial green time. Tamoff and Parsonson found that the variable initial and gap
reduction options of the volumedensity control did not improve the controller's performance
over that of a fullyactuated controller unless the option is used to reduce the vehicle
extension to a value that is less than the one used for the fullyactuated controller. Thus, if
the volumedensity controller is timed to provide a 3sec passage time and a 2sec minimum
allowable gap, its performance will be superior to that of a filllyactuated controller with a
constant 3sec allowable gap. Noted that the above simulation results given by Tamoff and
Parsonson do not properly account for the problem of premature termination of green due to
the variation in queue discharge headways that occur under normal operating conditions.
In 1985, Lin [24] studied the optimal timing settings and detector lengths for fully
actuated signals operating in presence mode using the RAPID simulation model. He
suggested the optimal maximum green for hourly flow patterns with a peaking hour factor of
1.0 was about 10 seconds longer than the corresponding optimal greens with a peaking hour
factor of 0.85, and the optimal maximum green was approximately 80 percent longer than the
corresponding optimal greens. This result was similar to the 1.5 times pretimed split
15
suggested by Kell and Fullerton [25]. Lin indicated that optimal vehicle intervals were a
function of detector length and flow rate. For detectors 30 ,50 and 80 ft long, the use of 2
sec, 1sec and 0sec vehicle intervals can lead to the best signal performance over a wide
range of operating conditions, respectively. The use of vehicle intervals greater than zero
second for detectors 80 ft or longer is not desirable unless the combined critical flow at an
intersection exceeds 1,400 vph.
In order to improve the VIPAS model, a new optimization algorithm and a new
intersection simulation were designed and programmed. The original VIPAS traffic
characteristics and vehicle generation routines were combined with these new models to
create the enhanced version called EVEPAS. In 1987, Bullen, Hummon, Bryer and Nekmat
[26] developed EVIPAS, a computer model for the optimal design of a trafficactuated signal.
The EVIPAS model was designed to analyze and optimize a wide range of intersection,
phasing, and controller characteristics of an isolated, fullyactuated traffic signal. It can
evaluate almost any phasing combination available in a two to eightphase NEMA type
controller and similar phasing structures for a Type 170 controller. The model has been field
tested and validated.
In 1987, Messer and Chang [27] conducted field studies to evaluate four types of
basic fullyactuated signal control systems operating at three diamond interchanges. Two
signal phasing strategies were tested: a) threephase and b) fourphase with two overlap.
Two smallloop (point) detection patterns (single and multipoint) were evaluated for each
type of phasing. They concluded that 1) singlepoint detection was the most costeffective
threephase design; and 2) multipoint detection was the more delayeffective fourphase
16
configuration. Fourphase control characteristically operates a longer cycle length than the
threephase for a given traffic volume. This feature may produce higher average delays unless
the cycle increase is controlled to the extent that the internal progression features of four
phase control can overcome this deficiency.
In 1989, Courage and Luh [28] developed guidelines for determining the traffic
actuated signal control parameters which would produce the optimal operation identified by
SOAP84. They also evaluated the existing signal control parameters on an individual traffic
actuated signal. The significant conclusions are summarized as follows:
Under low volumes, the maximum green settings have little or no effect on the
performance of actuated signal controllers. Under moderate volumes, shorter maximum
greens increase the average delay considerably. Longer maximum greens, however, have no
significant effect on delay. Under high volumes, the maximum green settings become more
important. There is a setting which minimizes average delay. Other settings with longer or
shorter maximum greens will produce more average delays. The optimal maximum green
setting can be achieved by running SOAP under actuated control with an optimal saturation
level set in the BEGIN card. They indicated that the settings that are optimal at some time
may not be appropriate in other times of day.
The value of 0.95, which is the default value used in SOAP actuated control, was
suggested for multiphase operation and a slightly higher saturation level may be desirable for
twophase operation. For approaches with a reasonably even distribution of traffic volume
by lane, settings of 4.0, 2.0 and 1.4 seconds were recommended by the study for one, two and
three lanes as the best values for unit extension, respectively.
17
In the same year, Bullen [29] used the EVIPAS simulation and optimization model
to analyze trafficactuated traffic signals. The variables studied were detector type, detector
placement, minimum green time and vehicle interval. The evaluation criterion was minimum
average vehicle delay. The study showed that the optimum design of a trafficactuated signal
was specific for some variables but relatively unaffected by others. The design was critical
only for high traffic volumes. At low volumes, vehicle delay is relatively unaffected by the
design parameters studied in his paper. The most critical variable Bullen found was vehicle
interval, particularly for passage detectors, where it should be at least 4.0 seconds regardless
of detector placement and approach speed. This conclusion somewhat contradicts previous
study results. However, it should be noted that the EVIPAS model used by Bullen considered
variable queue discharge headways.
Detector configuration is essential to the success of actuated control. Kell and
Fullerton [30] in their second edition of the Manual of Traffic Signal Design in 1991 indicated
the small area detector might ideally be located three or four seconds of travel time back from
the intersection, with the allowable gap set accordingly. Similar principles were proposed in
previous research by Tamoff and Parsonson. Kell and Fullerton also indicated that, in some
states, the detectors setback were determined on the safe stopping distance. The main
purpose is to avoid the dilemma zone in which a vehicle can neither pass through the
intersection nor stop before the stopline. For long loop detectors, they indicated the concept
of loop occupancy can provide good operation when vehicle platoons are well formed. The
use of several smaller loops instead of one long loop was suggested to solve the problem of
random vehicles causing excessive green.
18
In 1993, Bonneson and McCoy [31] proposed a methodology for evaluating traffic
detector designs. They indicated that the safety and efficiency of a traffic detector design can
be determined by the probability of maxout and the amount of time spent waiting for gapout
and the subsequent phase change. The stopline detector and advance loop detector with
presence and pulse mode were discussed, respectively. The methodology presented by
Bonneson and McCoy determined the optimal combination of design elements in terms of
safety (via infrequent maxout) and operations (via a short waiting time for phase change).
The design elements included detector location, detector length, vehicle speed, passage time
settings, and call extension setting). They concluded a large maximum allowable headway
will have an adverse effect on performance by increasing the maxout probability and the
length of wait for phase change.
Effects of Coordination and Phase Skipping for Trafficactuated Control
In 1986, Jovanis and Gregor [32] studied the coordination of actuated arterial traffic
signal systems. In the past, all optimization methods required that each actuated signal be
converted to its nearest equivalent pretimed unit. Using bandwidth maximization as a starting
point, a new procedure was developed by Jovanis and Gregor that specifically accounts for
actuated timing flexibility. Yield points and force offs at noncritical signals are adjusted so
they just touch the edges of the throughband while critical signals are unmodified. This
method was applied to a data set describing midday traffic conditions on an urban arterial
system of six signals in central Illinois. Simulation was used to evaluate these signal timings
and compare them with corresponding pretimed alternatives. They were surprised to find out
that pretimed, coordinated control appeared superior in general to actuated coordinated
19
control in this experiment. They also concluded that the level of service of side streets was
much more important for pretimed than actuated strategies.
In 1989, Courage and Wallace [33] developed the guidelines for implementing
computerized timing designs from computer programs such as PASSER II, TRANSYT7F
and AAP in arterial traffic control systems. The coordination of a group of trafficactuated
signals must be provided by some form of supervision which is synchronized to a background
cycle length with splits and offsets superimposed. Both external and internal coordination of
the local controllers were addressed.
This report focused on the external coordination of traffic signal controllers.
Permissive periods were introduced to indicate the time interval following the yield point
during which the controller is allowed to yield to cross street demand. If the computed splits
are longer than the minimum phase times, it might be possible to establish a permissive period
without further sacrifice or compromise on the rest of the sequence. The methodology of
computing permissive periods was introduced. The effect of phaseskipping due to lack of
traffic demand was also presented. The Timing Implementation Method for Actuated
Coordinated Systems (TIMACS) program was developed to perform the computations of
permissive periods.
Since most previous studies were more specific to certain geometric and phasing
combinations, the qualitative and quantitative evaluation methodology for coordinated
actuated control needed to be fully investigated. In 1994, Chang and Koothrappally [34]
designed a field study to demonstrate the operational effectiveness of using coordinated,
actuated control. They concluded 1) there was significant improvement, based on both delay
20
and number of stops, between the semiactuated control, fullyactuated, and pretimed
coordinated timing during the study; 2) there were no significant differences in performance
among all the semiactuated operations as long as the progressionbased signal coordination
timing was developed correctly; and 3) the use of longer background cycle lengths generally
caused fewer arterial stops. However, it would generate much higher overall system delays.
Latenight. Lowvolume Operation of Coordinated Actuated Systems
Coordinating the timing of adjacent signals to promote progressive traffic movement
was recognized as one of the most effective means for reducing vehicular stops, delay, fuel
consumption and exhaust emissions. Early efforts on the subject of signal control always
indicated the need to interconnect signals into a single system and to work toward maximizing
progressive movement during peak periods.
In 1990, Luh and Courage [35] evaluated the latenight traffic signal control strategies
for arterial systems. They stated that latenight, lowvolume arterial signal control involved
a tradeoff between the motorists on the artery and those on the cross street. The
conventional measures of effectiveness such as stops, delay, and fuel consumption were not
appropriate for evaluating this tradeoff Luh and Courage proposed a methodology to
choose between coordination and free operation on arterial roadways controlled by semi
actuated signals when traffic is fight. The choice was made on the basis of a disutility function
that was a combination of the number of stops on the artery and the average crossstreet
waiting time. The results indicated that this method provides a promising tool for latenight
arterial signal control.
21
Evaluation of Trafficactuated Control by Simulation
Simulation modeling has become an extremely important approach to analyzing
complex systems. After 1980, more and more simulation modeling was used in traffic
operations. In 1984, Lin and Percy [36] investigated the interactions between queuing
vehicles and detectors for actuated controls, which govern the initiation, extension, and
termination of a green duration. They emphasized that a model used in the simulation analysis
should be calibrated in terms of observed characteristics such as queue discharge headway,
arrival headway, the relationship between the arrival time of a queuing vehicle and the
departure time of its leading vehicle, the number of queuing vehicles in a defined area at the
onset of a green duration, and the dwell time of a vehicle on the detection area. They also
indicated, under a presence control, the chance for premature termination of a green duration
increases when detector lengths are shortened and a detector length of longer than 80 ft can
effectively eliminate the premature termination. Using long detectors, however, results in
longer dwell times and may reduce control efficiency.
Lin and Shen [37] also indicated that the modeling of the vehicledetector interactions
should take into account the stochastic aspects of queuing in relation to detectors. The use
of average characteristics of departure headway could result in underestimates or
overestimates of the probabilities of premature termination of the green.
Later, Lin [38] evaluated the queue dissipation simulation models for analysis of
presencemode fullyactuated signal control. The queue dissipation models used in the
NETSIM program and the VIPAS program were evaluated. He indicated that both models
were capable of producing realistic departures of queuing vehicles from the detector area.
22
The models were rather weak, however, in representing other aspects of vehicledetector
interactions. A major weakness of the model in NETSIM was that the simulated movements
of queuing vehicles have little to do with the discharge times generated separately from a
probability distribution. The weakness of VIPAS was that the Pitt carfollowing model used
in VIPAS did not provide a flexible model structure for calibration. Therefore, the outputs
of the model could not be made to conform easily and simultaneously with observed
departure, arrival and dwell characteristics of queuing vehicles.
In 1988, Chang and Williams [39] investigated the assumption that independent
vehicle arrivals at traffic signals, such as in the Poisson distribution, have been widely used
for modeling delay at urban intersections. The study introduced an effective yet economic
approach to estimate the degree of correlation among arriving vehicles under given conditions
and geometric characteristics. With the proposed technique, traffic professionals can easily
determine if the existing delay formulas and other traffic simulation models based on the
Poisson distribution are applicable.
The presence of high variability in traffic simulation results often leads to concern
about their reliability, and consequently precludes a rigorous evaluation of the target traffic
system's performance under various control strategies. In 1990, Chang and Kanaan [40]
presented the variability assessment for NETSIM. The batchmeans method, which allows
the user to assess the variability of parameters, such as the average delay per vehicle, through
a single relative long run, was introduced. This study provided a good contribution to traffic
simulation users, given the large expenditures on computer simulation.
23
Prediction of Phase Times and Cycle Length for Trafficactuated Control
Trafficrelated phenomena at a signalized intersection, such as lane capacity, delay and
queue length are influenced by the green times (or phase times) and cycle length. For traffic
actuated control, green split and cycle length fluctuate with respect to the traffic demand.
Consequently, it becomes desirable to predict the average phases times and cycle length. The
phase time is equal to the green time displayed plus intergreen time (clearance interval or
duration of yellow plus allred).
In 1982, Lin [7] began to develop a model to estimate the average phase duration for
fullyactuated signals. The model was developed primarily on the basis of probabilistic
interactions between traffic flows and the control. He assumed the arrival at the upstream
side of an intersection would be at random, so the arrival pattern in each lane was represented
by a Poisson distribution. Later, Lin and Mazdeyasna [8] developed delay models for semi
actuated and fullyactuated controls that employ motion detectors and sequential phasing.
These models were based on a modified version of Webster's formula. The modifications
included the use of average cycle length, average green time, and two coefficients of
sensitivity reflecting the degree of delay sensitivity to a given combination of traffic and
control conditions. In 1992, Lin [2] proposed an improved method for estimating average
cycle lengths and green intervals for semiactuated signal operations as mentioned before.
In 1994, Akselik [9, 10] proposed an analytical methodology for the estimation of
green times and cycle length for trafficactuated signals based on the bunched exponential
distribution of arrival headway. The discussions in his papers were limited to the operation
of a basic actuated controller that used passage detectors and a fixed allowable gap setting.
24
Both fullyactuated and semiactuated control cases were studied. A discussion of arrival
headway distributions was presented since the estimation of arrival headways is fundamental
to the modeling of actuated signal timings. The formulae were derived to estimate the green
times and cycle length based on the bunched exponential distribution of arrival headway.
The bunched arrival model was proposed by Cowan [41] and used extensively by
Troutbeck [42, 43, 44, 45, 46, 47] for estimating capacity and performance of roundabouts
and other unsignalized intersections. The bunched arrival model considers that the bunched
relationship between vehicles increases when the flow arrival rate increases. Since the
bunched arrival model appears to be more representative of reallife arrival patterns in
general, Akcjelik used this arrival model for deriving various formulae for the analysis of
trafficactuated signal operations. The random arrival model which uses negative exponential
or shift negative exponential distribution of arrival headway can be derived as a special case
of the bunched arrival model through simplifying assumptions about bunching characteristics
of the arrival stream. The methods given in his papers provide essential information (average
green times and cycle length) for predicting the performance characteristics (capacity, degree
of saturation, delay, queue length and stopped rate) of intersections.
Delay Models for Trafficactuated Control
With the increase of computer software, the comparison of different traffic programs
for pretimed and actuated controls became intuitively appealing. In 1974, Nemeth and
Mekemson [48] compared the delay and fuel consumption between deterministic Signal
Operations Analysis Package (SOAP79) and the microscope and stochastic NETSIM
simulation for pretimed and actuated controls. They indicated that in terms of delay
25
prediction, SOAP79 and NETSIM were found to be entirely compatible except for the
difference in delay definitions.
In 1988, Akxjelik [49] evaluated the 1985 HCM [1] delay formula for signalized
intersections. He stated that the HCM formula predicted higher delays for oversaturated
conditions. An alternative equation to the HCM formula was proposed. This formula gave
values close to the HCM formula for degrees of saturation less than 1.0, and at the same time,
was similar to the Australian, Canadian and TRANSYT formulas in producing a delay curve
asymptotic to the deterministic delay line for a degree of saturation greater than 1.0.
The signalized intersection methodology presented in the 1985 HCM [1] introduced
a new delay model. Lin [3] evaluated the delay estimated by the HCM with field observed
delay in 1989. Some inconsistency existed in the delay estimation between the HCM results
and field observation. He suggested improving the progression adjustment in the HCM
procedure and using a reliable method to estimate average cycle lengths and green durations
for trafficactuated signal operations.
In 1989, Hagen and Courage [50] compared the HCM [1] delay computations with
those performed by the SOAP84 and TRANSYT7F Release 5. The paper focused on the
effect of the degree of saturation, the peakhour factor, the period length on delay
computations and the treatment of left turns opposed by oncoming traffic. They indicated
that all of the models agreed closely at volume level below the saturation point. When
conditions became oversaturated, the models diverged; however, they could be made to agree
by the proper choice of parameters. The computed saturation flow rates for left turns
opposed by oncoming traffic also agreed closely. However, the treatment of protected plus
26
permitted left turns produced substantial differences. It was concluded that neither SOAP nor
HCM treats this case adequately.
A delay model was recommended in the HCM [1] for levelofservice analysis at
signalized intersections. The use of this model for the evaluation of trafficactuated signal
operations required the knowledge of the average green times and cycle length associated
with the signal operation being analyzed. Since the method suggested in the HCM to estimate
delay of trafficactuated signal operations was not reliable, Lin [2] proposed an improved
method for estimating average green times and cycle length in 1990. The method was
appropriate for semiactuated signal operations. Lin stated that the method was sufficiently
simple and reliable. Realistic examples were used to illustrate the application of the method.
In 1993, Li, Rouphail and Akcpelik [4] presented an approach for estimating overflow
delays for lane groups under trafficactuated control using the 1985 HCM [1] delay model
format. The signal timing used in the delay model was from a cyclebycycle simulation
model. This study was limited, however, to twophase singlelane conditions. The results
indicated that the signal timings are much related to the controller settings, with longer
extension times producing higher cycle length. It was found that overflow delay increases
with longer extension times. Further, by applying the 1985 HCM delay formula to the
simulated signal settings, the resultant delays were much higher. This implies the need for
calibration of the second delay term to account for the actuated control effects.
Signalized Intersection Capacity Models for Trafficactuated Control
Intersection capacity analysis is essential for measurements of most traffic control
effectiveness. The first U.S. Highway Capacity Manual (HCM) in 1950 contained a chapter
27
for estimating the capacities of signalized intersections. Numerous studies were undertaken
to evaluate the different aspects of signalized intersections, and many capacity methods were
developed. In 1983, May, Gedizlioglu and Tai [51] began the evaluation of eight available
methods for capacity and trafficperformance analysis at signalized intersections including
pretimed and actuated controls. The eight methods included the U.S. Highway Capacity
Manual method (1965), British method (1966), Swedish method (1977), Transportation
Research Board (TRB) Circular 212 planning method (1980), TRB Circular 212 operations
and design method (1980), Australian method (1981), National Cooperative Highway
Research Program (NCHRP) planning method (1982), and NCHRP operations method
(1982). They concluded that the NCHRP operations method and the Australian method were
found to be the most costeffective.
In 1991, Prevedouros [5] studied the traffic measurements and capacity analysis for
actuated signal operations. He verified that the methodology in Chapter 9 of the 1985 HCM
[1] was not appropriate to treat the pretimed and actuated controls identically, especially
concerning the estimation of capacity and performance of existing intersections. The main
sources of error and their potential impacts were presented. He developed a comprehensive
data collection and analysis methodology to complement the procedure in the 1985 HCM.
Overview and Evaluation of EVIPAS
EVIPAS [52] is an optimization and simulation model for actuated, isolated
intersections. It is capable of analyzing and determining the optimal settings of controller
parameters for a wide range of geometric configurations, detector layouts, and almost any
phasing pattern available in a single or dualring NEMA and Type 170 controllers. It will
28
generate the optimized timing settings for controllers ranging from pretimed to volume
density actuated controllers. The optimum settings of timing parameters include minimum
green time, maximum green time, unit extension, minimum gap, time before reduction, time
to reduce, variable (added) initial and maximum initial for each phase.
The value of optimal timing is defined as the timing setting which results in the
minimum "total cost." The model allows the user to define "total cost: to include a variety
of measures of effectiveness, such as delay, fuel consumption, depreciation, other vehicle
costs and emissions. The EVIPAS model allows for two modes of operation. In its
optimization mode, the model is used to obtain optimal timing settings by a multivariate
gradient search optimization module and an eventbased intersection microscopic simulation.
In the simulation mode, EVIPAS allows the evaluation of a prespecified signal plan just by
microscopic simulation.
For the capacity and level of service of trafficactuated control, the performance
outputs are primarily concerned, which includes the summary of delays and signal
performance. The summary of delay table provides delay statistics for the intersection and
for each approach and lane. The summary of signal performance table shows the average
phase length and average cycle length. All above delay measures, average phase length, and
average cycle length are based on the microscopic simulation results.
Since both EVIPAS and TRAFNETSIM are microscopic simulation models, the
phase time comparison between these two models becomes necessary. The phase times
estimated from the EVIPAS simulation model will be compared with those from NETSIM
simulation model later in this chapter.
29
Preliminary Model Development
The purpose of this study is to accurately predict the average phase times and
corresponding cycle length for actuated operations. The preliminary model developed in this
study is limited to through movements and left turns with "protected only" phasing from an
exclusive lane. However, this preliminary model is very useful for later development of a
complete and comprehensive model.
It is important to note that the proposed preliminary model is mainly based on the
methodology proposed by Courage and Ak^elik [6] for evaluating the operation of a traffic
actuated controller in their working paper NCHRP 3481 for National Cooperative Highway
Research Program (NCHRP) project 348, "Capacity Analysis of Trafficactuated Signals."
The proposed analytical model for predicting average phase times and corresponding
cycle length applies several traffic engineering concepts and theories. They include traffic
actuated operation logic, dualring control concept, average phase time prediction for traffic
actuated signals, queue accumulation polygon (QAP) concept, vehicle arrival headway
distribution, circular dependency relationship and sequential process. These concepts and
theories are used for both preliminary and comprehensive model development, and then
model implementation.
In the discussion of the preliminary model, the method in the Appendix II to HCM
Chapter 9 will initially be reviewed following the model development issues. Then, each
concept and theory used in the model development will be presented. Finally, the
computational framework proposed by Courage and Ak?elik [6] for modeling trafficactuated
controller operations will be summarized.
30
Review of the Appendix II Method to HCM Chapter 9
In the HCM [1] Chapter 9 Appendix II methodology, an actuated signal is assumed
to be extremely efficient in its use of the available green time. Thus, the average cycle length
is estimated using a high critical volume over capacity ratio (v/c) which is approximately equal
to 0.95. In other words, the controller can be effective in its objective of keeping the critical
approach nearly saturated. The formula for the average cycle length may be stated as
Cw = L/(1Y/Xc) (21)
where
C^ = the average cycle length;
L = the total lost time per cycle, i.e., the sum of the lost times associated with the
starting and stopping of each critical lane group in the phase sequence;
Y = the critical flow ratio, determined as the sum of the flow ratios (v/s) for the
individual lane groups that are critical in each phase. The flow ratio for each
lane group is defined as the ratio of the traffic volume (v) to the saturation
flow rate (s); and
Xc = the target degree of saturation (volume/capacity ratio or v/c ratio). AvaluÃ©
of 0.95 is suggested in Appendix II for trafficactuated control.
After the average cycle length has been computed, the average effective green time
(gÂ¿) for each lane group I can be determined by dividing the average cycle length (CJ among
lane groups in proportion to their individual flow ratios ( (v/s)j ) over target degree of
saturation (Xc). The formula of average effective green time for each lane group may be
stated as
31
& = C,, [ (v/s), / Xc ] (22)
The effective green time, rather than the signal displayed green time, is usually used in signal
timing computation which is the signal displayed green time plus the intergreen time (change
interval or yellow plus allred clearance) minus the lost time in the phase.
As mentioned before, the Appendix II method for estimating the signal timing for
actuated operation has been questioned in the literature. There are three major problems with
the Appendix II methodology:
1. The assumption that a trafficactuated controller will maintain 95% saturation on
the critical approach to each phase has not well been accepted. Several studies
have indicated that a somewhat lower degree of saturation often results.
2. The effects of actuated design parameters such as minimum green time, maximum
green time, unit extension and detector configuration are not reflected in the
formula for average cycle length, so it is not sensitive to the above parameters.
3. The simplistic nature of this model does not provide for realworld complications
such as minimum or maximum green time setting, sharedlane permitted left turns,
left turns that are allowed to proceed on both permitted and protected phases,
phase skipping due to lack of demand, constraints imposed by coordination, etc.
In their working paper, Courage and Akijelik [6] indicated that the limitations of
Appendix II technique can be overcome, but not without adding considerable complexity to
the computational procedures. The HCM has traditionally dealt with "single pass" analytical
models that may be described in manual worksheets. The updated version (1994) of HCM
Chapter 9 worksheets are analytically much more complicated, however, they have retained,
32
with one minor exception, their "single pass" characteristics. Therefore, Courage and Aki^elik
proposed a model with a sequential process of multiple iterations to improve the model
addressed in Appendix II with "single pass."
Model Development Issues
Since the entire Chapter 9 methodology has reached the limits of singlepass
procedures, the limitations of Appendix H, as mentioned before, cannot be addressed without
resorting to complex iterative procedures. Because the limitation of the Appendix II
technique is a result of the primitive treatment of actuated control, it may only be overcome
by improving the actuated control model. Thus, the model to be developed in this study must
be able to perform effective comparisons between the pretimed and trafficactuated control
modes. The model must also be functionally capable of providing reasonable estimate of
operating characteristics (timing and performance measures) of trafficactuated controllers
under the normal range of practical design configurations. It must be sensitive to common
variations in design parameters. The design parameters include
â€¢ Actuated controller settings (minimum green time, maximum green time and
allowable gap);
â€¢ Conventional actuated vs. volumedensity control strategies;
â€¢ Detector configurations (length and setback);
â€¢ Pedestrian timings (Walk and Flashing Don't Walk, FDW);
â€¢ Left turn treatments (permitted, protected, permitted and protected, and not
opposed); and
â€¢ Left turn phase positions (leading and lagging).
33
Additional input data are needed to improve the accuracy of the analysis methodology.
The information that is already required by the Chapter 9 procedure will naturally be used to
the fiillest extent possible to avoid the need for new data. Most of the additional data items
are related to the operation itself. The proposed model will be based on the standard eight
phase dualring control concept that is more or less universally applied in the U. S. A. In this
study, a standard assignment of movements to phase is adopted. It can greatly simplify the
development and illustration of all modeling procedures without affecting the generality of
the capacity and level of service results.
It is difficult to analytically deal with the very low volume operation that typically
occurs late at night. Under this condition, the repetitive cyclical operation upon which the
analysis is based no longer applies. The effort required to develop a model for dealing
accurately with delays of a few seconds per vehicle (i.e., level of service A) is difficult to
justify. An approximation of the operating characteristics for very low volumes will generally
be acceptable from a capacity and level of service perspective.
In the literature, many analytical studies on trafficactuated operation assume that
passage detectors are used, whereas in actual practice, presence detectors are much more
common. Passage detectors transmit a short pulse to the controller upon the arrival of each
vehicle. Presence detectors transmit a continuous signal to the controller as long as the
vehicle remains in the detection zone. For purpose of this study, variable length presence
detectors will be assumed. The operation of using passage detectors to detect vehicles may
be approximated by using short length presence detectors.
34
Trafficactuated Operation Logic
Actuated operation is one kind of traffic control which uses the information collected
by detectors to determine the signal timing of an intersection. The detector type can be either
passage or presence. The main advantage of trafficactuated control is that the traffic signal
can properly display the green times according to traffic demand. There are three types of
actuated controllers. They are semiactuated, fullyactuated and volumedensity.
The operation of the semiactuated signal is based on the ability of the controller to
vary the length of the different phases to meet the demand on the minor approach. Maximum
and minimum green times are set only for the minor street. Detectors are also placed only on
the minor street. On the other hand, fullyactuated controllers are suitable for an intersection
at which large fluctuations of traffic volumes exist on all approaches during the day.
Maximum and minimum green times are set for each approach. Detectors are also installed
on each approach. The volumedensity control is one kind of actuated control with added
features which 1) can keep track of the number of arrivals, and 2) reduce the allowable gap
according to several rules. It is usually used at intersections with high speed approaches. For
illustration purposes on actuated control logic, a passage detector will first be assumed
because it is simple. Some basic term definitions are addressed as follows:
â€¢ Initial interval is the first portion of the green phase that an actuated controller has
timed out for vehicles waiting between the detector and stopline during the green
time to go through the intersection.
â€¢ Vehicle interval, also called "unit extension" or "allowable gap" is the time that the
green time is extended for each detector actuation.
35
â€¢ Maximum green time is simply the total green time allowed to the phase.
â€¢ Minimum green time is the shortest green time that can be displayed.
To avoid vehicles being trapped between the detector and stopline, it is necessary that the
vehicle interval be at least the "passage time" of a vehicle from the detector to the stopline.
* Detector actuation on phase with rightofway
H Unexpired portions of vehicle intervals
Figure 21. The operation of an actuated phase under significant demand.
Figure 21 shows the operation of an actuated phase under significant demand. Prior
to the beginning of the figure, a "call" for green had been put in by the arrival on the studied
approach. Then, the phase with rightofway on this approach will first display the initial
interval plus one unit extension for the arrival. The sum of initial interval and one unit
extension is usually called minimum green time. During the minimum green time, if an
36
additional vehicle arrives, as shown in Figure 21, a new unit extension is begun from the time
of detector actuation. The unexpired portion of the old vehicle interval with the shaded area
shown in the figure is wiped out and superseded. If vehicle actuation continues, the green
time will also be extended with the same process until the maximum green time is reached.
The total extension time after the minimum green time is referred to as the extension period.
If the traffic volume is less intense, the extension period will not reach the maximum
green time. When a vehicle interval expires without an arrival of a new vehicle (indicated by
an asterisk [*]), the green time will be terminated and the signal light will turn to yellow plus
red clearance if there is a vehicle waiting for the next subsequent phase. Since in this
illustrated example significant demand is assumed, the maximum green time is reached.
Dualring Control Concept
In a pretimed controller, the controller operates under a single ring sequential timing
process. Each phase is taken as an interval of time in which specified traffic movements are
serviced. Of course, it is possible to have a given movement served on more than one phase
of the sequence, and it is expected that a combination of two nonconflicting movements (two
throughs, two left turns or a left turn plus through) will be serviced on any one phase.
However, the vast majority of modem traffic control systems use NEMA standard
trafficactuated controllers which employ a dualring concurrent timing process. By keeping
the nonconflicting phases in separate rings, it is capable of displaying them simultaneously
to optimize the combinations of movements which are displayed on each cycle. Since the
standard eightphase dualring operation is more or less universally applied in the U. S. A.,
and in this study a standard assignment of traffic movements is also based on the dualring
37
NEMA phase configuration, it is essential to be familiar with the dualring concurrent phasing
scheme with assigned movements. The dualring phasing scheme and operation logic will
be presented next.
The standard dualring concurrent phasing scheme using NEMA phase definition is
shown in Figure 22. In Figure 22 phases 1, 2, 3 and 4 are belong to ring 1, while phases 5,
6, 7 and 8 are belong to ring 2. A specific traffic movement is assigned to each NEMA phase
as shown at the comer of each phase box. For example, NEMA phase 2 is an eastbound
through movement and NEMA phase 7 is the southbound left turn. In a standard dualring
concurrent phasing scheme, eastwest movements are assigned to the left side of barrier
(phases 1, 2, 5, 6), whereas northsouth movements are assigned to the right side of barrier
(phases 3,4, 7, 8). The barrier can be reversed to assign northsouth movements to the left
side and eastwest movements to the right side if needed.
Traffic movements for phases 1 and 2 conflict with each other. It is also true for
phases 3 & 4, 5 & 6, and 7 & 8. Since the conflicting phases on each ring are sequential, on
the side of the barrier, none of the phases within ring 1 will conflict with any of the phases
within ring 2. In such a way, nonconflicting phases can be displayed simultaneously to
optimize the combinations of movements.
An example of the dualring concurrent phasing scheme based on the eastwest
movement in Figure 22 is presented as follows. The phase sequence begins with the nonÂ¬
conflicting combination of NEMA phases 1 and 5. The next phase sequence can be either the
combination of NEMA phases 1 and 6 or NEMA phases 2 and 5 according to the traffic
demand. If the demand for eastbound left turns is heavier than that of westbound left turns,
38
in general, the combination of phases 2 and 5 will display most of the time. Finally, NEMA
phases 2 and 6 will display.
It is a standard convention to assign the odd number to the left turn in any phase pair
(12, 34, 56, 78), and the even number to the through movement. This reflects the
popularity of leading left turn protection. When the lagging left turn protection is to be
implemented, the phase assignment may be reversed (i.e., even number to the left turn).
Although any phase may be theoretically designated as the coordinated phase in each ring, it
is common to designate the phase with through movement on the left side of the barrier as
the coordinated phase. It is necessary to note that the above phasing assignments conform
to those used by the PASSER II arterial signal timing. It has also been adopted by the
WHICH program for mapping data into NETSIM.
Barrier
Barrier
Figure 22. Dualring concurrent phasing scheme with assigned movements.
39
Average Phase Time Prediction for Trafficactuated Signals
The main objective of this study is to accurately predict the average phase times for
trafficactuated signals. The average phase time includes two major portions of timing. One
is the queue service (clearance) time and the other is the extension time after queue service.
Therefore, accurate phase time predictions are mainly dependent on the accurate predictions
of both queue service times and extension times after queue service.
Before the illustration of the methodology to predict average phase times and cycle
length, some key term definitions need to be addressed first. The phase time is the signal
displayed green time (controller green time) plus the intergreen time. In the signal timing
analysis, the effective green time and the effective red time are frequently used. Therefore,
appropriate conversion of the displayed green time to an effective value is required before the
signal timing analysis.
Figure 23. The relationships among the components in the phase time.
40
The relationship among phase time (PT), displayed green time (G) and effective green
time (g) shown in Figure 23 is expressed as follows:
PT = G + I = t, +g = t, +gqst + ge (23)
subject to PT^ < PT < PTmax
In more detail, Equation 23 can be expressed as follows:
PT  tsl + Gqst + Eg + I  tsl + gqst + eg +1  ts, + gqst + ge + tsl (24)
subject to PTmin < PT < PTmax
where
I
t,
gqst?
egâ€™
ge
PTâ€ž
PT
max
intergreen time (yellow plus allred);
lost time, which is the sum of startup lost time, tsâ€ž and end lost time, te];
the queue service time (saturated portion of green), where gqst = Gqst;
the green extension time by gap change after queue service, where eg =
Eg, and the total extension time, EXT, is defined as (eg+I) or (Eg+I);
the effective extension time by gap change after the queue service period,
where ge = eg + Itd; (25)
the minimum phase time, PTmm = G^ + I, where G^ is minimum green
time; and
the maximum phase time, IyI nuK = G^ + 1, where G,^ is maximum green
time.
Queue Accumulation Polygon (QAP) Concept
The analysis of queue accumulation polygon (QAP) is an effective way to predict the
queue service time, g^, (= Gqsl). The QAP is a plot of the number of vehicles queued at the
41
stopline over the cycle. For a single protected phase which could be the through phase or the
protected left turn phase, when traffic volume does not exceed its capacity, QAP is just a
single triangle as shown in Figure 24. In Figure 24, gs stands for actual queue service time
(in this case, gqst = g.), while ge is the effective extension time after queue service. More
complex polygons occur when a movement proceeds on more than one phase.
Based on the vehicle arrival rate qr during effective red time, the accumulated queue
(Qr) before the effective green time can be estimated. The time taken to discharge the
accumulated queue can be computed simply by dividing the accumulated queue of Qr with the
net departure rate (s  q^) which is equal to the departure rate (s) minus the vehicle arrival rate
(q^) during the effective green time. For this simple protected phase, the departure rate s is
equal to the saturation flow rate. The target v/c ratio may be considered in the peak hour
analysis. However, it must be set to 1.0 to determine the actual queue service time. In order
to determine the critical queue service time (gqst) of different lane groups within the same
phase, a lane utilization factor is considered in the computation of actual queue service time
(gs). In general, gs can be estimated from the following formula:
g 8ff. ^
8s q u s(q/XT)
(26)
where
fq = a queue length calibration factor [7] proposed by Ak?elik to allow for
variations in queue service time, where
fq = 1.08  0.1 (G / Gmax)2
(27)
42
fu = a lane utilization factor for unbalance lane usage based on the HCM Table
94;
qn qg = qr is red arrival rate and qg (veh/sec) is green arrival rate (veh/sec);
XT = a specified target volume/capacity (v/c) ratio; and
r, s = r is red time (sec) and s is saturation flow (veh/sec).
In multilane cases, the saturated portion of green time should represent the time to
clear the queue in the critical lane (i.e. the longest queue for any lane) considering all lanes
of an approach in the signal phase. More complex polygons occur when a movement
proceeds on more than one phase. The computation for queue service time is mainly based
on the QAP concept.
Figure 24. Queue accumulation polygon for a single protected phase.
43
Vehicle Arrival Headway Distributions
Arrival headway distributions play a fundamental role in the estimation of green
extension time, eg (or E^), at actuated signals. The bunched exponential distribution of arrival
headways was proposed by Cowan [36], which considers that the bunched relationship
increases among the arriving vehicles when the traffic volume increases. The free
(unbunched) vehicles are those with headways greater than the minimum headway (A), and
the proportion of free vehicles (
distributed headways. Thus, the measurement of the proportion of free vehicles (cp) depends
on the choice of minimum headway (A). The proportion of bunched vehicles in the arrival
stream is (1cp). In this arrival model, all bunched vehicles are assumed to have the same
intrabunched headway (A). The cumulative distribution function, F(t), for this bunched
negative exponential distribution of arrival headways, representing the probability of a
headway less than t seconds, is
F(t) = 1  cpe *A) for t > A (28)
= 0 for t < A
where
A = minimum arrival (intrabunch) headway (seconds);
(p = proportion of free (unbunched) vehicles; and
44
X = a parameter calculated as
i =
1Aq
subject to q < 0.98/A
(29)
where
q = total equivalent through arrival flow (vehicles/second) for all
lane groups that actuate the phase under consideration.
A detailed discussion of the application of this model on actuated control and the
results of its calibration using reallife data for singlelane and multilane cases are given in
Akielik and Chung [53], The more commonly used simple negative exponential and shifted
negative exponential models of arrival headways are special cases of the bunched exponential
model Therefore, in this study, the bunched arrival model is used to estimate the extension
time after queue clearance.
The method for estimating the green extension time, eg, for an actuated controller that
uses a passage detector and a fixed gap time (unit extension) setting (e0) was described by
Ak9ehk [34]. In this study, presence detectors are assumed. The headway (h) between two
consecutive vehicles is equal to the sum of the gap time (e) and the detector occupancy time
(t0). Therefore, the headway, h0, that corresponds to the allowable gap time setting, e0, is
hc = e0 + to (210)
where t0 is the detector occupancy time given by
t0 = (Ld + Lv)/v (211)
where
45
Ld = effective detector length (ft);
Lv = vehicle length (ft); and
v = vehicle speed (ft/sec).
There is no need for the estimation of an extension time if the actual queue service
time, gp is less than the minimum effective green time, gmm, or gs is greater than the maximum
effective green time, g^. If gs < gnun then g will be set to g^ and if g, > g^ then g is equal
to gn,^. Detection of each additional vehicle between gmin and g^, in general, extends the
green period by an amount that is, in effect, equal to the headway time, h0. The green period
terminates when the following two conditions are satisfied.
1. the headway between two successive vehicle actuations exceeds the headway that
corresponds to the gap time setting, h > h0 (gap change); or
2. the total green extension time after the expiration of minimum green time equals
the maximum extension setting. It is equivalent that g is equal to g^.
During a gap change, the green period terminates after the expiration of the gap time.
Assuming that the termination time at gap change is the headway corresponding to the gap
time setting (h0 = e0 + t 0), the green extension time, eg, by gap change can be estimated from
the following formula [6, 9, 10] based on the bunched exponential headway distribution.
e*(<=0+toA)
x
(212)
Once the green extension time, eg, is obtained, the effective extension time, ge, is just equal
to the sum of eg and the intergreen, I, minus the end lost time, td, as shown in Equation 25.
46
As mentioned before, the more commonly used simple negative exponential and
shifted negative exponential models of arrival headways are special cases of the bunched
exponential model. For simple negative exponential model, use
A = 0 and (p = 1 (therefore X = q) (213)
and for the shifted negative exponential model (normally used for singlelane traffic only), use
cp = 1 (therefore X = q / (1 Aq)) (214)
These two models unrealistically assume no bunching ((p =1) for all levels of arrival flows.
The bunched model can be used either with a known (measured) value of (p, or more
generally, with a value of cp estimated as a function of the arrival flow rate. The following
relationship suggested by Akijelik and Chung [53] can be used for estimating the proportion
of unbunched vehicles in the traffic stream (cp)
The recommended parameter values based on the calibration of the bunched exponential
model by Ak^elik and Chung [53] are:
Singlelane case:
A = 1.5 seconds and b = 0.6
(216a)
Multilane case (number of lanes =2):
A = 0.5 seconds and b = 0.5
(216b)
Multilane case (number of lanes > 2):
A = 0.5 seconds and b = 0.8
(216c)
47
Effect of Phase Skip
The minimum phase time requires more attention when the phase may be skipped due
to low traffic volume. The minimum phase time would only be valid if the controller was set
to recall each phase to the minimum time regardless of demand. On the other hand, the real
significance of the minimum phase time in an actuated controller is that a phase must be
displayed for the minimum time unless it is skipped due to lack of demand. This situation may
be addressed analytically by determining the probability of zero arrivals on the previous red
phase. Assuming a bunched arrival headway distribution, this may be computed by using the
following equation:
Pov =
where
Pov â€” probability of zero arrivals during the previous red phase; and
R = previous red phase time.
So, assuming that the phase will be displayed for the minimum time, except when no vehicles
have arrived on the red, the adjusted vehicle minimum time then becomes
AVM = MnV(lPJ (218)
where
AVM = the adjusted vehicle minimum time; and
MnV  the nominal minimum vehicle time.
The similar concept for adjusted vehicle minimum time may also be applied to compute an
adjusted pedestrian minimum time.
48
If the phase may be skipped due to lack of demand, the adjusted minimum phase time
is the maximum of adjusted vehicle minimum time and adjusted pedestrian minimum time.
It will be used as lower bound of the predicted phase time. When the Pov for a phase is not
zero, the estimated phase time must also be modified by multiplying the (1 Pov) factor to the
original total extension time. Therefore, the predicted phase time becomes
PT = tsl + Gqst + (1  Pov) (Eg + I) (219)
Circular Dependency Relationship and Sequential Process
The determination of required green time using the Appendix II method is relatively
straight forward when the cycle length is given. However, trafficactuated controllers do not
work on this principle. Instead, they determine, by a mechanical analogy, the required green
time or phase time given only the length of the previous red interval. The green time or phase
time required for each phase is dependent on the green time or phase time required by the
other phases. Thus, a circular dependency relationship exists between actuated phase times.
There are two way to resolve this type of circular dependency. The first one is
simultaneous solutions of multiple equations. The second one is a sequential process
involving repeated iterations that converge toward a unique solution. Either method could
be applied to solve this dependency problem. Since the simultaneous solution will not lend
itself to the complications that must be introduced to solve the more general problem,
Courage and Ak9elik [6] proposed and set up an iterative procedure that will apply to the
general problem. This iterative procedure is adopted in this study to predict the average
phase time for general cases, not just limited to the protected phases.
49
An initial set of values for all phase times must be established before the iterative
procedure may begin. With each iteration, the phase time required by each phase, given all
of the other phase times, may be determined. If the minimum phase times turn out to be
adequate for all phases, the cycle length will simply be the sum of the minimum phase times
of the critical phases. If a particular phase demands more than its minimum time, then a
longer red time will be imposed on all the other phases. This, in turn, will increase the phase
time required for the subject phase. Through a series of repeated iterations, the circular
dependency will come to an equilibrium and converge to a unique solution. When the
convergence of cycle length is reached, the final cycle length and phase times are determined.
This convergence may be demonstrated easily by using an simple example. Consider
the intersection shown in Figure 25. This is a trivial intersection with four identical singleÂ¬
lane approaches carrying the through volume of 400 vph. A saturation flow rate of 1900
vphgpl is assumed. Each phase has assigned the following constant parameters:
Detector: 30 feet long, placed at the stop line
Intergreen time (I): 4 seconds
Lost time (t,)
Startup lost time (tsl):
Minimum phase time:
Allowable gap:
Maximum phase time:
No pedestrian timing features.
3 seconds per phase
2 seconds per phase
15 seconds
3 seconds
50 seconds
No volumedensity features.
50
HE1NS NB
Figure 25. The intersection used as an example for circular dependency illustration.
The QAP for the first iteration in this example is shown in Figure 26. Initially, the
"trial time" is the nominal minimum vehicle time (15 seconds in this case) for each phase.
Although this operation has four through phases, it can actually be treated as a twophase
operation because the northbound through phase is identical to the southbound through phase
and the eastbound through phase is the same as the westbound through phase.
Hence, the trial cycle length is equal to 15x2 = 30 seconds. This initial timing would
result in an effective red time of 18 seconds for each phase. The traffic volume for each
approach is 400 vehicles per hour. In other words, the arrival rate is equal to 400/3600 =
0.11 vehicles per second. Therefore, during the effective red time, the accumulated queue
can be computed as the product of arrival rate and effective red time, which is equal to 0.11
x 18 = 2 vehicles.
51
4>
3
4>
3
cr
4>
JZ
â– 44
c
CA
O
IE
V
>
<4
o
Â©
Figure 26. Queue accumulation polygon in the first iteration of the illustrated example.
The departure rate is the saturation flow rate (1900 vehicles per hour), so the phase
can discharge (1900/3600) = 0.53 vehicles per second. Therefore, the net service rate is equal
to (0.53  0.11) = 0.42 vehicle per second. Since fq is about 1.07 and fj, equals 1.0, the actual
queue service time, g., taken to discharge the queue will be (1.07 * 2) / 0.42 = 5.16 seconds.
The extended green time, eg, is 5.3 seconds and intergreen time, I, is 4 seconds. Thus, the
total extension time, EXT (= eg + I), is 9.3 seconds (= 5.3 + 4) and the effective extension
time, ge, equals 8.3 seconds (= 5.3 + 4  1). By using Equation 23, the phase time, PT,
equals the sum of the lost time, t,, the queue service time, gqst, (= gs in this example) and the
effective extension time, ge, which is about 16.46 seconds (= 3 + 5.16 + 8.3). By using
Equation 24, PT is equal to the sum of tsl, gqst (= gs in this example) and EXT which is also
about 16.46 seconds (= 2 + 5.16 + 9.3). The new phase times produce a new cycle length
52
of (16.46 x 2) = 32.92 seconds. This will generate another version of Figure 26 with
different dimensions. By repeating these calculations with a new cycle length each time, the
computed cycle length will converge to within 0.1 second. Convergence for this example is
especially rapid. The process is very rehable. Table 21 shows the iteration result and
convergence for this trivial example.
Table 21. The iteration results and its convergence for the illustrated example.
Itera
Cycle
Old
Acc.
Total
Total
New
New
Differ
tion
phase
queue
service time
ext. time
phase
cycle
ence
time
(= tsi + gs)
(= eg +1)
time
(sec)
(sec)
(sec)
(sec)
(sec)
(sec)
(sec)
1
30.0
15.0
2.00
7.16
9.3
16.5
32.9
2.9
2
32.9
16.5
2.16
7.57
9.3
16.9
33.7
0.8
3
33.7
16.9
2.21
7.68
9.3
17.0
33.9
0.2
4
33.9
17.0
2.22
7.71
9.3
17.0
34.0
0.1
Computational Process
The computation framework with five worksheets proposed by Courage and Ak?elik
[6] for modeling trafficactuated controller operations for simple through and protected left
turn phases is adopted by this study as the basis for more complicated and general model
development. This computation process will be introduced here. The worksheets play a very
important part in overcoming the "black box" image of a complex model such as the one in
this study. They provide a structure for presenting the results of intermediate computations
in a common form that is compatible with their proposed techniques.
53
Worksheet 1 is "Trafficactuated Control Data Input". "Lane Group Data" is shown
in Worksheet 2. Worksheet 3 is "Trafficactuated Timing Computation" and Worksheet 4
is "Required Phase Times". The last worksheet, worksheet 5, is "Extension Times Based on
Allowed Gaps". The worksheet format offered a clear and concise way to document the
information. This format is also consistent with the current HCM. While the worksheets
themselves are quite simple, the overall procedure contains iterative loops. In this research,
the worksheets proposed by Courage and Ak
computation of more general and complicated scenarios, not just limited to simple protected
scenarios. The complete procedure involving the five worksheets is illustrated in Figure 27.
This figure shows the five worksheets, the main information flow path and two iterative
loops indicated as "Loop A" and "Loop B".
1. Data
Input
H2. Lane
Groups
4. Required
Times
l
T
Ã
3. Cycle
Time
Adjustments
5. Phase
Extension
Times
B
SYMBOLS
Main
Information
Flow
Worksheets
Iterative Loops Â¡
Figure 27. Iterative loops in the phase time and cycle time computation procedure.
54
â€¢ Loop A. Required Time  Cycle Time Adjustment: This is an external iteration
between Worksheets 3 and 4. It is required to make the phase times converge
to a stable cycle length. Worksheet 4 must also refer to Worksheet 5 if phase
time extensions are required to compute the required phase times.
â€¢ Loop B. Phase Extension Time: This is an internal iteration within Worksheet 5.
It is only required when gap reduction is employed. When the allowable gap is a
function of the phase time, the phase time cannot be computed without iteration.
Simulation Models
Simulation is one of the most powerful analysis tools available to those responsible
for the design and operation of complex process and systems. Simulation might have more
credibility because its behavior has been compared to that of a real system, or because it has
required fewer simplifying assumptions and thereby has captured more of the true
characteristics of the real system.
NETSIM, a popular and powerful microscopic traffic simulation model, has been
continually developed by the Federal Highway Administration (FHWA) for many years.
NETSIM is able to model an eightphase, dualring controller explicitly, recognizing all of the
phasespecific parameters. EVIPAS is an optimization and simulation model for actuated
controlled, isolated intersections. In the simulation mode, it is also capable of providing
simulated phase times for a wide range of actuated parameter settings. Thus, both the
NETSIM and EVIPAS simulation models could be used as tools to verify the phase time
estimation from the proposed analytical model.
55
Comparison between NET SIM and EVIPAS Simulation Results
Since both NETSIM and EVIPAS are simulationbased models, it becomes necessary
to compare the simulation results between EVIPAS and NETSIM. The current version of
NETSIM (P version 5.0) produces very detailed tables of several performance measures. It
does not, however, provide sufficient information on the operation of the controller itself in
the standard output tables. To obtain this information, it was necessary to develop a
postprocessor to extract the operational data from special files used to support the animated
graphics features of NETSIM.
The actuatedcontroller data for each second of operation are recorded and stored in
a text file that is given a file name with extension of ".F45" by NETSIM. The format of
".F45" files is hard to read. After it is properly converted, a readable text file can be produced
with extension of ".X45". Then, a postprocessor was developed to read the .X45 file and
produce a summary of the operation. Both conversion and postprocessor were combined into
a program called "NETCOP" for "NETSIM Controller Operation Postprocessor." It provides
phasespecific information such as percent skipped, percent gapout, percent maxout, average
cycle length, average phase time, adjusted cycle length and adjusted average phase time. The
"adjusted cycle length" is computed by subtracting the number of seconds of dwell (i.e., the
time during which no demand was registered on any phase) from the total number of seconds
simulated before dividing by the number of cycles. The adjusted phase time is computed
according to the adjusted cycle length. Since the adjusted phase time from NETSIM can
represent the effective use of phase time, it is adopted for later phase time comparison.
56
Although the simulation techniques used in EVIPAS and NETSIM may differ in some
degree, theoretically, the phase time estimates for the same traffic conditions, geometric
configurations and actuated timing settings should be close. Thus, an evaluation has been
made by comparing the simulated phase times from both NETSIM and EVIPAS based on 9
hypothetical examples with trafficactuated operations. These examples cover both two
phase and multiphase actuated operations. The comparison result is shown in the Figure 28.
In a simple regression analysis between the above two simulated phase times, a 0.96
coefficient of determination, R2, was achieved. As expected, the simulated phase times from
EVIPAS are very close to those from NETSIM simulation, which demonstrates that the
EVIPAS model has the similar effectiveness on phase time estimation as NETSIM.
Figure 28. Phase time comparison between EVIPAS and NETSIM.
57
Arterial Considerations
As urban roadways become more congested, and resources available for building new
facilities become more limited, transportation professionals are exploring all possible
alternatives to improve the existing transportation systems. Fullyactuated traffic signals are
powerful for isolated intersections, but not proper for coordinated intersections. One major
area that holds great potential in reducing urban congestion is the implementation of
coordinated semiactuated traffic signals on arterial streets. Unlike pretimed signals, semi
actuated signals are intrinsically more intelligent and complex to implement and they provide
a better coordination than pretimed signals [34],
In semiactuated operation, detectors are placed only on the minor street and
exclusive left turn lanes on the major street. No detectors are installed for the through
movements on the major street. Under this operation, once there is no detection on the minor
movements, the green will always come back to the through (coordinated) movements on the
major street. Therefore, the major benefit of using semiactuated control is to assign unused
minor street green to the major street. This concept is fundamental to the signal timing
prediction for coordinated semiactuated operation.
In pretimed control, the phase time of each movement is fixed, so the effective green
over cycle length ratio (g/C) for each movement is a constant. Unlike pretimed signals, the
phase time of each lane group for actuated signals does not stay constant but fluctuates from
cycle to cycle, so the g/C ratio for each movement fluctuates. Therefore, the major difference
between pretimed and trafficactuated intersections lies in the g/C. The g/C ratio is important
because it is required for the capacity and delay computation. It is necessary to note that the
58
coordination for actuated signals must be provided by some form of supervision which is
synchronized to a background cycle length. Since coordinated semiactuated control is
frequently used at intersections along an artery, the g/C ratio of the critical throughlane
group on the major street is especially important.
The true g/C ratio of each movement is difficult to access in current practice directly
from a traffic controller. Therefore, an alternative for obtaining the g/C ratio is needed. It
is found, in general, that the g/C ratio on a major street is high when the demand on min nr
streets is low, and vice versa. This observation suggests the potential for using minor street
traffic demand measures to predict the major street g/C ratio. To verify the concept of the
assignment of unused minor street green to the major street, attempts have been made to
quantify the relationship between the major street g/C ratio and minor street traffic demand.
Figure 29. Conceptual relationship between major street g/C and minor street demand.
59
Since traffic volume and detector occupancy are easy to measure with reasonable
accuracy for minor street demand, a conceptual model focusing on these two variables was
developed to predict the major street g/C ratio. As the minor street demand, x, increases
from zero, the major street g/C ratio, y, should start as a sharply decreasing function. The
rate of decrease should attenuate as x increases. The conceptual relationship between y and
x is shown in Figure 29.
Data Acquisition
Data from a closed loop signal system were used for the calibration of the candidate
models. The data set includes 98 intersection records generated from four coordinated semi
actuated intersections during seven time periods along SW 34th St. in Gainesville, Florida.
A layout of the arterial system is shown in Figure 210. The SW 34th St. artery is a major
street, and Radio Rd., Hull Rd., SW 20th Ave. and Windmeadows are four minor streets.
Protected left turn signals exist on the major street at all four intersections.
Figure 210. The location of four studied intersection.
60
The Traffic Actuated Controller Monitor/Analyzer (TACMAN) computer package
[54] uses information collected by a microcomputerbased control system, the Signalized
Intersection Monitor (SIMON) [54], to produce hourly phasespecific descriptive information
and performance measures. The descriptive information includes traffic volume, detector
occupancy, etc., and performance measures include stops, delay and fiiel consumption. The
measures used in the study pertain to the critical movements.
Model Calibration
Statistical Analysis System (SAS) [55] programs were applied to perform correlation
and regression analyses. Regression techniques were used to calibrate the parameters of the
conceptual models. Regression results show that either the minor street volume or detector
occupancy can explain most of the variation in the major street g/C. Furthermore, the F and
t values indicate that both candidate models are overall significant and the coefficients in each
model are also individually statistically significant. The power model (volume model)
produced the highest adjusted R2 using the traffic volume data, while the logarithmic model
(occupancy model) was better for detector occupancy data. These two models can be
expressed as follows:
MAJG =100(1+0.01 VOLUME) 03045 Adj. R2 = 0.88 (220)
MAJG = 100  12.0954 LN(1 + OCCUPANCY) Adj. R2 = 0.91 (221)
where
MAJG = g/C ratio (%) for the major street critical through movement;
VOLUME = hourly volume for the minor street critical movement; and
OCCUPANCY = hourly detector occupancy for the minor street critical movement.
61
The curves for these two minor street demand measures are shown in Figures 211
and 212, respectively. As expected, the shape of both curves conforms to the described
conceptual model. Although the occupancy model might be slightly better than the volume
model, the volume model may frequently be used because minor street volumes are often
known, estimated or forecast when no information is available about detector occupancy.
Based on the concept that the unused minor street green time is assigned to the major
street in coordinated semiactuated operation, the relationship between the g/C ratio of the
critical throughlane group on a major street (major street g/C ratio) and the traffic demand
of the critical movement on minor streets (minor street demand) was quantified by the above
volume model and occupancy model. In the further study, this concept will continue to be
implemented in the phase time estimation for coordinated semiactuated operation.
Figure 211. Prediction of the major street g/C ratio based on a power model for
minor street traffic volume.
62
Figure 212. Prediction of the major street g/C ratio based on a logarithmic model for
minor street detector occupancy.
CHAPTER 3
MODEL DEVELOPMENT
Introduction
The scope of the preliminary model development presented in chapter 2 was limited
to basic through movements and protected left turn movements from an exclusive lane. This
chapter continually explores the analytical basis for extensions of the preliminary methodology
to cover permitted left turns in both shared and exclusive lanes and the complicated
compound left turn protection (i.e., protected plus permitted phasing or permitted plus
protected phasing).
Determination of Arrival Rates
In the previous analytical work, the arrival and departure rates were constant
parameters determined externally. The arrival rates were determined by the specified traffic
volumes and the departure rates were determined by the saturation flow rates. Neither
depended on the signal timing. In fullyactuated operation which is very often used at an
isolated intersection, the progression effect is not considered, therefore, the arrival type 3
(green arrival rate = red arrival rate) is appropriate. For coordinated semiactuated operation,
since the progression effect is an important consideration, the use of different arrival types to
represent progression quality is required. The derivation of arrival rate is presented first in
this chapter for later application on coordinated semiactuated intersections.
63
64
With arrival type 3, the arrival rate is constant over the whole cycle at q veh/sec. With
other arrival types, two different arrival rates must be computed. qg is the arrival rate on the
green phase, and qr is the arrival rate on the red phase. For a given average arrival rate, the
values of qg and qr will depend on the platoon ratio, Rp, associated with the arrival type, and
the green ratio, g/C, which is a part of the timing plan. The HCM defines the platoon ratio
as follows:
Rp=PC/g (31)
where
P = the probability of arrival on the green;
g = the green time for the phase; and
C = the cycle length.
Basic Continuity Relationship: qrr + qgg = q(r+g)
O
a
&
>
&
q = average arrival rate
qr
r
qg
g
Time (seconds)
Figure 31. Arrival rate over a full cycle with coordinated operation.
65
From Equation 31,
P = Rpg/C
Now, with arrival type 3, R,, = 1, so P = g/C, and q = qg = q,. On the other hand, if Rp * 1,
then the arrival rates will be different on the red and green phases, as illustrated in Figure 31.
The problem is to determine qr and qg given q, Rp, g and C.
From Equation 31:
R = p(r+g)
But, by definition,
So,
or,
P = gqs
q(r+g)
p . gqg
â€™ q(r+g)g
Therefore,
q = qR
(32)
As an extension of this derivation, the red arrival rate may be determined from the continuity
relationship shown on Figure 31.
66
q/ + qgg = q(r+g)
From which,
qrr = q(r+g)  (qR)g
Therefore,
^ = q(r^g)  (qR,)g (3.3)
Permitted Left Turn Phasing
Before beginning the discussion of permitted left turn (LT) phasing, the concept of
green time determination for a protected phase is briefly reviewed first. This concept is based
on the queue accumulation polygon (QAP) shown in Figure 32 which was presented earlier.
It is convenient to be shown here again for the illustration. The QAP shows the number of
vehicles accumulated in a queue on a signalized approach over one cycle of operation. Each
cycle is assumed to repeat the same pattern indefinitely. The number of vehicles accumulated
at any time in the cycle may be determined as the difference between the cumulative arrivals
and departures since the start of the cycle.
The queue accumulation increases throughout the red phase at the rate of qr veh/sec.
The maximum accumulated queue occurs at the end of the red phase, and is indicated on
Figure 32 as Qr During the green phase, the queue decreases at the net departure rate, (s 
q^), until it has been fully serviced. The time required to service the actual queue is indicated
on Figure 32 is g,. The green phase will continue until the occurrence of a gap in the arriving
67
traffic of sufficient length to cause the controller to terminate the phase. The effective
extension time is indicated on Figure 32 as ge. Of course, this whole process is subject to
a specified maximum phase time. An analytical model for predicting gs, gc and average phase
time, PT, was presented in the preliminary methodology. In this simple case, the queue
accumulation polygon is just a triangle. In the remainder of the cases to be discussed in this
dissertation, the QAP will assume a more complex shape.
Permitted Left Turns from Exclusive Lanes
The basic QAP concept may be extended to cover a slightly difficult case in which
a permitted left turn is from an exclusive lane, yielding to oncoming traffic, instead of a
protected movement. This introduces a couple of important changes in the QAP. Since the
number of opposing lanes, n^, may influence the net arrival rate during the period when the
opposing queue is being serviced, it will be considered for the permitted left turns form
68
exclusive lanes. Based on the number of opposing lanes, the QAPs for condition 1 (nopp > 1)
and condition 2 (nopp =1) shown in Figures 33 and 34 are discussed, respectively.
If the number of opposing lanes is greater than one (see Figure 33), the queue
continues to accumulate throughout the first part of the green with the arrival rate of while
the opposing queue is being serviced. The time required to service the opposing queue is
indicated on Figure 33 as gq. There is no chance for a permitted left turner to make a
maneuver during the period of gq. The maximum queue, indicated on Figure 33 as Qq, can
be computes as follows:
Qq = Qr+ fig * gq (34)
If the number of opposing lane is equal to one (see Figure 34), the left turns from the
opposing lane do create the chance for the left turns from the exclusive left turn lane to make
maneuvers. According to the HCM Chapter 9, the adjusted saturation flow rate, sq, during
the period of gq can be computed using the following formula:
Sq = S / El2 (35)
where
sq = the permitted saturation flow rate during the period of gq;
s = the protected saturation flow rate; and
El2 = the left turn equivalence as determined from Equation 922 in the HCM.
the queue continues to accumulate throughout the period of gq with the net green arrival rate
of (q^  sq) while the opposing queue is being serviced. The maximum queue, indicated on
Figure 34 as Qq, can be computes as follows:
Qq = Qr + (%  Sq) *gq
(36)
69
Thereafter, the LT vehicles will filter through the opposing traffic at a rate determined
by the opposing volume. This is indicated on Figures 33 and 34 as the permitted saturation
flow rate, sp. The net departure rate is shown as the difference between the permitted
saturation flow rate and the green arrival rate, which is equal to (sp  q^). Fortunately, the
HCM Chapter 9 worksheets already provide the means to compute these values. The value
of gq is determined explicitly on the supplemental worksheet for permitted left turns. The
value of permitted saturation flow rate, sp, may be determined as
sp = s/EL1 (37)
where
sp = the permitted saturation flow rate;
s = the protected saturation flow rate; and
EL1 = the left turn equivalence as determined from Figure 97 in the HCM.
Figure 33. Queue accumulation polygon for a permitted left turn from an exclusive
lane with opposing lane number greater than one.
70
1>
4>
4>
.a
Qr qg
Qq
Cfl
4)
\ 1
O
â€¢ Â«4
// 
a
Â©
>
1 ///
\] sp  qg
Â©
qrJ/
Â©
z
/ r
8q
Is 1 ge
Time (seconds)
Figure 34. Queue accumulation polygon for a permitted left turn from an exclusive
lane with opposing lane number equal to one.
Green Time Extension for Permitted Movements
The model for estimating the effective green time extension, ge, assumes that the
arrivals after the queue has been serviced will be freeflowing as they cross the detector. This
will not be the case for permitted left turns. A complex stochastic model would be required
to treat this situation in detail.
It should, however, be possible to use the left turn equivalence, Eu, described above
as an approximation in this situation. In other words, the equivalent through volume, VL E^,
would be used in place of the actual left turn volume, VL The green extension time must be
determined using an equivalent through volume of (VT + VLEn) in place of the actual volume
of (VT + VL).
71
Effect of Sneakers
Sneakers are permitted LT vehicles that exit the intersection at the end of the green
phase, usually during the intergreen interval. It is common to assume that a maximum of two
vehicles per cycle may be released from the queue. Sneakers are treated implicitly in the
Chapter 9 worksheets by imposing a lower limit of two vehicles per cycle on the capacity of
each exclusive LT lane with permitted movements. For purposes of this analysis, sneakers
must be recognized explicitly in the QAP. This requires the definition of some new terms:
â€¢ Maximum Sneakers, Sm: The maximum number of LT vehicles released at the end
of the green phase assuming that the LT queue has not already been serviced.
â€¢ Permitted phase terminal queue, Qp: The number of vehicles accumulated at the
end of the permitted phase before sneakers have been released.
â€¢ Adjusted permitted phase terminal queue, Qp: The number of vehicles accumulated
at the end of the permitted phase after sneakers have been released.
â€¢ Actual Sneakers, Sa: The actual number of sneakers released at the end of the green
phase. This is determined as Min (Sm, Qp).
For the purpose of illustration, the effect of sneakers on the QAP for the condition,
Uopp > 1, is shown in Figure 35. This illustrates the case in which the phase is terminated by
the maximum green time before the queue of LT vehicles is completely serviced. If Qp is
greater than zero, then the maximum phase length will be displayed as a pretimed equivalent.
The adjusted permitted phase terminal queue, Qp', is equal to Qp minus Sa. If Qp is greater
than zero, then the v/c ratio for the approach will be exceeded. These parameters will be
involved in a more complex way in the analysis of compound left turn protection.
72
Figure 35. Queue accumulation polygon for a permitted left turn from an exclusive
lane with sneakers.
MultiLane Approaches
If LT vehicles are accommodated in an exclusive lane, it is reasonable to assume that
there will be additional lanes available to handle the through traffic. It is also expected that
the detectors installed in both the through and left turn lanes will activate and extend the same
phase. Under these conditions, the queue service time, gqst, for the through and LT lanes will
be different. The required phase time (RPT) is the sum of lost time (t,), effective extension
time (ge = eg + I  tel) and the maximum value of through queue service time, gqst (= gj, and
left turn queue service time, gqst (= gq + gs):
RPT = Max ( Through gqst, Left turn gqst) + t, + ge (38)
and eg must be determined using an equivalent through volume of (VT + VLEL1) in place of the
actual volume of (VT + VL).
73
Shared Lane Permitted Left Turns
The shared lane permitted left turn case is only slightly more complicated than the
exclusive lane permitted left turn case. The additional complication may be seen in the QAPs
shown in Figures 36 and 37. The concept of free green, gf, must be introduced here. In an
exclusive left turn lane, the first vehicle in the queue will always be an LT vehicle. However,
in a shared lane, the first vehicle could be either a through or LT vehicle. The portion of
effective green blocked by the clearance of an opposing queue is designated as gq. During the
time, an LT vehicle may be stopped by the opposing traffic, but a through vehicle will not.
Until the first leftturning vehicle arrives, however, the shared lane is unaffected by left
turners. The free green represents the average green time from the beginning of green that
will be available to move through vehicles in the shared lane. The Chapter 9 supplemental left
turn worksheets provide a method for computing gq and gf. As indicated on Figures 36 and
37, there will be a net discharge rate of (s  q^) during the free green interval, and the queue
remaining at the end of the interval is represented as Qf.
The computation for queue service time, gqst, is more complicated for a shared lane
than that for an exclusive left turn lane or through lane. Basically, the gqst for a shared lane
can be divided into two parts. One is the green time before the beginning of the actual queue
service time (gj, and the other one is gs itself.
In Figure 36, since gq is greater or equal to gâ€ž the gqst is just equal to the sum of gq
and gs. Note that according to the HCM Chapter 9, Qq can be computed based on the number
of the opposing lanes. The detail description for the computation of Qq is in the HCM
Chapter 9. Figure 37 represents the scenario that gq is less than gf. The accumulated queue,
74
Qn which belongs to through vehicles, will be served at a net service rate of (s  qg). Assume
the time to clean all of these accumulated through vehicles is designated as gt. If gf is less than
gâ€ž then gqst will equal the sum of gf and gs. On the other hand, if gf is greater or equal to gâ€ž
then g^ just equals g, because g, is zero for this condition. The time to clear all accumulated
through vehicles, gâ€ž may be represented by Equation 26. The computation for gqst may be
summarized as the following equations. If gq is greater than or equal to gf, the queue service
time, gqst, can be computed as
gqs. = gq + gs (39)
If gq is less than gf, the formula for the computation of the queue service time, g^,, becomes
gqs. = gf + g, when gf
gqs. = g. when gf>gt (311)
The remainder of Figures 36 and 37 follows the same process as the exclusive lane
cases shown in Figure 33 and 34. The permitted movement saturation flow rate for the
shared lane must, however, be computed somewhat differently. In an exclusive LT lane, the
left turn equivalence, EL1, was applied to all of the vehicles in the LT lane. In a shared lane,
it is only appropriate to apply this factor to the LT vehicles. So, sp should be computed as
s
Sp " 1 + Pl(Eu  1) (312)
where
PL = the proportion of left turns in the shared lane, as computed by the supplemental
worksheet for permitted left turns, and all other terms are as defined previously.
75
eg should be computed in the same manner as described for the exclusive LT lane case and
using an equivalent through volume of (VT + VL EL1) instead of the actual volume.
2
v
2
Time (seconds)
Figure 36. Queue accumulation polygon for a permitted left turn from a shared lane
(gq>gf)
Figure 37. Queue accumulation polygon for a permitted left turn from a shared lane
(&,<&)â€¢
76
Compound Left Turn Protection
The QAP concept may be extended to cover the case in which an LT movement
proceeds on both permitted and protected phases from an exclusive lane. One important
difference between the simple permitted LT phasing and the compound protected LT phasing
is the assignment of detectors to phases. It is assumed that detectors will be installed in all
LT lanes to ensure that LT vehicles will not face a permanent red signal. The discussion of
simple permitted LT phasing assumes that the detector in the LT lane (either shared or
exclusive) will actuate the same phase as the concurrent through traffic. On the other hand,
it is logical to assume that a protected left turn will have a detector that actuates the protected
left turn phase. This has very important implications for the analysis of compound left turn
protection. It means that LT vehicles will not extend the permitted phase. When they occupy
the detector during the permitted phase, they will simply be placing a call for their own
protected phase. In the analysis of compound left turn protection, it is necessary to make a
strong distinction between protected plus permitted (leading), and permitted plus protected
(lagging) left turn phasings. Each of these cases will be analyzed separately.
Protected Plus Permitted Phasing
The QAP for protected plus permitted phasing is presented in Figure 38. In Figure
38, it is necessary to note that if the number of opposing lanes, nopp, is greater than one, sq
will be equal to zero. Keep in mind that the QAP is used for the purpose of determining the
length of the protected phase only. The length of the permitted phase will be determined by
the simple process of its corresponding through phase because there are no permitted left
turns that actuate the detector. The The most important piece of information provided by
77
the QAP in this case is the size of the queue accumulated at the beginning of the green arrow,
C^,. With protected phis permitted phasing, this is equal to the queue at the end of effective
red time, Qr. Given Qga, the determination of green time follows the simple procedure for
protected movements.
Time (seconds)
Figure 38. Queue accumulation polygon for protected plus permitted LT phasing with
an exclusive LT lane.
Permitted Plus Protected Phasing
This case is illustrated in Figure 39, which is essentially the same as Figure 38,
except that the order of the phases has been reversed. It is very important to note that the
protected (green arrow) phase must be presented last in both cases, because this is the phase
whose length we are trying to determine.
Again, it is needed to know the number of vehicles accumulated at the beginning of
the green arrow phase, Qga, which is equal to Q, in this case. This will raise an interesting
78
question. Suppose that the value of Qp is zero. This could happen if the permitted phase was
able to accommodate all of the left turns. Theoretically, the protected phase should never be
called under these conditions. However, there is a stochastic element which dictates that all
of the phases will be called occasionally. In this scenario, the adjusted minimum phase time
will be used to estimate the phase time for this protected phase.
4>
3
U
3
Time (seconds)
Figure 39. Queue accumulation polygon for permitted plus protected LT phasing with
an exclusive LT lane.
Applications
The analysis presented in this chapter fills the gaps left in the preliminary
methodology. The complete analytical basis for a practical computational method to predict
traffic actuated signal timing are conducted. This method should be sensitive to a wide range
of actuated controller parameters. The QAP concept is especially attractive because it can
provide a clear picture for estimating the signal timing. Another essential benefit is that it can
79
also provide a direct estimate of the uniform delay that is compatible with the current HCM
Chapter 9 delay model. The methodology presented in this chapter will be incorporated into
the computational framework described in the preliminary model structure to develop a
complete model implementation for predicting the signal timing at a trafficactuated signalized
intersection. The model implementation and model evaluation will be presented in the next
two chapters, respectively.
CHAPTER 4
MODEL IMPLEMENTATION
Introduction
A specific analysis program, ACT348, was developed by Courage and Lin in this
study as a tool to implement the developed analytical model and procedure to predict the
trafficactuated signal timing. The original worksheets have also been modified in accordance
to the analytical model to cover all possible movements described in Chapter 3. The ACT3
48 program can produce intermediate outputs in a format identical to the modified
worksheets. The computer program is required because the iterative nature of the procedure
makes it totally impractical for manual implementation. The program is able to evaluate the
proposed analytical models using a variety of data. In this chapter, the computer program
structure and logic are presented.
The analytical model developed in this study is for isolated mode of actuated
operation. An effective method to predict the phase times for coordinated mode of actuated
operation is to apply the analytical model for isolated mode to predict the phase times of
actuated phases and then properly assign the unused phase times to the nonactuated phases
(arterial through movements). By appropriate implementation of the analytical model for
isolated mode, a procedure has been built to predict the phase times for coordinated mode,
which will also be addressed in this chapter.
80
81
Structure and Logic of the ACT348 Program
The major structure of the ACT348 program is shown in Figure 41. It is not
difficult to recognize an iterative loop inside the flow chart. The iterative loop is required to
make the cycle time converge to a stable value. The program structure is divided into six
major parts: 1) Data Input, 2) Lane Group Specification, 3) Accumulated Queue
Computation, 4) Extension Time Computation, 5) Required Phase Time Computation, and
6) Cycle Time Adjustments. These six parts will be addressed separately.
Data Input
The data input for the ACT348 program is from the WHICH program, which not
only has a userfriendly input scheme, but also provides sufficient information for actuated
operations. After the data is input, the ACT348 program can be executed from WHICH to
process these data and compute phase times.
In the "control specification" shown in Figure 41, control treatments are determined
first according to the input data. These treatments include left turn types (protected,
permitted or compound protection), phase swaps and overlaps. In addition, a left turn
equivalence, E^, is computed. Finally, the phase sequence pattern is recorded.
The phase sequence pattern needs to get more attention because in each iteration, it
is required for the accumulated queue computation and phase time prediction. The
computation of most time elements such as g, r, g, and gq in the QAP are also based on the
phase sequence pattern. The initial phase pattern is from the input of WHICH. Due to the
dualring control logic, the phase sequence pattern may change during the iterative process.
Therefore, possible phase sequence patterns are required to be considered in the program
82
Start
A
Worksheet 3
Worksheet 4
and
Worksheet 5
V
Dualring
Operation
Shared Lane
Group
Specification
Yes / \ No
Multilane
/Opposing w
Single Lane
Scenario
\Lane > 17/ ^
Scenario
?f,*qandPL ,
Computations
No
Final Cycle
Length and
Phase Times
End
Figure 41. Major structure of the ACT348 program.
83
There are eight possible cases of phase sequence patterns in all. For the purpose of
illustration, only the phase sequence patterns in the northsouth direction are shown in figures.
Case 1 is a standard case for permitted turns which is shown in Figure 42. Case 2 is the
phase sequence for leading green which is shown in Figure 43. In contrast to Case 2, Case
3 is the phase sequence for lagging green which is presented in Figure 44. Case 4 shown in
Figure 45 is the phase sequence for leading and lagging green. Case 5 is a left turn phase
with leading green which is shown in Figure 46. Case 6 is leading dual left turns, and Case
7 is lagging dual left turns. Cases 6 and 7 are shown in Figures 47 and 48, respectively. In
Cases 6 and 7, the phases for dual left turns will terminate simultaneously. Finally, Case 8
shown in Figure 49 is leading and lagging with dual left turns. Case 4 and Case 8 are
interchangeable. For example, when the volume of northbound left turn volumes are heavy
and through traffic is light, Case 4 may become Case 8.
3 4
X
'
X
Ã
7 8
Figure 42. Case 1: Phase sequence for simple permitted turns.
84
3 4
J
1
X
>
k
7 8
Figure 43. Case 2: Phase sequence for leading green.
Hr*
3 4
T
X
t
7 8
Figure 44. Case 3: Phase sequence for lagging green.
Hr* \Â¡fr 4^
Figure 45. Case 4: Phase sequence for leading and lagging green.
85
A
V
A
8
Figure 46. Case 5: Phase sequence for LT phase with leading green.
3 4
\
r
>
k
7 8
Figure 47. Case 6: Phase sequence for leading dual left turns.
3 4
T
\
t
7
V.
8
Figure 48. Case 7: Phase sequence for lagging dual left turns.
86
Figure 49. Case 8: Phase sequence for leading and lagging with dual left turns.
In "actuated parameter specification", the actuated parameters are specified based on
each NEMA phase which was defined in Chapter 2. The actuated parameters consist of
minimum initial, maximum initial, minimum phase time, maximum green time, allowable gap
recall, detector configuration and so on. Based on the control specification and the actuated
parameter specification, Worksheet 1: Trafficactuated Control Input Data can be produced
by the ACT348 program.
Lane Group Specification
In "lane group specification", the ACT348 program will determine the phase
movements for each NEMA phase and the lane group movement within each NEMA phase.
For example, if a NEMA phase includes all left turns, through traffic and right turns, the phase
movement of this NEMA phase will be specified as "LTR". If a lane group within the NEMA
phase is just for through and right turns, it should be presented as "TR". The purpose for this
specification is to associate each of the lane group with its NEMA phase.
87
The lane group specification is convenient and necessary for later computation. For
example, the phase time computation for permitted left turn movement from an exclusive lane
("L") will be different from that for through and right turn movements ("TR"). In addition,
the ACT348 program will also determine the traffic volume (veh/hr), arrival rate (veh/sec),
saturation flow (veh/hr) and departure rate (veh/sec) for each lane group based on the input
data from WHICH. Worksheet 2: Lane Group Data is then generated.
Accumulated Queue Computation
In a new iteration, the most important step is to create a new queue accumulation
polygon (QAP). With the phase sequence pattern, phase times and other information from
the last iteration, the new QAP can be produced easily for simple through or protected
phases. It becomes more difficult in computation for permitted left turns from either an
exclusive or a shared LT lane and compound left turn protection because more information
is required before accumulated queues can be computed.
In the analytical model for permitted left turns from an exclusive lane, the opposing
queue service time, g^, is needed for QAP. For the permitted left turns from a shared LT lane,
both gq and free green, gÂ¡, are required. In the compound LT protection, an exclusive LT lane
is assumed, so must be obtained. Fortunately, the method for estimating gq and gf has been
presented in HCM Chapter 9, which is used in this study to compute gq and gf. In the ACT3
48 program, the computation of gq is based on 1994 version of HCM Chapter 9. Since the
computation of g, is based on the length of green time in the latest HCM version which may
cause unreliable convergence of cycle length, the method presented in 1985 HCM Chapter
9 is used instead. Based on the number of opposing lanes, there are two scenarios described
88
in the HCM Chapter 9 for the computation of gq and gf. If the number of opposing lanes is
one, the single lane scenario is applied. Otherwise, the multilane scenario is used.
For the shared lane condition, the PL factor must be considered, which is the
proportion of left turns in the shared lane. The value of PL is influenced by many factors such
as proportion of left turns, number of lanes, left turn saturation factor, effective green in the
lane group and so on. In each iteration, the value of PL will be computed by the ACT348
program using the method described in HCM Chapter 9. The value of PL will influence the
volumes on the shared LT lane and other existing through lanes in the next iteration. Thus,
the arrival rate of each lane group will be slightly changed.
Since the behavior of left turns from a shared lane is more complicated than that from
an exclusive lane, the treatment for the shared lane should be different. A shared lane group
specification is necessary and will be made by the ACT348 program. The movement of the
first lane group for the phase with a shared lane will be specified as "LT". However, if there
is only one lane total, it will be specified as "LTR". The method of specification for other lane
groups is the same as before. Based on the value of PL, the arrival rates for the shared lane
condition will be modified. Note that according to the HCM Chapter 9, the saturation flow
rate for the other through lanes in the same approach with the shared lane will be reduced to
91 percent of its original value due to the shared lane effect. The departure rates for the
through lanes also need to be modified.
Next, based on the derivation in the model development, green arrival and red arrival
rates are then computed based the arrival type of the movements. For fullyactuated
operation, progression effects are not important, so arrival type 3 is adopted for fullyactuated
89
operation. Therefore, the red arrival rate is the same as the green arrival rate. For
coordinated semiactuated operation, the arrival types other than type 3 can be specified for
the coordinated phases on the artery.
Now, it is ready to compute the accumulated queues in the QAP. Basically, there are
different kinds of queues required to be computed by the ACT348 program for the phases
with permitted left turns. The first kind of queue is called Qr which is the queue at the
beginning of the effective green time. This queue is mainly accumulated during the red
period. The second one is called Qft which is the queue accumulated at the end of free green
gf The third kind of queue is called Qq, which is the queue accumulated at the end of eg. For
the through movements or simple protected LT movements (not compound left turn
protection), Qq = Qf = Qf.
For the compound protection, according to the analytical model, the Qq of LT
movements in the permitted portion of protected plus permitted phasing is the only the
accumulated queue during gq period. The queue of LT movement at the beginning of
protected portion of permitted plus protected phasing is the residual queue of the permitted
phase minus the sneakers.
Extension Time Computation
In the extension time computation, the parameters such as the minimum headway (A)
and the proportion of free vehicles ((p) and X are calculated first. Next, the equivalent
through volume described in Chapter 3 is computed to accommodate the effect of permitted
left turns. The equivalent through volume is used in place of the actual volume in the
90
extension time computation. The extension time will be computed based on the method
specified (bunched arrival model or random arrival model) by the program user. If the HCM
Chapter 9 Appendix II method is specified, no extension time computation will be performed.
Required Phase Time Computation
In the "green model", the required phase times of an iteration are computed. The
required phase times include two major parts. One is the queue service time and the other
one is the extension time after queue service. Based on the accumulated queue length and net
vehicle departure rate (net service rate), the queue service time, gqst, can be obtained. The
effective extension time, ge, can also be computed based on the extension model. The lost
time per phase, t,, is an input value. Thus, the phase time, PT, is just the sum of gqst, ge and
tj. However, it cannot exceed the maximum phase time or fall below the adjusted minimum
phase time. Worksheets 3, 4, and 5 will then be produced by the ACT348 program.
Cycle Time Adjustments
In each iteration, the new estimated phase times must be processed through the dualÂ¬
ring operation according to the phase swap specification and termination type (independent
or simultaneous). After the dualring operation, the phase times and their corresponding cycle
length are obtained. This cycle length will be compared with the previous cycle length. If the
convergence of cycle length is reached or the number of iterations exceeds 40, the ACT348
program will terminate and produce the final cycle length and phase times. If not, the
program will proceed with the associated adjustment related to the phase time and continue
next iteration. It is necessary to note that the phase sequence pattern will be checked here to
keep the later computation on the right track.
91
Extension of the Development of Coordinated Operations
Pretimed coordination often performs very well under high volumes and predictable
conditions. However, it is unable to provide the flexibility for a low volume scenario or
variable demand. On the other hand, actuated controllers have the capability to improve the
shortcoming of pretimed control and handle variable demand. Semiactuated operation has
been successfully adopted at isolated intersections and coordinated systems [34].
The phase times of an isolated semiactuated operation can be easily estimated by
setting the maximum recall to the arterial in the previous developed analytical model for fully
actuated operation. Although the analytical model in the isolated mode is not valid for the
coordinated one, it is possible to apply the analytical model iteratively to converge to a
solution that satisfies all of the requirements of coordination. The analytical model and
procedure for predicting the signal timing for fullyactuated operation have already been
implemented in the ACT348 program. A separate procedure that makes iterative use of
ACT348 as an external module to predict the signal timing for coordinated semiactuated
operations will be demonstrated in this section.
Description of the Procedure
In the isolated mode of actuated operation, the phase times and cycle length are
mainly dependent on the traffic demands indicated by vehicle detectors. In a coordinated
mode, the controller is constrained to operate on a specified background cycle length with the
constraints placed on the length of all of the phases. Some of the benefits of trafficactuated
operation are eliminated. However, the coordinated mode produces the benefits of improved
progression and reduced delay of the arterial traffic.
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Due to the constraint of the specified background cycle length, the signal timing for
a coordinated intersection is based on a pretimed equivalent. The actuated controller must
operate within the constraint but any green time not used by the actuated phases may be
reassigned to the through movements on the arterial street which generally carries heavier
traffic volumes. Therefore, an effective method to estimate the phase times for coordinated
node is to apply the proposed analytical model for isolated mode to predict the phase times
of actuated phases and then properly reassign the difference between the computed cycle
length from the model and the specified background cycle length to the nonactuated phases
(arterial through movements).
The procedure [56] for adopting the ACT348 program to coordinated operation
involves the following steps:
1. Set up the controller timing parameters for the ACT348 initial run. The
coordinated arterial phases (usually 2 and 6) should be set for recall to maximum.
The maximum green times for all phases should be determined by their respective
splits in the pretimed signal timing. No recall modes should be specified for any
of the actuated phases.
2. Perform the timing computations with ACT348 to determine the resulting cycle
length. If the maximum green times have been specified correctly in step 1, then
the computed cycle length will not exceed the specified cycle length.
3. If the computed cycle length is equal to the specified cycle length, then there is no
green time available for reassignment. In this case the procedure will be complete
and the final signal timing will be produced.
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4. If the computed cycle length is lower than the specified cycle length, then some
time should be reassigned to the arterial phases. This is accomplished by
increasing the maximum green times for phases 2 and 6. In the procedure, one
half of the difference between the computed cycle and the specified cycle is
assigned to the arterial phases. This provides a reasonable speed of convergence
without overshooting the specified cycle length.
5. Repeat steps 2 through 4 until the computed and specified cycle lengths converge.
This procedure has also been implemented in software. A program called NONACT
was developed in cooperation with the ACT348 program to predict the phase times for
coordinated semiactuated operation. The computational procedure is simple and an iterative
procedure is also involved. The NONACT program can set up the input data, execute ACT3
48 as an external program and read results. Since the ACT348 program obtains its data from
WHICH data file, the NONACT program must make changes to that file to implement steps
2 through 4 as described above. The NONACT program will run ACT348 iteratively until
the computed cycle length converges to the specified background cycle length.
CHAPTER 5
MODEL TESTING AND EVALUATION
Introduction
The structure and details of the proposed analytical model and procedure for traffic
actuated operation in both isolated and coordinated modes have been described. The model
and procedure which are implemented in the ACT348 program may be used to predict the
average phase times and cycle length which are generated by a trafficactuated controller with
specified traffic data and operating parameters. In this chapter, testing is performed first to
evaluate the developed analytical models by NETSIM simulation and field data for fully
actuated operation. Then, other testings are performed to examine the performance of the
NONACT program which implements the proposed procedure to predict the phase times of
coordinated semiactuated operation. Finally, an intensive evaluation is conducted to explore
the headway distributions of vehicular arrivals at the stopline (due to the use of presence
detectors) produced by the analytical model and the NETSIM simulation model which may
cause the difference on the phase time prediction for fullyactuated operation.
Fullyactuated Operation
Three major tasks were performed to evaluate the analytical models for fullyactuated
operation. The first task is to compare the predicted cycle length between the analytical
model and NETSIM with a very simple example with a twophase trafficactuated operation.
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95
The second task is to compare the phase time estimates between the analytical model and
NETSIM with different hypothetical examples including four HCM Chapter 9 sample
calculations and five hypothetical examples. The last task is to compare the predicted phase
times between the analytical model and NETSIM with those from real field data.
Cycle Length Comparison with a Twophase Trafficactuated Example
The objective of this testing focuses on the comparison of estimated cycle lengths
among the HCM Appendix II method, proposed analytical model and NETSIM simulation.
The cycle lengths were determined as a function of the traffic volume level by four methods:
1) the HCM Appendix II method given in Equation 21 assuming the recommended 95% v/c
ratio; 2) the HCM Appendix II method based on the iterative procedure with adjusted vehicle
minimum; 3) the proposed analytical model with bunched exponential arrivals; and 4)
simulation by NETSIM, using the trafficactuated control option. Note that methods 2 and
3 were performed by the ACT348 program and the results of each NETSIM run were
summarized by the NETCOP postprocessor.
Consider the intersection shown in Figure 25. This is a trivial intersection with four
singlelane approaches carrying the same through traffic. All approaches are configured
identically. For simplicity, a saturation flow rate of 1800 vphgpl, corresponding to a headway
of 2 seconds per vehicle, will be assumed. A 30ft long detector is placed at the stopline for
each approach. Each phase has been assigned the same constant parameters as follows.
Intergreen time is 4 seconds. Lost time is 3 seconds per phase. Minimum phase time and
maximum phase time are set at 20 and 70 seconds, respectively. Assuming there are no
pedestrian timing features and no volumedensity features.
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Relatively long maximum phase times have been selected to ensure that the timing is
not constrained artificially. This will give a better insight into the cycle computation
procedure. The traffic volumes and the allowable gap setting were both varied to examine
the sensitivity of the analytical model and the NETSIM simulation model to these parameters.
The volume was varied throughout the range of 100 to 800 vehicles per hour, per approach.
Three allowable gap settings of 1.5, 3.0 and 4.5 seconds were used to represent low, medium
and high values respectively. The results are presented on four figures:
Figure 51: representing a 1.5sec allowable gap setting.
Figure 52: representing a 3.0sec allowable gap setting.
Figure 53: representing a 4.5sec allowable gap setting.
Figure 54: representing a composite of Figures 51, 52, and 53 for comparison.
Â±~ Appendix II â€”Adj. Min. â€”Model s NETSIM
Figure 51. Cycle length computation for a 1.5sec allowable gap setting.
Predicted Cycle Length (sec) Â« Predicted Cycle Length (sec
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Appendix II â€”Adj. Min. â€¢ Model b NETSIM
52. Cycle length computation for a 3.0sec allowable gap setting.
100 200 300 400 500 600 700 800
Traffic Volume per Lane (vph)
Appendix II â€”*â€” Adj. Min. â€”Model b NETSIM
Figure 53. Cycle length computation for a 4.5sec allowable gap setting.
98
Figure 54. Composite cycle length computations with all gap settings.
Some interesting observations may be made from these figures:
1. It is quite clear that all of the computational techniques yield longer cycle length
estimates than the current Appendix II method.
2. All of the models tested showed a credible sensitivity to the allowable gap setting.
As the gap setting increased, the cycle length increased. The specified maximum
cycle length of 140 seconds was reached for the proposed model and NETSIM
simulation at volume levels ranging from 750 to 800 vph on each approach.
3. All of the techniques produce a more gradual increase in cycle length throughout
the volume range than the Appendix II method. Note that the Appendix II cycle
length remains below the 40sec minimum value until the volume exceeds 700
vph, and then rises very rapidly to an value of about 100 seconds. The other
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methods all predict much longer cycle lengths than those form the Appendix II
method at much low volumes.
4. The bunched exponential gap extension model predicts cycle lengths that are very
close to those predicted by the gap extension model that assumes random arrivals.
The results of both models were plotted as a single curve in the figures.
5. NETSIM's cycle length estimates tend to be somewhat longer than the
corresponding estimates from the proposed analytical model. The reasons for
these differences will be explained in more detail later in this chapter.
Figure 55. Percent of phases terminated by maximum green time for each gap setting.
The stochastic nature of the NETSIM model provides a more detailed picture of the
variability of the operation from cycle to cycle. Based on the same traffic volume scale as the
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previous figures, Figure 55 shows the percent of phases terminated on the maximum for the
three specified gap extension settings. This information was produced from the NETSIM
results by the NETCOP postprocessor. In Figure 55, the percent of phases terminated by
the maximum is almost negligible with the 1.5sec gap setting, even at the highest traffic
volume. On the other hand, all of the phases will terminate on the maximum time at higher
volumes for the longer gap settings.
Phase Time Comparison with Hypothetical Examples
To provide a general comparison between the HCM Chapter 9 Appendix II method
and the proposed analytical model, several example data sets, including four HCM Chapter
9 sample calculations and five hypothetical examples, were subjected to phase time estimates
by both models. Some of the traffic and operational data were modified slightly to increase
the range of conditions included in this analysis. NETSIM was used as the evaluation tool.
The results are plotted graphically in Figures 56 and 57. Both figures plot NETSIM phase
time estimates against the corresponding estimates from the analytical model.
Figure 56 shows a phase time comparison between the Appendix II method and
NETSIM. A considerable dispersion of the data points is evident in this figure. By
inspection, the slope of the linear regression line indicates that the simulated phases times are
much longer than those estimated by the Appendix II method. The correlation is low, as
evident in the R squared value of only 0.70. Figure 57 shows a phase time comparison
between the proposed model and NETSIM. The dispersion of the data points is much
smaller, indicating a much better agreement between the two techniques. This is confirmed
by a high R square value of 0.93. The regression line is also close to 1:1 slope.
Phase Time from Analytical Model â€™ Phase Time from the Appendix II Method
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Phase time comparison between the Appendix II method and NETSIM.
Figure 57. Phase time comparison between the proposed model and NETSIM.
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Phase Time Comparison with Field Data
To further verify the analytical model, a field study was conducted at the intersection
of Museum Road and Northsouth Drive on the campus of the University of Florida in
Gainesville, Florida. In total, 32 hours of data were used in this evaluation which included
the morning peak, midday and the afternoon peak of three weekdays. The site is a fourÂ¬
legged intersection with one through lane and one exclusive left turn bay about 250 feet in
length on each approach. The configuration of the studied intersection for the field data
evaluation is shown in Figure 58.
NS Drive NB
Figure 58. Intersection configuration of Museum Road and Northsouth Drive on
the campus of the University of Florida.
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Standard dualring phasing applies with protected plus permitted left turns. The ideal
saturation flow rate is 1900 vehicles/hour. Pedestrian recall was set in the controller and the
duration for WALK phis Flashing DON'T WALK was 22 seconds. The intergreen time was
5 seconds. The allowable gap setting was 3.5 seconds for through movements and 2.5
seconds for left turns. All detectors were 25 feet in length placed at the stopline. The
minimum green time was set at 16.5 seconds for through phases and 10 seconds for left turns.
The maximum green time was set at 45 seconds for through phases and 15 seconds for left
turns on the heavier street. The corresponding maximum green time settings for the minor
street were 30 and 10 seconds, respectively.
Figure 59 shows a phase time comparison between the estimates from the analytical
model and field data. Two groups of data points are shown in the figure because the through
traffic phases tended to be longer than the left turn phases. Although the phase time estimates
from the model are slightly higher than the measured field data for left turn phases (low
volume), the regression line is close to 1:1 slope. The dispersion of the data points is small,
indicating that the phase time estimates from the model are close to the field data. This is
confirmed by a very high R squared value of 0.95.
Figure 510 shows a phase time comparison between NETSIM and field data. Two
groups of data points are also shown in the figure because the through traffic phases tended
to be longer than the left turn phases. The phase times estimated by NETSIM are close to
the field data indicated by a very high R square value of 0.96. By inspection, the regression
line is close to 1:1 slope but slightly above it. NETSIM slightly overestimated the phase times
at this intersection.
Phase Time from ACT3â€”48 (sec
104
Figure 59. Phase time comparison between the analytical model and field data.
Figure 510. Phase time comparison between NETSIM and field data.
105
Coordinated Actuated Operation
In order to examine the capability of the NONACT program which implements the
proposed procedure to predict the phase time of coordinated operation. NETSIM is also
used as the evaluation tooL The estimated phase times from NONACT were compared with
those estimated by NETSIM simulation with ten different scenarios based on possible
intersection configuration, left turn treatments and traffic conditions.
Phase Time Relationship between a Cross Street and an Artery
A simple data set was used to examine how the timing of phases change as the cross
street volume increases. The hypothetical intersection has four singlelane approaches
carrying only the through traffic. It is a twophase coordinated semiactuated operation. The
minimum and maximum phase times for the minor street are 15 and 30 seconds, respectively.
The allowable gap for the minor street is 3 seconds. The detectors are 30 feet long placed
at the stopline of minor street approaches. The traffic volume on the arterial street is fixed
at 800 vph, while it varies from 100 to 800 vph on the cross street. The common background
cycle length is specified as 60 seconds, and the initial split is 30 seconds for both phases.
Figure 511 is the phase time comparison for arterial and cross streets between NONACT and
NETSIM under the simplest scenario of coordinated operation.
Figure 511 shows a reasonable relationship of phase times between the arterial street
and cross street for both NONACT and NETSIM's results. When the cross street volume
increases, the phase times required by the cross street increase. Relatively, the phase times
assigned to the arterial street decrease, which is equal to the background cycle length minus
the minor street phase times. When the minor street volume is about 800 vph, the maximum
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phase time, 30 seconds, on the cross street is reached. Since the background cycle length is
60 seconds, 30 seconds of phase time are also assigned to the arterial street.
Therefore, the curves of phase times for both the arterial and cross streets converge
at 30 seconds. It is easy to observe that the phase times estimated by the NONACT program
are very close to those estimated by the NETSIM simulation, which demonstrates that the
proposed procedure in the NONACT program is capable of predicting similar phase times for
coordinated semiactuated operation to those by NETSIM simulation in the simplest scenario.
J H l 1 1 1 1 1
100 200 300 400 500 600 700 800
Cross Street Traffic Volume (vph)
Â« NONACT(A) â€”11â€” NETSIM(A) NONACT(C) A NETSIM(C)
Figure 511. Phase time comparison between arterial street and cross street.
Phase Time Comparison with Hypothetical Scenarios
The objective of this test is to examine the performance of the NONACT program
which implements the proposed procedure to predict the phase time of coordinated actuated
107
operation. The hypothetical data sets fall into 10 categories based on intersection
configuration, left turn treatment and number of lanes. These scenarios represent a wide
variety of conditions. The reason for using so many data sets is to generally test the
prediction capability of the proposed procedure for coordinated actuated operation. The
parameters are fixed for these 10 scenarios as follows:
Background cycle length: 120 seconds
Unit extension (all phases): 3 seconds
4 seconds
1800 vehicles/hour
Intergreen (all phases):
Saturation flow rate:
Minimum green time: 11 seconds (through movements)
6 seconds (left turns)
Maximum green time: 56 seconds (approaches without left turn protection )
46 seconds (through phases)
26 seconds (protected left turn phases)
Figure 512 shows the phase time comparison between NONACT and NETSIM.
Note that in this comparison, all phase time estimates belong to the actuated phases. The
predicted phase times from the NONACT program are very close to those estimated by
NETSIM. A very high R squared value of 0.97 is achieved which indicates the proposed
procedure can accurately predict the phase times for coordinated actuated operation in the
chosen examples. The NONACT program is able to provide credible estimates of phase times
for coordinated operation of a trafficactuated controller.
108
Figure 512. Relationship of estimated phase times between NONACT and NETSIM.
Further Evaluation of the Analytical Model
In general, NETSIM simulation produces longer phase times than those from the
analytical model for most simulated phase times and shorter phase times when the simulated
phase times are short. A trafficactuated controller terminates a given phase whenever a gap
appears at the detector that exceeds the allowable gap specified for that phase. Therefore,
the length of a phase will depend heavily upon the probability of a gap extended in the traffic
flow after the queue has been serviced. For example, a vehicular arrival distribution with a
higher accumulated probability to actuate a detector to extend the allowable gap after the
queue clearance will, in general, produce a longer phase time. If the analytical and simulation
models do not have the same vehicular arrival headway distributions at the stop line (due to
the use of presence detectors), then systematic differences will be built into any phase time
109
comparison that will cause the results to diverge. Hence, an effective approach to explore
these systematic differences is to examine the headway distribution of vehicular arrivals at the
stopline produced by NETSIM and the proposed analytical model.
Distribution of Arrivals by Bunched Model and NETSIM
The arrival headway distribution for the proposed analytical model is the bunched
negative exponential model which was described in Chapter 2. For the convenience of
explanation, its cumulative distribution function F(t) is expressed as follows:
F(t) = 1  A (51)
= 0 for t < A
The definitions of
of the parameters needed in Equation 51, its accumulative probability of the bunched arrival
model can be computed. Equation 212 may be used to predict the expected extension time
eg before a gap of a specific length occurs to terminate the green time.
In the current version of NETSIM, it is impossible to specify the characteristics of the
arrival distribution. Vehicles are released into each external link from a mythical entry node
with constant headways that form a uniform distribution. NETSIMâ€™s queue propagation
algorithm causes some bunching of vehicles to occur as they proceed though the link. The
actual shape of the arrival distribution at any point downstream may depends variability of
speeds of vehicle types and the length of the link. It is very difficult to predict analytically.
To demonstrate NETSDVTs arrival headway distribution mechanisms, several runs were made
110
in which traffic streams with different flow rates were introduced into singlelane links with
different link lengths. Link lengths of 100, 1000, 2000 and 3000 feet are represented in
Figures 513 to 516, respectively. Traffic volumes of 100, 300, 500, 700 and 900 vph are
shown in each of the figures as separate curves. In these figures, the arrival headway is on
the horizontal axis, and the accumulated probability is on the vertical axis.
Figure 513 illustrates the uniform distribution of entering vehicles which travel only
100 feet after they are introduced into the link. The shape of the arrival distribution 100 feet
downstream is very similar to that at the entering node because little propagation occurs in
such short distance. Note that the accumulated probability proceeds almost vertically between
zero and 100 percent at a headway value that is very close to the average headway. For
example a volume of 300 vph reflects an average headway of 12 (=3600/300) seconds per
vehicle. The transition takes place very close to this headway value.
Figures 514 through 516 demonstrate the effect of increasing the distance between
the point of entry and the point at which the distribution is observed. As this distance is
increased, the abrupt transition of Figure 513 gives way to a smoother transition with the
characteristic shape of a bunched exponential distribution. It is found for the same traffic
volume that when the link length increases, the effect of bunching increases. For the same
link length, when the traffic volume increases, the effect of bunching also increases. From
these observations it may be seen that NETSIM is indeed capable of producing arrival
distributions that agree qualitatively with our expectations. However, the parameters of the
distributions vary with link length. This factor is not considered in the bunched exponential
distribution used in the analytical model.
Ill
Arrival Headway (seconds)
â€”â€¢*â€” 100 vph â€¢*â€¢â€” 300 vph â€”*â€” 500 vph
700 vph 900 vph
Figure 513. NETSIM arrival distributions for a singlelane link of 100ft length.
Arrival Headway (seconds)
â€”Â«â€” 100 vph ~+â€” 300 vph â€”500 vph
â– 700 vph â€”Aâ€” 900 vph
Figure 514. NETSIM arrival distributions for a singlelane link of 1000ft length.
112
Arrival Headway (seconds)
1 QQ Vph 300 yph â€”
*â€” 500 vph
Hâ€” 700 vph â€”Aâ€”â€¢ 900 vph
Figure 515. NETSIM arrival distributions for a singlelane link of 2000ft length.
Arrival Headway (seconds)
100 vph 300 vph 500 vph
* 700 vph 900 vph
Figure 516. NETSIM arrival distributions for a singlelane link of 3000ft length.
113
Comparison of Analytical and Simulated Arrival Distributions
The analytical distributions are independent of link length, but they naturally depend
heavily on the traffic flow rate. Figures 517 through 521 represent the comparison of arrival
distributions between the analytical model and NETSIM simulation on a single lane for low
of 100, 300, 500, 700 and 900 vph, respectively. Separate curves are plotted on each figure
for the analytical model and for the NETSIM distributions with different link lengths.
The results show a noticeable difference between the analytical and simulated
distributions with low traffic volumes as shown in Figure 517. When traffic volume
increases, the two methods tend to converge. However, even for the 900 vph level
represented in Figure 521, there is a visible difference between them, especially at headways
in the general range of typical unit extension times (i.e., less than 5 seconds) for traffic
actuated controllers. This suggests that, at least for single lane operation, there will continue
to be a disparity between the signal timings estimated by NETSIM and the proposed model.
If two models suggest a different probability of a gap equal to or less than the
specified vehicle interval for a given phase, then the model suggesting a higher probability will
also estimate a longer green time for that phase. Now, inspection of Figures 517 through
521 indicates that the proposed analytical model suggests a higher value of phase time with
low traffic volumes and a lower value with high traffic volumes. For midrange volumes, say
500 vph, comparison could go either way, depending on the link length. This result may
explain that in the previous phase time comparison, the proposed analytical model produces
longer phase times for low traffic volumes and longer phase times for medium and high
volumes than those from the NETSIM simulation model.
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Arrival Headway (seconds)
Bunched L= 1000 ft L= 2000 ft L= 3000 ft
Figure 517. Comparison of analytical and simulation model arrival distributions for singleÂ¬
lane, 100vph flow.
Arrival Headway (seconds)
Bunched â€¢*Â» L= 1000 ft
L= 2000 ft
L=3000 ft
Figure 518. Comparison of analytical and simulation model arrival distributions for singleÂ¬
lane, 300vph flow.
115
Arrival Headway (seconds)
â€¢ Bunched L= 1000 ft L=2000ft L=3000ft
Figure 519. Comparison of analytical and simulation model arrival distributions for
singlelane, 500vph flow.
Arrival Headway (seconds)
Bunched L= 1000 ft â€”L= 2000 ft A L= 3000 ft
Figure 520. Comparison of analytical and simulation model arrival distributions for
singlelane, 700vph flow.
116
Arrival Headway (seconds)
 Bunched L= 1000 ft â€”L= 2000 ft A L= 3000 ft
Figure 521. Comparison of analytical and simulation model arrival distributions for
singlelane, 900vph flow.
â€”h=2oec ~+~ h=3sec â€”h=4sec â€”Aâ€” h=5sec
Figure 522. Optimal NETSIM singlelane link length for various phase termination
headway settings.
117
It is possible to carry this analysis one step further and determine the link length at
which an equal probability of a gap of any specified length or shorter would be produced by
both models. The results are shown in Figure 522, which shows the "optimal" link length
for different traffic volumes and phase termination headways. The optimal link length is
defined here as the link length that would produce an equal probability of a headway of the
specified phase termination headway or shorter. The headway for phase termination must
be used here directly, as opposed to the gap, because the actual gap value for a given
headway will depend on the vehicle and detector lengths as well as the traffic speed. Note
that the optimal link lengths vary between 1000 and 3000 feet and decrease as traffic volumes
increase. The link lengths used in all of the sample problems were 2640 feet (one half mile).
Multiple Lane Arrival Headways
The preceding discussions and the results presented in Figures 517 through 522
assume a single lane operation. A similar comparison of arrival headway distributions for a
twolane operation with volumes of200, 600,1000 and 1800 vph is presented in Figures 523
through 526, respectively. Traffic volumes were increased because of the higher capacity
of twolane facilities. The same link lengths of 1000, 2000 and 3000 feet were used.
Examination of these figures shows a tendency that is similar to the single lane case
at low volumes (see Figure 523). The proposed analytical model produces higher
probabilities of headway in the range of the phase termination headways. However,
differences in these estimates disappear quickly as traffic volumes increase. At high volumes
(see Figure 526) they are barely discemable. This suggests that the proposed analytical
model should show better agreement with NETSIM with respect to the controller operation.
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Arrival Headway (seconds)
Bunched â€”L= 1000 ft â€”L=2000ft A L=3000ft
Figure 523. Comparison of analytical and simulation model arrival distributions for
twolane, 200vph flow.
Bunched L= 1000 ft â€”L= 2000 ft A  L= 3000 ft
Figure 524. Comparison of analytical and simulation model arrival distributions for
twolane, 600vph flow.
119
Arrival Headway (seconds)
Bunched L= 1000 ft L= 2000 ft L= 3000 ft
Figure 525. Comparison of analytical and simulation model arrival distributions for
twolane, 1000vph flow.
Arrival Headway (seconds)
Bunched â€”*â€¢ L= 1000 ft L= 2000 ft  A L= 3000 ft
Figure 526. Comparison of analytical and simulation model arrival distributions for
twolane, 1800vph flow.
120
Other Modeling Differences
The differences in arrival headway distributions are an important source of disparity
between NETSIM and the proposed analytical model. They are also the easiest to explain.
They are not however, the only differences between the two techniques. There are some
stochastic aspects of the operation that do not lend themselves well to deterministic
approximations. There is a significant divergence in the manner in which NETSIM and the
HCM treat traffic complexities such as permitted left turns from shared lanes. The proposed
analytical model has adopted the HCM approach as closely as possible in the treatment of
traffic. This is essential if the results of this work are to be incorporated into the HCM.
The simulation runs presented in this dissertation were performed with the latest
available version of NETSIM, a betatest release of Version 5. This version has overcome
several deficiencies which are evident in its predecessors, however, it is anticipated that
additional enhancements to NETSIM will appear in the near future. For example, the changes
in the vehicle generation algorithms will be forthcoming to allow user specified arrival
headway distributions.
One of the most serious limitations of NETSIM at this point is the resolution of the
input data for the average departure headway. This is currently 0.1 seconds, or about 5
percent of a typical departure headway. The HCM provides a method for estimating the
saturation flow rate to a level of precision that definitely exceeds its accuracy. This is a
currently insurmountable source of divergence between the two methods. For example,
departure headways of 1.9, 2.0 and 2.1 seconds conform to saturation flow rates of 1895,
1800 and 1714 vphgpl, respectively. Saturation flow rates between these values are not
121
recognized by NETSIM. This problem was avoided in the most examples described in this
dissertation by setting the saturation flow rates to 1800 vphgpl. It is suggested that, when
a signalized intersection is operating at capacity, that 5 percent capacity increments are too
coarse for an accurate analysis.
CHAPTER 6
EXTENDED REFINEMENT OF THE ANALYTICAL MODEL
Introduction
The previous chapters described a fully functional computation model to compute the
average phase times and cycle length given the intersection configuration, traffic volumes,
phasing and controller parameters. The model recognized all types of standard left turn
treatments including permitted, protected and compound left turn protection (protected plus
permitted or permitted phis protected). Permitted left turns could be made from either shared
or exclusive lanes. The model was implemented in a program called ACT348, with data
obtained directly from a data set created and edited by the WHICH program, which eliminates
the need for a separate input data editor and facilitates the comparison of the ACT348 results
with the corresponding results from other methods such as NETSIM. The results of the
model evaluation in the last chapter are very encouraging. The model is analytically sound
and the computational framework in which it has been implemented is robust. At this point,
the model is ready for further refinement. In order to enhance the model to achieve a stronger
capability to predict phase times and cycle length for actuated operation, some additional
refinements of the analytical model are presented in this chapter. These refinements and
enhancements include
122
123
1. Refinement of the analytical model for volumedensity operation;
2. Refinement of the analytical model to incorporate free queue parameter; and
3. Incorporation of the analytical model into the HCM Chapter 9 procedure.
Refinement of the Analytical Model for Volumedensity Operation
Volumedensity operation is one version of trafficactuated control which is best
suited for an intersection with heavy volume on all approaches and a high approach speed
(>35mph). In this operation, the controller employs a more complex set of criteria for
allocating time and terminating the phase. In addition to actuated design parameters in fully
actuated operation, volumedensity controllers have variable initial and gap reduction
features, and detectors are usually placed at a distance from the stopline.
Volumedensity Control Description
In volumedensity control, the minimum initial interval (Mnl) is the minimum assured
green that is displayed. It must be long enough to allow vehicles stopped between the
detector on the approach and the stopline to get started and move into the intersection. On
some controllers the minimum green includes a minimum initial time plus a passage time. The
minimum initial interval should be small to clear a minimum of vehicles expected during light
volume. Another timed interval called variable initial interval (or added initial interval) will
be added to the minimum initial interval. The length of the variable initial interval shown in
Figure 61 is equal to the product of the number of vehicle arrivals on red and clearance
intervals and the specified time interval for each vehicle actuation. This feature increases the
minimum assured green so it will be long enough to serve the actual number of vehicles
waiting for the green between the detector and the stopline.
124
Figure 61. Variable initial feature for volumedensity operation.
Another feature is gap reduction. The purposes of gap reduction are to reduce the
probability of "maxout" and to prevent phase termination with vehicles in the "dilemma zone".
The gap reduction feature shown in Figure 62 is accomplished by the following functional
settings: time before reduction, passage time, minimum gap and time to reduce. These terms
need to be defined.
The time before reduction period begins when the phase is green and there is a
serviceable conflicting call (e.g. at time t in Figure 62). The passage time is the time
required for a vehicle moving at average approach speed to travel from the detector to the
stopline. The normal approach speed is assumed to be the 85th percentile speed. Upon
completion of the time before reduction period, the linear reduction of the allowable gap
125
begins from the passage time to the minimum gap. The specified time for gap reduction is
called time to reduce. Thus, the gap reduction rate is equal to the difference between the
passage time and minimum gap settings divided by the setting of time to reduce. The
purpose of gap reduction from the passage time to the minimum gap is to reduce the
probability of maxout. In volumedensity control, the last vehicle that actuates the detector
before the allowable gap expires can extend the phase by one passage time. Therefore, this
vehicle can safely pass the intersection and avoid the dilemma zone.
Figure 62. Gap reduction feature for volumedensity operation.
Modeling of Volumedensity Control
The previously developed analytical model is used to predict the phase time of any
movement in a follyactuated operation. However, it can also be applied to estimate the
126
phase duration for through vehicles and protected left turns for volumedensity control if
proper refinements of the analytical model are done. In this study, the time before reduction
is assumed to be zero for simplicity and the gap reduction begins at the green phase. The
proposed refinements to the model will be introduced next and a simple example application
will follow.
Refinement of the Analytical Model
The main differences between the volumedensity and basic fullyactuated operations
are the minimum green time settings, the detector configuration, the gap reduction feature and
the passage time setting for the last vehicle actuation. The refinement of the analytical model
for volumedensity operation focused on these areas.
The initial interval (II) (adjusted minimum green time) for volumedensity operation
is equal to the specified minimum green time (Smn) plus variable initial (added initial)
subjected to the constraint of specified maximum initial setting, where the specified minimum
green time here is equal to the minimum initial interval (Mnl) plus starting gap (SG). It is
common to choose a value for the starting gap which is equal to the passage time from the
detector to the stopline. The variable initial interval is the product of the number of vehicles
arrival on red the phase and the specified time for each vehicle actuation. The value of
variable initial interval can be computed as follows:
Variable Initial Interval (VII) = Qr * t^, (61)
where
Qr = number of arrivals during previous red and clearance intervals; and
tac, = specified time per actuation.
127
Then, the initial interval (II) is equal to the sum of the specified minimum green (Smn)
and variable initial interval (VII). However, this value cannot exceed the specified maximum
initial interval (Smx). Therefore,
Initial Interval (II) = Min. (Smn + VII, Smx) (62)
where
Smn = specified minimum green time; and
Smx = specified maximum initial interval.
The analytical model applies the queue accumulation polygon to compute the queue
service time and the bunched arrival model to estimate the vehicle extension time after queue
clearance. Based on the computation of total queue service time, QST (= tsl + gqst), and total
vehicle extension time, EXT (= eg + I), the final phase time, PT, can be obtained which is
equal to the sum of QST and EXT. To estimate the phase times for the volumedensity
operation, the computation of the total queue service time, QST, needs to be modified
because the location of presence detector is not necessarily at the stopline.
In the analytical model for fullyactuated operation, the detector is assumed to be
placed at the stopline. However, It is common with volumedensity control that the detector
setback is greater than zero. In the queue discharge process when the signal turns green, the
length of moving queue will decrease gradually if the volume to capacity ratio (v/c) is less
than 1.0.
The last moving queue will pass through the upstream detector first and then the
stopline. The queue service time is defined as the time required to serve the queue beyond
the detector. Therefore, the queue service time for volumedensity control, in general, is
128
shorter than that for fullyactuated operation. The proposed refined model will use the total
queue service time of the fullyactuated operation minus a passage time to estimate the queue
service time for the volumedensity operation. This will be called computed queue service
time (CQST).
The initial interval (adjusted minimum green) is the assured green that will be
displayed. IÂ£ at the end of the initial interval, the length of the farthest backup queue (FBQ)
from the st op line does not reach the upstream detector, the final queue service time should
be equal to the minimum value of the initial interval and computed queue service time. For
example, if the initial interval is less than the computed queue service time, the final queue
service time is the initial interval because for the upstream detector the queue has been cleared
at the end of initial interval. If the FBQ exceeds the upstream detector, the final queue service
time is just equal to the computed queue service time.
An easy way to determine whether or not the FBQ reaches the upstream detector is
to compare the FBQ and the maximum storage of vehicles (MSV) between the upstream
detector and stopline. A vehicle is assumed to occupy 25 ft, so MSV is equal to the distance
between the upstream detector and the stopline divided by 25. The length of the FBQ may
be estimated from the average vehicle arrivals during the red and initial interval using the
following formula:
FBQ = q, * (R + II)
(63)
The computation for QST may be summarized as follows:
QST = Min. (CQST, II) if FBQ < MSV
(64)
QST = CQST
if FBQ > MSV
(65)
129
Example Problem
With the above refinements, the model is able to predict the phase times of protected
movements for volumedensity operation. A simple scenario with a twophase volume
density operation was examined as a basic evaluation. Each approach has just one lane and
carries the same through traffic. The traffic volume is varied from 100 to 800 vph per
approach to examine the sensitivity of the proposed method. The minimum and maximum
green times are 6 and 60 seconds, respectively. The maximum initial is 16 seconds. The
minimum allowable gap setting is set to 2 seconds. The detector is 30 feet in length. Each
vehicle actuation during the red phase can add 2 seconds to the minimum green time. Three
specific values of detector setbacks were used to represent short, medium and long values,
respectively. The estimated phase times from the model were compared with those from
NETSIM simulation runs.
The results for 0ft, 150ft and 300ft detector setbacks are shown in Figures 61, 62
and 63, respectively. Both the proposed analytical model and the NETSIM simulation model
show a credible sensitivity to the detector setback. As the detector setback increases, the
predicted phase times from both model computation and NETSIM simulation decrease
because the probability of accumulated queue beyond the detector decreases when the
detector setback increases.
Generally speaking, the phase times estimated from the model are close to those from
NETSIM simulation. Therefore, within the limits of this simple example, it appears that the
proposed analytical model is able to provide reasonable estimates of phase times for volume
density operation.
130
Figure 63.
Figure 64.
100 200 300 400 500 600
Traffic Volume (vph)
700
800
Model
NETSIM
Phase time comparison for volumedensity operation with a zero detector
setback.
~m~ Model
NETSIM
Phase time comparison for volumedensity operation with a 150ft detector
setback.
131
Model â€”NETSIM
Figure 65. Phase time comparison for volumedensity operation with a 300ft detector
setback.
Refinement of the Analytical Model to Incorporate "Free Queue" Parameter
The free queue parameter indicates the number of leftturning vehicles that may be
stored in a shared lane waiting for gaps in the opposing traffic without blocking the passage
of the following vehicles. Therefore, both the left turn equivalence, EL1, and the shared lane
saturation flow rate are affected by the free queue parameter. The current HCM procedure
assumes that the first waiting left turn will block all of the following vehicles in the shared
lane. This produces pessimistic results in some cases.
At this point, only the SIDRA model considers the free queue explicitly which adopted
the use of an average saturation flow to count for the effect of free queue. Because of its
importance to trafficactuated control, it is essential that the proposed analytical model
132
recognizes this phenomenon. The analytical basis of the model for free queue is described in
this dissertation. A set of curves is developed to illustrate the effect of free queue on the
estimated phase times as a function of the approach volume. Because NETSIM does not
recognize the free queue explicitly, it was not possible to test this model by simulation.
Computation of New Throughcar Equivalents
Leftturning vehicles will select gaps through the opposing flow after the opposing
queue clears. During this unsaturated period, the HCM Chapter 9 assigns EL1 throughcar
equivalents for each leftturning vehicle. Normally, the permitted saturation flow rate of a
shared lane can be computed based on the assigned value of EL1 and the proportion of left
turns, PD in the shared lane. However, if a free queue exists, the block effect of leftturning
vehicles may be reduced. Therefore, the value of EL1 needs to be modified to account for the
effect of the free queues. The permitted saturation flow rate may become large because of
reduced block effect.
The new EL1 for a leftturning vehicle on a shared lane with free queues can be
computed based on 1) the value of EL1 for each combination of vehicles affected by the left
turning vehicle during its maneuver time; and 2) the probability of each combination. The
proposed theory and method for computing the new Eu are described below.
If old El, is equal to n, the original maneuver time required for the leftturning vehicle
is equal to the maneuver time required for n through vehicles. That means this leftturning
vehicle may block (n1) following vehicles which can be left turns or through vehicles
including right turns. Thus, these (n1) vehicles following the leftturning vehicle need to be
considered if a free queue exists because they are affected by the leftturning vehicle.
133
If no free queue exists, the individual El, for any vehicle combination is always the
same because during the original maneuver time of the leftturning vehicle, only this left
turning vehicle can departure. The following (n1) vehicles have no chance to leave due to
the block by the leftturning vehicle. Therefore, the throughcar equivalents for this left
turning vehicle is still equal to n.
If a free queue exists, the individual EL1 for a vehicle combination will be different if
the combination of the following (n1) vehicles is different. For example, assuming there
exists one free queue, if the following (n1) vehicles are all left turns, the new left turn
equivalence for this combination is still equal to n because only this leftturning vehicle can
departure during its original maneuver time. However, if the following (n1) vehicles are all
through vehicles, the new left turn equivalence for this combination is equal to one because
all n vehicle can departure during the original maneuver time of the leftturning vehicle. No
block effect occurs. Due to the existence of one free queue, this leftturning vehicle is
equivalent to one through vehicle. Hence, the new value of EL1 may be computed as an
weight average of the individual El, based on its probability of vehicle combination.
The proportion of left turns in a shared lane, PL, is a very important factor for the
computation of the probability for each combination of the following (n1) vehicles. Because
the following vehicles are belong to either left turn category (L) or through category (T),
there are a total of 2(n'1) combinations. For each combination, the individual left turn
equivalence and its probability can be computed. By taking the weight average of individual
Elâ€ž the new value of EL, for the leftturning vehicle can be obtained. A simple example for
the computation of new left turn equivalence is illustrated below.
134
Example: The throughcar equivalents of a leftturning vehicle, EL1 = 3; and
The proportion of left turns in a shared lane, PL = 0.2
The computation of the new throughcar equivalents is as follows:
Total combinations = 2 (n']) = 2 (3'1} = 4
The probability of a leftturning vehicle in a shared lane = 0.2
The probability of a through vehicle in a shared lane
Combination:
i
2
3
4
Left turn:
L
L
L
L
Following vehicles:
L
L
T
T
L
T
L
T
Probability:
0.04
0.16
0.16
0.64
Individual El,:
3
3
2
1
Therefore,
New El, = (0.04 x 3) + (0.16x3) + (0.16 x 2) + (0.64 x 1) = 1.56
The range of original (old) El, vales presented in the HCM Chapter 9 is from 1.05 to
16.0 for permitted left turns in a shared lane and the range for PL is from 0 to 1.0. The
reasonable maximum value of the free queue considered in this study is 2.0 vehicles. Based
on the proposed method, the new Eu values for one and two free queues are shown in the
Tables 61 and 62, respectively. If the old El, value, PL value or the number of free queues
is not a specified value in the tables, the new EL1 can be estimated by interpolation.
135
Table 61. Throughcar equivalents, EL1, for permitted left turns in a shared lane
with one free queue.
Old
The Proportion of Left Turns in the Shared Lane, PL
Eu
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.05
1.05
1.05
1.05
1.05
1.05
1.05
1.05
1.05
1.05
1.05
1.05
2
1.05
1.10
1.20
1.30
1.40
1.50
1.60
1.70
1.80
1.90
2.00
3
1.05
1.29
1.56
1.81
2.04
2.25
2.44
2.61
2.76
2.89
3.00
4
1.05
1.56
2.05
2.47
2.82
3.13
3.38
3.58
3.75
3.89
4.00
5
1.05
1.90
2.64
3.23
3.69
4.06
4.35
4.57
4.75
4.89
5.00
6
1.05
2.31
3.31
4.06
4.62
5.03
5.34
5.57
5.75
5.89
6.00
7
1.05
2.78
4.05
4.94
5.57
6.02
6.34
6.57
6.75
6.89
7.00
8
1.05
3.30
4.84
5.86
6.54
7.01
7.33
7.57
7.75
7.89
8.00
9
1.05
3.87
5.67
6.80
7.53
8.80
8.33
8.57
8.75
8.89
9.00
10
1.05
4.49
6.54
7.76
8.52
9.00
9.33
9.57
9.75
9.89
10.00
11
1.05
5.14
7.43
8.73
9.51
10.00
10.33
10.57
10.75
10.89
11.00
12
1.05
5.82
8.34
9.71
10.51
11.00
11.33
11.57
11.75
11.89
12.00
13
1.05
6.54
9.27
10.70
11.50
12.00
12.33
12.57
12.75
12.89
13.00
14
1.05
7.29
10.22
11.69
12.50
13.00
13.33
13.57
13.75
13.89
14.00
15
1.05
8.06
11.18
12.68
13.50
14.00
14.33
14.57
14.75
14.89
15.00
16
1.05
8.85
12.14
13.68
14.50
15.00
15.33
15.57
15.75
15.89
16.00
136
Table 62. Throughcar equivalents, Eu, for permitted left turns in a shared lane with
two free queue.
Old
The Proportion of Left Turns in the Shared Lane, PL
El,
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.05
1.05
1.05
1.05
1.05
1.05
1.05
1.05
1.05
1.05
1.05
1.05
2
1.05
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
3
1.05
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
4
1.05
1.3
1.6
1.9
2.2
2.5
2.8
3.1
3.4
3.7
4.0
5
1.05
1.4
1.8
2.2
2.6
3.0
3.4
3.8
4.2
4.6
5.0
6
1.05
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
7
1.05
1.6
2.2
2.8
3.4
4.0
4.6
5.2
5.8
6.4
7.0
8
1.05
1.7
2.4
3.1
3.8
4.5
5.2
5.9
6.6
7.3
8.0
9
1.05
1.8
2.6
3.4
4.2
5.0
5.8
6.6
7.4
8.2
9.0
10
1.05
1.9
2.8
3.7
4.6
5.5
6.4
7.3
8.2
9.1
10.0
11
1.05
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0
12
1.05
2.1
3.2
4.3
5.4
6.5
7.6
8.7
9.8
10.9
12.0
13
1.05
2.2
3.4
4.6
5.8
7.0
8.2
9.4
10.6
11.8
13.0
14
1.05
2.3
3.6
4.9
6.2
7.5
8.8
10.1
11.4
12.7
14.0
15
1.05
2.4
3.8
5.2
6.6
8.0
9.4
10.8
12.2
13.6
15.0
16
1.05
2.5
4.0
5.5
7.0
8.5
10.0
11.5
13.0
14.5
16.0
137
When the value of new throughcar equivalents, EL1(new), for a shared lane permitted
left turn is known, the new permitted saturation flow, s^,^ of a shared lane can be computed
as follows:
s
SP (new) i . p 7p _ i \ (66)
1 + *L (^Ll (new)
where
s = protected saturated flow rate (veh/sec); and
PL = the proportion of left turns in the shared lane.
Estimation of Free Green. gf. with Free Queue Parameter
The free green, gÂ¡, originally described in the HCM needs to be modified when the free
queue parameter is considered. When the green is initiated, the opposing queue begins to
move. While the opposing queue is being served, left turns from the subject shared lane are
effectively blocked. The portion of effective green blocked by the clearance of an opposing
queue is referred as gq in the HCM. Until the first leftturning vehicle arrives, however, the
through vehicles on the shared lane are unaffected by left turners. The portion of effective
green before the arrival of the first leftturning vehicle is referred to as free green, gt, in the
HCM. Basically, free green represents the time during which the through vehicles in the
shared lane are not affected by a left turner when the green initiates.
Generally, signal timing models assume that the first permitted left turn at the stopline
will block a shared lane. This is not always the case, as the through vehicles in the shared lane
are often able to "squeeze" around one or more left turns or leftturning vehicles wait near
138
the intersection center. A reasonable value of free queues is between zero and two. The
proper number of free queues can be observed from field. A leftturning vehicle in the free
queue will not block the following vehicle in the shared lane, so the free green will increase.
The proposed method to estimate the new free green with the existence of free queue is
describe as follows.
Based on the number of opposing lanes, nopp, and the relationship between gq and gf,
the permitted saturation flow rate, sp, can be determined as follows:
s
Sp " 1 + PL (Â£U  1)
if nopp = 1 and gq > gf (67a)
s
1P = 1 + PL (Eucnew ~ D
others
(67b)
where
s = protected saturated flow rate;
PL = proportion of left turns in the shared lane;
EL1(neW) = new throughcar equivalents for each leftturning vehicle during the
unsaturated green period; and
El2 = throughcar equivalents for each leftturning vehicle during the period of
(gq gf) when gq is greater than gf and the number of the opposing lane nopp
is equal to one.
Assume the average maneuver time (waiting time) for a LT vehicle in the free queue
to leave is x seconds. This waiting time can be derived as follows:
139
1
opL)
s
+ PT
X
Therefore,
x
s  sn + Sn PT
p p L
S S P.
P L
(68)
The key to estimate the new gf for permitted left turns in a shared lane with free
queues is to estimate the time when a left turn arrival will block further flow in a shared lane.
In order to estimate new gf, the probability of blocking effect needs to be computed first
which is the probability of at least one left turn arrival before one free queue space in the free
queue location is available. If one free queue space in the free queue location is always
available before one left turn arrives, no blocking effect will happen.
For the convenience of computation, "t" is defined as the average time allowed for a
leftturning vehicle to go into the free queue location without blocking the further traffic flow.
For example, the number of free queues available in a free queue location is two (n=2). The
leftturning vehicle in the free queue location takes 8 seconds to leave (i.e. x = 8 seconds)
on average. Then, t will be equal to 4 seconds (= x/n = 8/2). Assume the number of free
queues is n (0
t = x/n ifn>l
t = x if 0
Note that when n is less than one, the number of free queues will be assumed to be
one first. Later, the free green will be modified based on the real number of free queues
140
according to its probability. This process will avoid a very large t when n is very small.
During t seconds, the probability of left turn arrivals is P. According to the bunched arrival
distribution, the probability P can be computed as the product of bunched cumulative
distribution and the probability of left turn arrivals in a shared lane:
P  [ 1 (pe'1(t'A)]PL (69)
where
A = minimum arrival (intrabunch) headway (seconds);
(p = proportion of free (unbunched) vehicles; and
A = a parameter calculated as
A =
1Aq
subject to q < 0.98/A
where
q = total equivalent through arrival flow (vehicles/second) for all
lane groups that actuated the phase under consideration.
During the maneuver time of x seconds for the leftturning vehicle, the probability of
block effect due to left turn arrivals is assumed P. P can be computed by the following
equations. Note that, at this stage the number of free queues, n, is still treated as one if it is
less than one.
P = F if n > 1 (610a)
P = P
if 0
(610b)
141
The new free green, can be computed as follows:
gf(new) = gf(old) + tfD>1 (6'lla)
gf (new) = gf (old) + n y, if 0 < n < 1 (6lib)
In Equation 61 lb, the extended time of free green (x/p1) is multipbed by n to account its
occurrence probabihty of one free queue because it is assumed one in the previous
computation. If free queues exist, the phase times of trafficactuated operation may be
influenced. The degree of difference between the phase times with and without free queues
for a shared lane is mainly dependent on the combined effects of free green and throughcar
equivalents of a leftturning vehicle. The effect of the free queue parameter is especially
important for a single shared lane.
The phase time analysis for free queue parameter is best illustrated with a simple
example. Consider a trivial intersection with four singlelane approaches. All approaches
are configured identically and carry the same traffic volume. In each approach, the portions
of left turns, through and right turns are 0.2, 0.7 and 0.1, respectively. This is a simple two
phase fullyactuated operation. The minimum phase time for each approach is 15 seconds and
the maximum phase time is 84 seconds. Detectors are 30 feet long and placed at the stopline.
The allowable gap is 3 seconds. In each phase, the intergreen time is 4 seconds, and the lost
time of 3 seconds is assumed.
Each approach volume varies from 100 to 800 vph, while the range of free queue is
set from 0 to 2. Based on the proposed method, the phase time prediction for different free
queues is shown in Figure 66. In this figure, the x axis represents the approach volume, the
142
y axis shows the number of free queues, and the vertical axis is the predicted phase from the
proposed analytical model The effects of free queues may be easily observed from this three
dimensional surface diagram.
Figure 66. Phase time prediction for single shared lane with free queues.
In this example, left turns only occupy 20 percent of the total approach volume.
When approach volume is low, the headway between vehicles is large, and a left turn
maneuver is relatively easy to make. Therefore, the block effect caused by left turns is very
small. Theoretically, there will be nearly no difference of predicted phase times between
different free queues. This phenomenon can be shown in Figure 66 when approach volume
143
is below 400 vph. The left turn maneuver will become more and more difficult when the
approach volume becomes heavier, because the number of acceptable gaps for left turns
during the unsaturated portion of the opposing queue decreases. In other words, Eu become
large with the increase of the approach volume.
For the same number of free queues, the phase times will increase with the approach
volume due to the increasing block effect by left turns in the shared lane. On the other hand,
if the number of the free queues increases and the approach volume is fixed, the block effect
is reduced because leftturning vehicles are able to wait in the free queue before turning left.
The larger the free queue, the smaller the blocking effect.
These two phenomena can be clearly shown in Figure 66 when the volume is
between 400 vph and 720 vph and the value of free queues is between 0 to 1.2. It is clear that
the phase times will be mainly dependent on the combined effects of approach volume and
free queues. In Figure 66, it is also easy to observe that the effect of free queue is reduced
when the approach volume becomes very large. In this example, when volume exceeds 720
vph and the free queue exceeds 1.2, the phase times are always equal to the maximum phase
time (84 seconds in this case). This indicates that the effect of the free queue is too small to
prevent the phase time from reaching its maximum.
Incorporation of the Analytical Model into the HCM Chapter 9 Procedure
The HCM Chapter 9 Appendix II method is used to estimate the phase times for
trafficactuated operation. In the previous evaluation, the Appendix II method showed its
limit to accurately predict the trafficactuated phase times. The evaluation results indicated
that the analytical model developed in this study can provide a much better prediction on
144
trafficactuated signal timing than the Appendix II method. Thus, the analytical model may
be used to replace the Appendix II model in the HCM Chapter 9 procedure.
The major difference in capacity computation between pretimed and actuated
controlled intersections lies in the use of the effective green/cycle length (g/C) ratio. Unlike
pretimed signals, the lane group g/C ratio for actuated operation does not stay constant but
fluctuates from cycle to cycle. For actuated control, once the average g/C ratio of the lane
group is known, the lane group capacity can be computed, as the product of the adjusted lane
group saturation flow rate and its g/C ratio. Based on this basic method described in the
HCM Chapter 9 for capacity computation, the analytical model can compute the average lane
group g/C ratio and its capacity, which is Usted in the output of the ACT348 program.
The traditional delay formulation used by virtuaUy all analytical models is based on
two components representing uniform delay and incremental delay respectively. The sum of
the two components produces the computed delay per vehicle. Since the QAPs must be
developed in detail by the proposed analytical model to determine the phase times, the value
of the uniform delay term (i.e., the area contained within the QAP) may be computed by a
simple extension to the existing model.
The detailed development of the QAP for any possible phase sequence and vehicle
movement was presented earlier in this dissertation. The areas contained within the QAPs
may be calculated readily from their geometry as an extension of the procedure now used in
the supplemental worksheet for delay computation with compound left turn protection
presented in the 1994 HCM update. The uniform delays can be determined using only those
variables (volumes, saturation flow and signal timing) that are used by the existing HCM
145
Chapter 9 methodology. The uniform delay formulas developed in this study for each
possible phase sequence associated with vehicle movement are shown in the Appendix. The
ACT348 program is able to provide the uniform delay computation for each lane group. It
can also provide lane group volume/capacity (v/c) ratios which may be very useful for the lane
group incremental delay computation.
In summary, the phase times predicted from the analytical model can be used as an
input to the HCM Chapter 9 procedure to estimate the capacity and delay of each lane group
for trafficactuated operation. The proposed analytical model has adopted the HCM
approach as closely as possible in the treatment of traffic and the computation of capacity and
delay. In addition, the worksheets developed in this study also provide a standard structure
for presenting the results of computations in a common form that is compatible with the
prescribed techniques. Therefore, the analytical model can be properly incorporated into the
HCM Chapter 9 procedure to estimate capacity and delay. From the delay estimates, the level
of service for each lane group and for the whole intersection can be determined
CHAPTER 7
CONCLUSIONS AND RECOMMENDATIONS
This dissertation has presented a comprehensive methodology and demonstrated a
practical analytical procedure for the prediction of trafficactuated signal timing for both
isolated and coordinated modes. A computer program called ACT348 has been developed
as a tool to implement the proposed analytical model and procedure. In comparison with the
primitive technique presented in Appendix II to the Highway Capacity Manual (HCM)
Chapter 9, the proposed analytical model has demonstrated its capability to provide a better
estimate of actuated phase times than the HCM Chapter 9 Appendix II method. In
comparison with simulation results and field data, the model has been shown to be a powerful
tool to predict the trafficactuated signal timing. The conclusions and recommendations
addressed in this chapter are offered as a result of this study.
Conclusions
Three major conclusions of the research and their supporting considerations are
presented below.
First, the proposed model can improve the analytical treatment of trafficactuated
control in the HCM Chapter 9 on signal timing prediction and the proposed methodology can
be incorporated into the corresponding HCM procedure. This conclusion is supported by the
following considerations:
146
147
1. This study considers the effects of actuated controller parameters and detector
configurations. The proposed analytical model is sensitive to common variations
in the actuated controller parameters and detector configurations.
2. The proposed analytical model considers all required inputs for actuated
operation and predicts the trafficactuated signal timing with strong theoretical
basis. It can eliminate the major problems of the invalid assumption and the
simplistic nature of the Appendix II technique in HCM Chapter 9.
3. The proposed analytical model has adopted the HCM approach as closely as
possible. A set of worksheets has been developed to provide a structure for
understanding the proposed technique and computational procedure. The ACT3
48 program developed in this study can also produce capacity and delay output;
thus, it is appropriate to be incorporated into the HCM Chapter 9 procedure for
trafficactuated signal timing prediction.
Second, the proposed model can deal with possible phase sequences given a specified
set of traffic volumes, actuated controller parameters, intersection configuration and detector
placements. The following considerations support this conclusion:
1. The proposed analytical model considers all possible phase sequences.
2. For each specified phase sequence, the model developed in this study is
functionally capable of providing reasonable estimates of operating characteristics
such as average phase times and cycle length under normal range of traffic
volumes, practical design of actuated controller parameters, intersection
configuration and detector placements.
148
Third, the proposed analytical model can accurately and quickly predict the signal
timing for trafficactuated operation. The proposed model is analytically sound and the
computational framework is robust. The following considerations support this conclusion:
1. The development of the trafficactuated signal timing prediction model, in this
study, is based on functionally and practically sound theories and concepts. The
main theories and concepts include actuated operation logic, dualring operation
logic, queue accumulation polygon concept (queuing theory), vehicle arrival
headway distribution, circular dependency relationship and sequential process.
2. In the comparison of phase times and cycle length, between the analytical model
and NETSIM simulation for fullyactuated operation based on a wide variety of
conditions, the results show the proposed model and NETSIM simulation
compare very favorably. These are confirmed by very high R square values.
3. In the limited comparison of phase times between the analytical model and actual
field data for fullyactuated operation, the analytical model is able to achieve
substantially the same results as field data.
4. This study proposes a procedure, which implements the analytical model for fully
actuated operation, to predict the phase times for coordinated semiactuated
operation. The results show that the procedure is capable of providing credible
estimates of phase times for coordinated operation of a trafficactuated controller.
The phase times predicted based on the proposed procedure are very close to
NETSIM estimates.
149
5. Most signal timing can be predicted by the ACT348 program in less than 10
seconds.
With regard to the refinements of the analytical model for the basic volumedensity
operation and for the incorporation of the free queue parameter, it is concluded that slight
modification of the analytical model for fullyactuated operation can be used to predict the
phase times and their corresponding cycle length for basic volumedensity operation and for
free queue scenarios.
Recommendations
The recommendations from the research described in this dissertation are divided into
two parts. The first part addresses further improvement of the current analytical model and
further investigation on the source of disparity between the proposed model and NETSEM.
The second part suggests areas for further research.
Recommended Model improvements
The proposed analytical model adopts the bunched exponential headway distribution
to predict the vehicle extension time after an accumulated queue has been served. The
bunched exponential headway distribution depends heavily on the traffic flow rate, but it is
independent of link length. From the theoretical view and simulation observation, link length
is a variable required to be considered in the bunched exponential headway distribution.
Further study may focus on the examination of the impact of link length to the bunched
exponential headway distribution and the proposed analytical model.
The length of a phase will depend heavily upon the probability of a gap extended in
the traffic flow after an accumulated queue has been served. A vehicular arrival distribution
150
with a higher accumulated probability to actuate a detector to extend the allowable gap after
the queue clearance will, in general, produces a longer phase time.
In the phase time comparison, it is found that, in general, NETSIM simulation
produces longer phase times for medium and heavy volumes and shorter phase times for low
volumes. The difference in arrival headway distributions between the NETSIM and bunched
arrival models at the detector were found to be an important source of disparity of phase
times between NETSIM and the proposed analytical model. They are also the easiest to
explain. They are not, however, the only difference between the two techniques. There are
some stochastic aspects of the operation that may not lend them well to deterministic
approximations. There is also a significant divergence in the manner in which NETSIM and
the analytical model treat traffic complexities such as permitted left turns from shared lanes.
It is anticipated that additional enhancements to NETSIM will appear in the near
future. The new version of NETSIM should allow users to specify an arrival distribution.
Further investigation should be conducted to compare phase time prediction between the
proposed analytical model and any subsequent versions of NETSIM.
Recommended Future Research
Level of service of an intersection is directly related to its total delay value. The total
delay formulation adopted by virtually all analytical models is equal to the summation of
uniform delay and incremental delay. Based on the signal timing predicted by the analytical
model developed in this study, the uniform delay for trafficactuated operation can be
estimated more accurately. Further research should focus on the development of the
incremental delay formulation for trafficactuated operation.
151
The phase time prediction model developed in this study covers basic volumedensity
operation. Further research may also expand the proposed analytical model to cover more
complex volumedensity operation and adaptive control strategies.
APPENDIX
UNIFORM DELAY FORMULAS
An analytical model describing the operation of a trafficactuated signal has been
developed in this study. The scope of this model is limited to the estimation of phase times,
cycle lengths and volume/capacity ratios. Delay estimates are also required to assess the level
of service (LOS) for each movement. Fortunately, the computational structure of the model
lends itself very well to the estimation of delay.
The traditional delay formulation used by virtually all analytical models is based on
two components, or terms, which are added together to produce the total delay per vehicle:
1. The uniform delay term, which determines the delay that would apply if all vehicles
arrived in a completely uniform manner. This term is computed as the area under
the queue accumulation polygon (QAP).
2. The incremental delay term, which adds a correction factor to compensate for
randomness in the arrival patterns and the occasional oversaturation.
Since the QAPs must be developed in detail by the proposed analytical model to
determine the phase times, the value of the uniform delay term (i.e., the area contained within
the QAP) may be computed by a simple extension to the existing model. The detailed
development of the uniform delay equations for computing the QAP areas of possible phasing
alternatives is presented in this appendix.
152
153
There are ten distinctive shapes that may be taken by the QAP, each of which is
associated with a specific phasing alternative. Each case is developed as a separate figure in
this appendix. Each figure shows the shape of the QAP and presents the derivation of an
equation that determines the uniform delay by computing the area of the associated polygon.
Note that the minimum value of each accumulated queue for each case is zero. A summary
of the phasing alternatives in Figures Al through A10 is presented in Table Al. The
derivations are presented in a format similar to the format used in the supplemental worksheet
now contained in HCM Chapter 9 for delay computations with compound left turn protection.
In all cases, the delay may be determined using only those variables (volumes, saturation flow
rates and signal timing) that are used by the existing Chapter 9 methodology.
Table Al. Summary of phasing alternatives for the computation of uniform delay.
Figure
Description of Phasing Alternative
Al
Single protected phase
A2
Permitted left turns from an exclusive lane (nopp >1)
A3
Permitted left turns from an exclusive lane (nopp = 1)
A4
Permitted left turns from a shared lane (gq > gf)
A5
Permitted left turns from a shared lane (gf < gq)
A6
Compound left turn protection: HCM Chapter 9 Case 1
A7
Compound left turn protection: HCM Chapter 9 Case 2
A8
Compound left turn protection: HCM Chapter 9 Case 3
A9
Compound left turn protection: HCM Chapter 9 Case 4
A10
Compound left turn protection: HCM Chapter 9 Case 5
No of vehicles in the queue
154
Qr = r qa
Qq = Qr
Qp
= 0
d,
0.5 [ r Qr + Qr2 / (s  qa) ]
qac
for isolated operation
0,5 [ r Qr + Qr2 / (s  qa) ] (1  P) f
qa c i  (g / c)
for coordinated
phases 2 & 6 only
Figure A1. Uniform delay for single protected phase.
No of vehicles in the queue
155
Qq
Condition 1: QST < gu
QP = QP = o
d _ 05 [ (r + gq) Qq + Qq2 / (sp  qa) ]
1 " qac
Condition 2: QST > gu
QP = Qq  gu (sp  qa)
d _ 05 [ (r + gq) Qq + gâ€ž (Qq + Qp) ]
1 " qa c
Figure A2. Uniform delay for permitted left turns from an exclusive lane (n^ > 1).
156
%
Q*
Qr = r qa qst =
Qq = Qr + gq (fla " Sq)
Condition 1: QST < gu
QP = QP = o
d _ 05 [ (r H gq) Qq + Qq2 / (sp  qa) ]
1 " qac
Condition 2: QST > gu
QP = Qq  gu (sp  qa)
d = 05 [ (r + gq) Qq + gu (Qq + Qp) 1
1 q c
Figure A3. Uniform delay for permitted left turns from an exclusive lane (nopp = 1).
157
Time (seconds)
Qr = r qa
Qf = Qr  gf (s  qa)
Qq = Qf + (gq  gf) qa
Qq = Qf + (gq ~ gf) (qa
QST
1 + PL (E^  1)
)
ÃfHopp> 1
ifnopP= 1
Condition 1: QST < gu
QP =
d _ 05 [ r Qr + gf (Qr + Qf) + (gq  gf) (Qf + Qq) + Qq2 / (Sp  qa) ]
1 qac
Condition 2: QST > gu
QP = Qq  gu (sp  qa)
QP/ = o
d _ 0 5 [ r Qr + gf (Qr + Qf) + (gq  gf) (Qf + Qq) + g, (Qq + Qp) ]
1 qac
Figure A4. Uniform delay for permitted left turns from a shared lane (gq > gj).
No of vehicles in the queue
158
Time (seconds)
Qr = r qa QST = â€” q
sP  qa
Qf = Qr  gf (s  qa)
Qq = Qr  gq (s  qa)
Condition 1: QST < gu
QP = %> = o
d = 05 [ r Qr + gf (Qr + Qf) + Qf2 / (Sp  qa)]
1 q c
Ta
Condition 2: QST > gu
QP = Qr  gu (sp  qa)
QP' = o
, = 05 [ r Qr + gf (Qr + Qf) + gu (Qf + Qp)]
Figure A5. Uniform delay for permitted left turns from a shared lane (gq < gf)
No of vehicles in the
159
Qq = gq (qa  sq) F
= 0 ifnopp>l
s/
sq " ][T~ (where sâ€™ = s/0.95) ifnopp=l
Condition 1: QST < gu
QP = QP' = o
d = 0 5 t r Qr + Or' 7 (S  qa) + gq Qq + Qq2 ' (Sp ~ q,) ]
1 " qa c
Condition 2: QST > gu
QP = Qq  gu (SP ~ qa)
%' =0
d = 05 [ r Qr + Qr2 / (s  qa) + gq Qq + gu (Qq + Qp) ]
1 ~ qac
Figure A6. Uniform delay for compound left turn protection (Case 1).
No of vehicles in the
160
Time (seconds)
Qr = r qa
Qp" = Qr  g (s  qa)
Qq = Qp" + gq (qa  Sq)
Sq = 0
Sq E
(where sâ€™= s/0.95)
L2
Q
QST = q
s  q
p â€œa
ifnopp> 1
ifHopp= 1
Condition 1: QST < gu
Qn = Qn' = 0
d. =
05 [ r Qr + g (Qr + Qp//) + gq (Qp, + Qq) + Qq2 / (sp  qa) ]
qac
Condition 2: QST > gu
QP = Qq  gu (SP ~ qa)
QP' = o
d = Â°5 [ r Qr + g (Qr + Qp//) + gq (Qp// + Qq) + gu (Qq + Qp) ]
' ~ qa C
Figure A7. Uniform delay for compound left turn protection (Case 2).
No of vehicles in the
161
Time (seconds)
Qr = + r qa
Qq = gq (qa  sq)
sq = 0 if noPP > 1
s;
sq _ (where sâ€™ = s / 0.95) if = 1
QP = Qq  gu (sp  qa)
where Sa = Min (Sneakers^ , Qp)
d. =
05 [ r (Qp' + Qr) + Qr2 1 (s ~ qa) + gq Qq + gu (Qq
qac
+ QP) 1
Figure A8. Uniform delay for compound left turn protection (Case 3).
No of vehicles in the queue
162
l Qq
sq (where sâ€™ = s / 0.95) if nopp = 1
a
Condition 1: QST < gu
QP = QP = o
d _ 05 [ r Qr + gq (Qr + Qq) + Qq2 / (sp  qa) ]
1 â€˜ qac
Condition 2: QST > gu
QP = Qq  gu (SP  qa)
QP' = 0
d _ 0S [ r Qr + gq (Qr + Qq) + g, (Qq + Qp) ]
1 ~ qa c
Figure A9. Uniform delay for compound left turn protection (Case 4).
No of vehicles in the queue
163
Qr = r qa
Qq = Qr + gq (qa " Sq)
Sq = 0 tfOopp5*1
s7
sq â€œ fT (where sâ€™ = s / 0.95) ifn = 1
I~'L2
QP = Qq  gu (sP  qa)
Q / = Q  S
where Sa = Min (Sneakers^ , Qp)
d . 05 (Q, * Qâ€ž) * gâ€ž (Qq + Q,) + QÂ¿ / (S  gâ€ž) ]
' â€™ q,c
Figure A10. Uniform delay for compound left turn protection (Case 5).
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BIOGRAPHICAL SKETCH
PeiSung Lin was bom in Hsinchu, Taiwan, on January 2, 1964. He attended
elementary and junior high schools in Hsinchu. After passing the competitive senior high
school entrance examination, he was admitted to the Hsinchu Senior High School as the
number two student among more than 5,000 participants.
In September 1982, he was admitted to the Department of Civil Engineering at the
National ChungHsing University. In September 1989, he attended the Graduate School of
the University of Texas at Austin. His specialized area was in transportation engineering. He
was awarded the Master of Science in August 1991. During the course of his studies, he was
a research assistant and participated in two research projects for the Texas State Department
of Highway and Public Transportation. During the course of his academic training, he
developed his interests in research.
In September 1992, he entered the Graduate School of the University of Florida where
he pursued the degree of Doctor of Philosophy in civil engineering, specializing in
transportation. In 1993, he was a graduate assistant in the Technology Transfer Center and
then he worked as a technical assistant in the Center for Microcomputers in Transportation
(McTrans Center) for transportation software testing and maintenance. In November 1993,
he won the first place of 1993 Florida ITE Past President Paper competition. In January
170
171
1994, he was honored to participate in the National Cooperative Highway Research Program
(NCHRP) project 348 concerning capacity of trafficactuated signalized intersections.
During his studies at the University of Florida, he received an award for his academic
achievement of earning a cumulative 4.0 grade point average from the Office of International
Studies and Programs.
Mr. PeiSung Lin was married to HuiMin Wen when he studied at the University of
Florida. He is a student member of Institute of Transportation Engineers.
I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fiilly adequate, in scope and quality, as a dissertation
for the degree of Doctor of Philosophy.
Professor of Civil Engineering
I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fiilly adequate, in scope and quality, as a dissertation
for the degree of Doctor of Philosophy.
Charles. E. Wallace
Professor of Civil Engineering
I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fiilly adequate, in scope and quality, as a dissertation
for the degree of Doctor of Philosophy.
/
1 r (k
Mang Tia (
i
Professor of Civil Engineering
I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fiilly adequate, in scope and quality, as a dissertation
for the degree of Doctor of Philosophy.
Sherman X. Bai
Assistant Professor of Industrial &
System Engineering
I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation
for the degree of Doctor of Philosophy.
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Anne WyattBrown
Assistant Professor of Linguistics
This dissertation was submitted to the Graduate Faculty of the College of Engineering
and to the Graduate Council, and was accepted as partial fulfillment of the requirements for
the degree of Doctor of Philosophy.
December 1995
Winfred M. Phillips
Dean, College of Engineering
Karen A. Holbrook
Dean, Graduate School
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1780
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