Modeling traffic-actuated control with TRANSYT-7F

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Modeling traffic-actuated control with TRANSYT-7F
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v, 196 leaves : ill. ; 29 cm.
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Hale, David
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Traffic congestion -- Research   ( lcsh )
Traffic flow -- Management   ( lcsh )
Civil Engineering thesis, Ph. D   ( lcsh )
Dissertations, Academic -- Civil Engineering -- UF   ( lcsh )
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Thesis:
Thesis (Ph. D.)--University of Florida, 2000.
Bibliography:
Includes bibliographical references (leaves 193-195).
Statement of Responsibility:
by David Hale.
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Printout.
General Note:
Vita.

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MODELING TRAFFIC-ACTUATED CONTROL WITH TRANSYT-7F


By

DAVID HALE
















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

UNIVERSITY OF FLORIDA


2000



















TABLE OF CONTENTS

Page

A B ST R A C T ..................................................................... ................ iv

CHAPTERS

1 INTRODUCTION .................................................. ......... ................. 1

Problem Statement ...................................................................... 2
O objectives ...... .................................... ................... ...... .. .. 3
Organization of Chapters.............................................................. ... 8

2 LITERATURE REVIEW ......... ...................................................... 10

Phase Time Estimation ....................................................... ......... 11
Vehicle Delay Estimation ..................................... ........................... ... 49
Control Parameter Design and Optimization.......................................... 55
Chapter Two Summary.................................................................... 61

3 MODEL DEVELOPMENT................................................................ 63

Queue Service Time ................................................................ ....... 64
Green Extension Time................. ...................... ........................... 70
Model Implementation ...................................................................... 88
Chapter Three Summary.................................................................. ..103

4 MODEL TESTING.............................. ..................................... ...... 105

List of Candidate Models.................................................................... 106
Testing Strategy ............................... ........................ .............. ....... 107
Calibration of CORSIM and TRANSYT-7F...................................... .. 109
Chapter Four List of Experiments......................................................... 110
Single Intersection Testing................................................................. 110
Arterial Street Testing....................................................................... 124






Optimization Applications Testing............................................. 147
Chapter Four Summary.......................... ..... ..... ........ ............. 154

5 CONCLUSIONS AND RECOMMENDATIONS...................................... 156

Conclusions ................. .................. ...... ........... ......... ......... 156
Summary of New Modeling Capabilities ......................... ..... ............... .... 163
Recommendations .......................................... ................ 164

APPENDIX

Brief Tutorial on Actuated Control..................................................... 167
Brief Tutorial on TRANSYT-7F........ .... ................ .......... ................ 171
Calibration of CORSIM and TRANSYT-7F............................................ ..177
Automated Process: Experimental Version of TRANSYT-7F......................... 190

REFERENCES .................................................. .............. .......... 193

BIOGRAPHICAL SKETCH............ ...................... ... ........... ............. 196


















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

MODELING TRAFFIC-ACTUATED CONTROL WITH TRANSYT-7F

By

David Hale

August 2000



Chair: Kenneth G. Courage
Major Department: Civil Engineering

Research suggests that traffic congestion in U.S. cities has grown rapidly in recent

years, and that numerous solutions are needed to address the problem. This dissertation

describes new research for producing basic improvements to the practice of traffic signal

timing optimization, in order to improve one of the many available weapons for fighting

congestion and delay.

TRANSYT-7F is one of the most comprehensive signal timing tools in existence,

and has evolved into a benchmark within the transportation profession. Although

TRANSYT-7F was developed in an era of pre-timed signal control, it was modified in

the 1980s to automatically estimate the average green times for actuated controllers.






Although effective at eliminating wasted green time, the existing actuated control

sub-model within TRANSYT-7F is oversimplified. The model does not recognize most

of the signal settings associated with today's controllers. In addition, this and other

actuated control models from the literature do not recognize numerous operational

characteristics affecting phase times. The end result is that performance estimates and

timing plans generated by the program are potentially less accurate and optimal.

The overall goal of this study was to develop an improved actuated control

methodology for usage within TRANSYT-7F, and perhaps within other programs and

procedures. A literature review was performed to ascertain available technology on

actuated control including phase time calculation, vehicle delay estimation, and control

parameter design or optimization. Subsequently, certain models from the literature were

chosen as candidates for improvement of TRANSYT-7F performance. In addition, new

prototype models were developed during the course of the study. Along with existing

literature models, these prototypes were subjected to a battery of tests in order to

scrutinize their strengths and weaknesses. The well-known CORSIM simulation program

was used as a reference point for model comparison.

Significant amounts of experimental data revealed dramatic improvement in the

accuracy of actuated phase time calculation when the candidate models were applied by

TRANSYT-7F. A smaller amount of data was also collected to demonstrate

improvements in the optimal timing plans, based on the new methodology. Conclusions

and recommendations, regarding new modeling capabilities and future research, are

provided in the final chapter.


















CHAPTER 1
INTRODUCTION



Research from the Texas Transportation Institute (TTI) suggests that traffic

congestion in U.S. cities has grown rapidly in recent years, and that "a full array of

solutions and measures are essential in addressing the mobility problem" [Lomax and

Schrank, 1998]. Simple solutions such as carpooling, or building additional roadway

lanes, are reportedly inadequate for dealing with increasing traffic problems. Lomax and

Schrank report that in 1997, the financial cost of congestion exceeded $72 billion per

year, up from $66 billion in 1996, and that increases in delay have been more prevalent in

small- to medium-sized cities than in the nation's largest cities.

Numerous congestion-reducing strategies have been proposed for improving

transportation efficiency in an existing roadway network. Some strategies involve

modification of driver behavior (e.g., the use of public transit), whereas other strategies

involve better traffic management. This dissertation focuses on one aspect of better

traffic management, namely the optimization of traffic signal timing plans in centrally

coordinated traffic control systems. While no single device or strategy can be expected

to "solve" the problem of traffic congestion by itself, signal timing optimization has been







demonstrated to be an extremely cost-effective strategy. When properly applied, it has

proven effective in reducing delay, stops, fuel consumption and other measures related to

operating costs and driver-perceived disutility [Deakin et al., 1984]. Any technique that

offers a potential improvement in traffic control system performance should provide a

useful contribution in combating this growing national problem.



Problem Statement



The importance of efficient traffic signal operation has been recognized for many

years. Various signal system simulation and optimization models are now available for

analysts and engineers. Simulation models offer a realistic interpretation of traffic flow

and performance, but their function is limited to evaluating the performance of a

specified operational alternative. In other words, they do not provide features that

explicitly optimize the performance. Optimization models, as the name implies, do

attempt to find the "best" set of operating parameters for a specified performance

objective. However, they often lack certain detailed treatment of traffic flow

characteristics found within simulation models. The simplifying assumptions required to

support a productive optimization process have, in many cases, compromised the quality

of the final product. The result is that the timing plans being implemented in many traffic

control systems today still have significant room for improvement.

One of the most promising areas for improvement is the modeling of "traffic-

actuated" control, in which instantaneous information from traffic detectors is

incorporated into the control tactics for fine-tuning intersection performance. Existing







optimization models apply the simplifying assumption of "pre-timed" control, in which

the operation at each intersection is characterized by a series of fixed-duration intervals.

The optimization process determines the optimal duration and position of each interval.

Some adjustments are made in an attempt to represent the effects of traffic-actuated

control, but the results to this point have not proven to be entirely satisfactory.



Objectives



The overall goal of this study is to develop an improved treatment of traffic-

actuated control for application within deterministic optimization models. Regarding the

type of actuated control to be analyzed, the scope of this study involves "basic" actuated

control, where presence detectors are installed at the stop line. To accomplish the overall

goal, it is necessary at the outset to choose a specific optimization model for

improvement, as well as a simulation model for evaluation of the improvements. These

two choices will establish the scope of the project.

The Traffic Network Study Tool (TRANSYT) program [Robertson, 1968] is the

most logical choice for the optimization model. TRANSYT was developed by the

Transport Research Laboratory in the United Kingdom. It is used extensively throughout

the world for traffic control system timing design and evaluation. The specific version of

the TRANSYT model to be used in this study will be TRANSYT-7F, release 8.

TRANSYT-7F was developed as a derivative work by the University of Florida

Transportation Research Center [Wallace et al., 1981]. It is distributed worldwide by the

University of Florida and currently has approximately 1,400 registered agencies







worldwide. The extensive recognition of TRANSYT-7F, combined with the institutional

support of the University of Florida, make it a natural choice for purposes of this project.

More detailed descriptions of the TRANSYT-7F modeling and calibration process are

presented in the appendix.

Ideally testing and validation of the project results would be accomplished

through the collection and analysis of field data; however, an adequate empirical

validation would require resources several orders of magnitude beyond those available to

this project. This limitation dictates the need for simulation as a surrogate for field data

collection.

The choice of a simulation model is not difficult in this case. The CORridor

SIMulation (CORSIM) [ITT Systems and Sciences Corporation, 1998] model has been

developed and enhanced continually over the past 25 years by the Federal Highway

Administration (FHWA). It was designed specifically for the purpose intended by this

project (i.e., a surrogate for field data) and is used extensively for this purpose.

CORSIM is especially strong in the treatment of traffic-actuated control. It

models this type of control explicitly, using a software module developed from the same

source code as the real-time control logic contained within the actual field hardware.

Chapter 2 (literature review) contains a reference that illustrates field validation of

CORSIM's actuated phase times. Therefore CORSIM will be used for testing and

validation of the optimization enhancements to be developed as a part of this project.

Consider, for example, the comparison between signal phase times estimated by a

deterministic optimization model (TRANSYT-7F) and a detailed microscopic simulation

model (CORSIM), as shown in figure 1-1.





5





40
R = 0.8063


30 *






10-


0-I I

0 10 20 30 40

TRANSYT-7F Phase Time (sec)



Figure 1-1: Actuated Phase Time Comparison CORSIM vs. TRANSYT-7F



The level of correlation evident in this comparison suggests that the optimization

model is not replicating simulation model conditions satisfactorily. A corollary to this

observation is that the "optimal" design (i.e., the final product of the optimization

process) will be based on incorrect information and will not therefore realize its potential

for optimizing system performance. It is therefore possible, and definitely desirable, to

improve the treatment of traffic-actuated control in the design and optimization of traffic

control system timing plans. This would provide the opportunity to improve efficiency of

performance at thousands of signalized intersections throughout the USA.








As an alternative, consider an updated comparison between phase times estimated

by TRANSYT-7F and CORSIM, given the new methodologies to be presented within the

body of this study, as shown in figure 1-2.


Figure 1-2: Updated Phase Time Comparison CORSIM vs. TRANSYT-7F



TRANSYT-7F and other optimization models are based on a series of simulation

or evaluation runs. Typically the simulation or evaluation run that results in the best

performance is reported as optimal. In other words, the effectiveness of optimization is

predicated on the accuracy of simulation or evaluation. Because of this, improvements in

actuated phase time calculation (as illustrated in figures 1-1 and 1-2) can result in an

improved optimization process. Table 1-1 shows an example of traffic network


40 -
R2 = 0.9574

,u,
30 -



S20


O **
S10

.)
0


0 10 20 30 40

TRANSYT-7F Phase Time (sec)







performance improvements that are possible under the updated methodologies for

actuated control.



Table 1-1: Sample Optimization Based on Improved Actuated Control Treatment

CORSIM output based on timing from:
Old New
T7F T7F
Control Delay 25.6 24.2
Total Delay 29.7 28.4
Stop Delay 22.0 20.5
Vehicle Trips 8116 8242


In summary, the objectives of this project are to improve the treatment of traffic-

actuated control within deterministic models, to demonstrate the improvements using

TRANSYT-7F release 8, and to validate the improvements using CORSIM. In support

of these objectives, the following tasks will be carried out:

1. Identify specific shortcomings of the existing TRANSYT-7F actuated timing model:

Related to this, generalized shortcomings of existing optimization models were

discussed earlier in this chapter. Technical details regarding shortcomings of the

existing TRANSYT-7F actuated timing model are provided in chapter 2.

2. Establish requirements for an improved model:

To obtain an improved actuated timing model, it is necessary to keep in mind the

minimum requirements for such a model. This prevents the possibility of wasted time

in evaluating a new model that contains unacceptable weaknesses.







3. Survey candidate models for improvement of TRANSYT-7F performance:

In the literature, there are a number of models that contain good ideas and

methodologies, related to the subject matter at hand. It is necessary to survey these

existing models, in order to learn whether existing methodologies may be helpful in

developing a new model for improvement of TRANSYT-7F performance.

4. Evaluate candidate models per requirements:

The minimum requirements, to be established by task #2, will be used to determine

the existing models that are appropriate for further consideration.

5. Select one or more models for additional testing and development:

Existing models that meet the minimum requirements for an improved model will be

selected for additional analysis and consideration.

6. Develop models:

Candidate actuated timing models must be developed for application in conjunction

with TRANSYT-7F.

7. Formulate a test plan:

Devise a comprehensive test plan to compile evidence of model effectiveness.

8. Test models per test plan:

Testing will be performed on a variety of field conditions, in order to compile

evidence on the effectiveness of the candidate models.

9. Recommend specific improvements:

Conclusions and recommendations, regarding TRANSYT-7F actuated control

modeling, will be formed based on the results from model testing.







Organization of Chapters



Table 1-2 illustrates the organization of chapters within this dissertation. It also

shows which chapters will be used to address specific tasks and objectives listed earlier.

The potential benefits of traffic signal timing optimization were briefly discussed in this

chapter. Also, shortcomings of the existing TRANSYT-7F actuated timing sub-model

were introduced, and the minimum requirements for an improved model were

established. Thus, this chapter was used to address task 1. In support of tasks 2-5,

chapter 2 provides background information on numerous models for traffic-actuated

control. The third chapter is used to provide a frame of reference for each objective in

this study. It describes technical aspects of the existing model including methodology,

sample calculations, strengths and weaknesses, and preliminary test results (task 6).

Chapter 4 outlines the testing plan, and contains the detailed testing results for the

candidate models (tasks 7 & 8). The fifth and final chapter discusses implementation

strategies, plus proposed additional testing and development of selected models (task 9).


Table 1-2: Study Objectives and Associated Chapters


Objective Chapter
1. Identify shortcomings of the existing model 1 Introduction
2. Establish requirements for an improved model 2 Literature Review
3. Survey existing models 2 Literature Review
4. Evaluate candidate models per requirements 2 Literature Review
5. Select models for additional testing 2 Literature Review
6. Develop models 3 Model Development
7. Formulate test plan 4 Model Testing
8. Test models per test plan 4 Model Testing
9. Recommend specific improvements 5 Conclusions and
Recommendations


















CHAPTER 2
LITERATURE REVIEW


This chapter summarizes the available literature on traffic-actuated control

modeling, because such literature may be useful in determining the best strategies for

improvement of TRANSYT-7F performance. Tasks 2 through 5 from chapter 1 (table 1-

2) are addressed by this chapter, in which models from the literature will be summarized,

evaluated, and possibly selected for further development. Because this discussion is

primarily targeted at persons with experience in traffic operations, tutorial summaries on

the basics of TRANSYT-7F and traffic-actuated control were moved from this chapter

and are presented in the appendix.

Throughout the literature, it appears that models for traffic-actuated control can be

classified into three major categories. This chapter contains three major sections for

distinguishing between these model types. One of the basic requirements for an

improved TRANSYT-7F model is that it must estimate average actuated phase times.

Actuated phase time inaccuracy is the most significant perceived deficiency of the

existing model. Because of this, models (in the literature) that are capable of estimating

average actuated phase times may be especially useful. In addition, an improved model

must be suitable for practical implementation within the TRANSYT-7F program.







Phase Time Estimation



Existing Model within TRANSYT-7F

Before investigating the candidate models for improvement of TRANSYT-7F

performance, it is helpful to better understand the existing model. A candidate model

must be considered superior to the existing model in order to warrant implementation,

which is one reason that the existing model should be understood. Another reason is that

one of the candidate models to be considered works similarly to the existing model.

Finally, general understanding of the existing model facilitates general understanding of

the candidate models and of actuated control.

The existing model for traffic-actuated control within TRANSYT-7F, developed

at the University of California-Berkeley [Skabardonis, 1988], is primarily based on target

degree of saturation. The model is designed to give actuated phases as little green time as

possible, and gives all remaining green time to the major street through movement. How

is it possible to give the actuated phases "as little green time as possible"?

It is necessary to give them a certain amount of green time that will result in near-

saturation on that phase. This is consistent with typical operation, because the basic

strategy of an actuated controller is to terminate the phase soon after the queue has been

serviced. This results in a degree of saturation somewhat lower than 100%, although the

exact degree of saturation is difficult to predict. The default value currently applied by

the TRANSYT-7F program is 85%. Figure 2-1 illustrates the minor movements at 85%

saturation.


































Figure 2-1: Existing Model Strategy Actuated Phases at 85% Saturation



Degree of saturation concept

At this time it is necessary to define "degree of saturation." Mathematically,

degree of saturation equals volume divided by capacity; or, X = v/c. Conceptually, if

there is only enough green time (on average) to service the initial queue (on average),

then that movement operates at 100% degree of saturation. In this case of 100%

saturation, the expected volume (during each cycle) will receive just enough green time

(during each cycle) to be served, and the capacity of the movement is equal to the

expected volume. If there were not enough green time to service the initial queue, degree

of saturation would exceed 100%. If there were enough green time such that the initial


85%








85%


885%







85%







queue could be served, plus some additional vehicle arrivals thereafter, degree of

saturation would be less than 100%.

Suppose that the left-turning vehicles shown in figure 2-2 have just been given the

green arrow to indicate the beginning of a protected left-turn phase. On the westbound

approach, the initial queue contains six vehicles, whereas on the eastbound approach, the

initial queue contains two vehicles. What if the eastbound approach were to receive

enough green time such that the initial two vehicles, plus the two straggling vehicles

behind them, were all served? Degree of saturation for that movement would be less than

100%. What if the westbound approach were to receive enough green time such that only

four out of the six vehicles in the initial queue were served? The "residual queue" would

be two vehicles, and the movement would be "oversaturated" with degree of saturation

greater than 100%. In order to know the exact value of degree of saturation in any of

these cases, it would be necessary to perform additional calculations regarding the value

of capacity. This is illustrated later.


Figure 2-2: Degree of Saturation Concept Example Using Left-Turn Movement


Volume (v)
Capacity (c)
Degree of Saturation (X= vic)







Returning to the discussion about the existing TRANSYT-7F model, it was stated

that the model is designed to give the actuated phases as little green time as possible, and

gives all remaining green time to the major street through movement. Further, in order to

give the actuated phases as little green time as possible, the model gives them enough

green time such that their movements achieve 85% saturation. Why 85%?

In the real world, arrival rates and queues vary from cycle to cycle. Although the

analyst typically knows the expected average arrival rate and average queue length, these

values should be exceeded about half of the time. It would be highly undesirable to

exceed 100% saturation during any given cycle, because when that occurs, vehicle delay

tends to rise exponentially. In the existing model, target degree of saturation should be

low enough such that 100% is rarely exceeded.

On the other hand, when target degree of saturation decreases for the minor

movements, their allotted amount of green time increases. This conflicts with the desired

objective of giving as much green time as possible to the major street through movement.

Any unnecessary, wasted green time on the minor movements would be better spent on

achieving arterial progression on the major street through movement. In the existing

model, target degree saturation should be high enough such that green time is not wasted

on the minor movements.

To summarize, in choosing target degree of saturation for an actuated phase, it is

desirable to have it as high as possible, provided that 100% saturation is rarely exceeded.

Skabardonis [1988] recommends target degree of saturation in the range of 85-90%. The

value of 85% has been chosen as the default value in TRANSYT-7F, although the user is






allowed to specify any value between 50 and 100%, applicable to specific phases, or

applicable to the entire network.

Sample calculation

To understand its relative effectiveness, it is helpful to walk through a sample

calculation with the existing model. Figure 2-3 illustrates a set of hypothetical conditions

at a signalized intersection.


Figure 2-3: Existing Model Sample Calculation Intersection Conditions


50 100 100


JL

100 50
500 --500
50 -- 100



100 100 50






20 sec 30 sec 20 sec 20 sec







1. Calculate Capacity

Consider the north-south left-turn phase in the figure 2-3 timing plan. The largest

individual movement volume on this phase is 100 vehicles per hour. In order to achieve

85% saturation, the phase must receive enough green time such that it could actually

serve 118 vehicles per hour. Thus, movement capacity is equal to 118 vehicles per hour.



Volume (v) =100 vehicles / hour

v
X = 0.85

v 100
c =118 vehicles / hour
0.85 0.85



Figure 2-4: Existing Model Sample Calculation Step #1



2. Calculate Required Percentage of Green Time per Hour

In step 1 it was shown that movement capacity must equal 118 vehicles per hour

in order to achieve 85% saturation. Next, it is necessary to determine the amount of

green time per hour needed to serve 118 vehicles on that movement. Suppose that the

movement is capable of serving 1710 vehicles per hour if it could have an hour's worth

of green time. If an hour's worth of green time results in 1710 vehicles served, how

much green time results in 118 vehicles served? By simple math, if the movement

received green time during 6.9% of the hour, then 118 vehicles would be served.






















Figure 2-5: Existing Model Sample Calculation Step #2



3. Calculate Phase Time

In step 2 it was shown that the movement must receive green time during 6.9% of

the hour. This means that it must also receive 6.9% of the green time available during

each signal cycle. The calculations illustrated show that, after adding on two seconds of




6.9% of the hour is required
Cycle Length (C) = 90 seconds
Total Lost Time (1) = 8 seconds


6.9%= green time
90-8
green time = 82* 0.069= 5.6 seconds
phase time = 5.6 + 2 8 seconds


Figure 2-6: Existing Model Sample Calculation Step #3


Capacity (c) = 118 vehicles / hour
S\ Saturation Flow (s) = 1710 vehicles / hour green


Required Time Capacity
Hour Saturation Flow

c 118
- = = 6.9% of the hour is required
s 1710







yellow and all red clearance time, the left-turn phase time is 8 seconds according to the

existing model.

4. Donate Unused Green Time to the Non-Actuated Phase

In step 3 it was shown that the existing model estimates the average length of the

first phase as 8 seconds. The same computations from steps 1-3 are performed to

estimate the average length of each actuated phase. Subsequently, all remaining green

time in the cycle is allocated to the non-actuated phase, as illustrated in figure 2-7.


8 66 8 8
I II \t

8 66 8 8


Figure 2-7: Existing Model Sample Calculation Step #4



The TRANSYT-7F output in table 2-1 presents the existing model sample

calculation results. Along the rows labeled "Intvl Length" and "Splits," the signal timing

table shows that 63 seconds have been allocated to the coordinated, non-actuated phase.

Along the row labeled "Phase Start," the signal timing table shows that phase number 4 is

the non-actuated phase (NAP). Along the row labeled "Links Moving," the signal timing

table lists the link numbers moving on each phase. For example, through and right-turn

links (105, 107, 111, 112) are moving during the non-actuated phase. Along the column

labeled "Deg Sat," the measures of effectiveness table shows that simulated degree of






19



saturation was approximately 85% for the critical actuated movements (102, 104, 101,


103, 106, 108).





Table 2-1: TRANSYT-7F Program Output for Sample Calculation


Intersection 1 Actuated Splits Estimated


Interval Number :

Intvl Length(sec):
Intvl Length (%):

Pin Settings (%):

Phase Start (No.):

Interval Type

Splits (sec):
Splits (%)
Links Moving


Offset = 0.0 sec


1 2 3 4 5 6 7 8


6.0 2.0 64.0
7 2 71


100/0


6.0 2.0
7 2


2.0
2


7 9 80 82 89 91 98


1 ACT 2 NA P 3 ACT 4 AC T

V Y V Y V Y V Y


8
9
106
108


66
73
105
107
111
112


8
9
102
104


8
9
103
101
109
110


0 %.





Movement/
Node Nos.


Deg/ Total
Sat Travel
% v-mi


Travel Time
Total Avg.
v-hr sec/v


101 : 83 50.02 4.20 151.3


102
103
104
105
106
107
108
109
110
111
112


50.02
50.02
50.02
250.10
50.02
250.10
50.02
25.01
25.01
25.01
25.01


4.52
4.20
4.52
10.91
4.52
10.91
4.52
1.62
1.62
1.06
1.06


162.9
151.3
162.9
78.5
162.9
78.5
162.9
116.7
116.7
76.4
76.4


Delay Total
Total Avg/LOS Stops
v-hr sec/v No. (%)


2.19 78.8E 140(140) 2 106


2.51
2.19
2.51
0.85
2.51
0.85
2.51
0.61
0.61
0.06
0.06


90.4F
78.8E
90.4F
6.1A
90.4F
6. 1A
90.4F
44.3D
44.3D
4.0A
4.0A


151(152)
140(140)
151(152)
190( 38)
151(152)
190( 38)
151(152)
50(101)
50(101)
14( 29)
14( 29)


NODE 1: 88 900.37 53.69 17.46 34.9C 1392( 77) 57.4


Max Back
of Queue
Est.Cap.


Fuel
Cons.
gal

4.2
4.5
4.2
4.5
12.6
4.5
12.6
4.5
1.8
1.8
1.2
1.2


106
106
106
106
106
106
106
106
106
106
106







5. Subsequent Simulation or Optimization

Once the existing model has arrived at its estimates for phase times, the resulting

timing plan is then used as a starting point in simulation or optimization. If optimization

has not been requested whatsoever, then the phase time estimates will not be modified

during simulation. If thorough optimization has been requested, then the phase time

estimates are simply used as a starting point in a hill climb search for a better signal

timing plan. If optimization of offsets-only has been requested, then TRANSYT-7F will

not modify the phase time estimates as it searches for better offsets.

If the initial timing plan is close to the global optimum solution, then the hill

climb procedure has a higher probability of locating that global optimum. Also, when

there is more green time available for the coordinated through movement, then there is a

higher probability of achieving progression. Thus, when the actuated model estimates

phase times and allocates extra green time to the coordinated movement, TRANSYT-7F

gets a better starting point for optimization of a congested artery.

Accurate phase time estimation can be critical. Inaccurate phase time estimation

will result in the wrong amount of green time being allocated to the coordinated

movement. Thus, the output measures of effectiveness and/or optimal offset timing

produced by TRANSYT-7F may be overly optimistic or pessimistic. It depends on

whether the amount of green time allocated to the coordinated movement, and the

resulting available green band throughout the arterial, is too large or too little.

Specific shortcomings

Although effective at eliminating wasted green time, as an actuated controller

would, the existing model for traffic-actuated control within TRANSYT-7F is







oversimplified. Predicted phase times are simply a function of the number of actuated

phases and the target degree of saturation. The target degree of saturation strategy is

inherently inaccurate because it is not responsive to numerous factors that affect actuated

phase lengths. As stated in chapter 1, actuated phase times and measures of effectiveness

reported by TRANSYT-7F are potentially less accurate, because the existing model is not

sensitive to several key factors. In addition, since actuated phase times are often estimated

prior to optimization, any phase time inaccuracies could lead to inferior optimization

results. What are these key factors, and how do they affect actuated phase times?

Gap setting: If a phase is actuated, then its associated lanes contain detectors that

search for a gap in the traffic stream. The gap setting indicates the size of the gap being

searched for, measured in units of seconds. Larger gap settings produce larger actuated

phase times. This is because large gaps in traffic occur less frequently than small gaps,

and phases will continue to last longer if the desired gap is not detected. The existing

model for actuated control within TRANSYT-7F gives the phase enough green time to

achieve 85% saturation, as stated previously. Theoretically, for a given phase, there

exists a gap setting that will produce a certain green time resulting in 85% saturation on

average. Using this gap setting, the existing model would produce accurate phase time

estimates. For example, suppose that someone in the field carefully observes the north

and southbound left-turn phase from figure 2-3 for several cycles of operation. Suppose

they conclude that the average phase time was indeed 8 seconds during that period of

observation, just as predicted by the existing TRANSYT-7F model in table 2-1. For

these conditions, the existing model is accurate.







But what if the associated gap setting were to be increased, and other factors and

variables held constant? In the field, average phase time would be expected to increase

along with the gap setting, thus reducing the average degree of saturation to somewhere

below 85%. Because the analysts are unaware of the degrees of saturation associated

with various gap settings, they are unable to estimate a target X other than 85%, which

causes inaccurate phase time estimates. This is how a change in the gap setting can

render the existing model less effective.

Detector configuration: As stated above, if a phase is actuated, then its

associated lanes contain detectors that search for a gap in the traffic stream. The

configuration includes the type (presence vs. passage), length, and lane location of

detectors. Longer presence detectors lead to larger actuated phase times. This is because

longer detectors have a better chance of detecting vehicles prior to a controller's

irrevocable decision to terminate the phase.

For a given phase, a given presence detector length exists that, in conjunction with

a given gap setting, will produce a certain green time resulting in 85% saturation on

average. If this hypothetical detector length is exceeded and all other factors and

variables are held constant, the resulting degree of saturation would fall somewhere

below 85%. Thus, a change in detector length can also render the existing model less

effective.

Force-off: As previously stated, if a phase is actuated, then its associated lanes

contain detectors that search for a gap in the traffic stream. What if traffic happens to be

heavy enough such that the desired gap is never detected? It is necessary to impose a

maximum green time setting on the actuated phase. The phase must not be allowed to





23

continue for an unreasonable amount of time. When signals are coordinated, the force-

off setting is used to terminate actuated phases that do not gap-out.

For a given phase, a range of force-offs exists that will allow green times resulting

in 85% saturation on average. In other words, if the force-off setting is sufficiently high,

the phase is capable of termination via gap-out, and 85% saturation may occur. But what

if this force-off setting was decreased, and other factors and variables held constant? In

the field, if the force-off occurred early enough in the cycle, the phase would be expected

to terminate via max-out before locating the specified gap, and thus increase average

degree of saturation to somewhere above 85%. Thus a change in force-off can also

render the existing model less effective.

Physical factors: The previous subsections discuss the way in which individual

actuated control parameters can affect average phase lengths. There are also some

additional factors that may affect average phase lengths, according to the literature

presented later in this chapter. These include vehicle length, number of lanes, and

approach speed. The existing model for traffic-actuated control within TRANSYT-7F

does not take these physical factors into consideration.

Operational characteristic effects: In the existing model, what if it were

possible to make target degree of saturation sensitive to all of the control parameters and

physical factors mentioned in the previous subsections? Would this fix the model? It

would be a step in the right direction; however, there would still be no clear-cut way for

dealing with operational characteristic effects on actuated phase times. The effects of

early returns to green, overlap phasing, stochastic behavior, progression, permitted left-

turns, spillback, and optimization, are based on performance at neighboring signals, and







are thus difficult to quantify without simulation. Chapters 3 and 4 illustrate the technical

aspects of operational characteristic effects with more technical detail.

Trying to predict degree of saturation: In the field, actuated phase times result

in a certain degree of saturation. If the user were able to predict degree of saturation

based on available input data, it would be possible to effectively use the existing model

by specifying the appropriate target degree of saturation for each phase. However,

degree of saturation is too difficult to predict. Non-uniform arrival rates, link length, lane

channelization, control parameters, and detector layout, for numerous phases and

intersections, interact as significant variables at many levels, and thus conspire to produce

complex and unpredictable results throughout the network. This is why programs such as

CORSIM (to be described later) and TRANSYT-7F are needed. This is also why an

alternative method for estimating actuated phase times, besides trying to forecast the

degree of saturation, is desirable.

Pitfalls of inaccurate phase time estimation: A simple example is helpful for

illustrating the potential pitfalls of inaccurate phase time estimation. The phasing

diagram in figure 2-8 illustrates a hypothetical signal timing plan. This signal timing

plan has leading left-turn phases with no overlaps. Average phase times are listed below

the box that represents each phase. Under pre-timed control, phase times should be

approximately equal for each phase in the event that traffic volume demands and

saturation flow rates are approximately equal for each movement. In the four-phase

situation illustrated by figure 2-8, phase times should be 25 seconds for each phase if the

cycle length is 100 seconds. Although left-turns typically have lower volumes and

saturation flow rates than through movements, suppose for this simple example that they







have equal volumes and saturation flow rates, and that phase times should be equal in

order to optimize the situation.









25 25 25 25



Figure 2-8: Sample Phasing Diagram with Average Phase Times


Now suppose that control type at this signal is to be converted to coordinated-

actuated, with the east-west (left-to-right) through movement to be served by a

coordinated phase. This means that the coordinated phase will have priority, and that the

minor movement actuated phases are to be terminated as soon as possible after their

initial queues have been served, such that the coordinated phase will receive extra green

time. What will the new signal timing plan look like? Presumably something like the

updated timing plan illustrated in figure 2-9. In this timing plan, actuated phase times are

now much lower than their original pre-timed counterparts, and the coordinated phase

benefits by receiving the extra green time. This type of control is typically preferable for

achieving progression along the major street, provided that performance on the actuated

phases does not deteriorate to unacceptable levels.



















Figure 2-9: Sample Timing Plan Computed by the Existing Model



As mentioned earlier, accuracy of the existing actuated phase time model within

TRANSYT-7F leaves much room for improvement. Figure 2-10 illustrates a

hypothetical outcome of this situation. Actuated phase times that materialize in the field

are actually 14 seconds apiece instead of 10, and the coordinated phase time occurring in

the field is actually 58 seconds instead of 70. In the context of capacity analysis, the

result would be an inappropriately pessimistic analysis, in terms of vehicle delay and

level of service, of the actuated phases. Perhaps more dangerous, such results would

cause overly optimistic analysis of the coordinated phase serving the major street

movements. In the context of signal timing optimization, inaccurate phase time estimates

can result in compromised estimates of the available green band, or green window,

available for optimization of offsets or phasing to achieve progression along the major

street.


10 10 10 70

















Figure 2-10: Example of Model-Predicted vs. Actual Actuated Phase Times

NCHRP Model

The model for estimating actuated phase times in appendix II of the 1997

Highway Capacity Manual is an example of a method that provides an alternative

strategy to forecasting the degree of saturation. This model was developed as part of

National Cooperative Highway Research Program (NCHRP) Project 3-48 [Courage et al.,

1996]. An upcoming description of its methodology will be followed by a sample

calculation using the same data from the existing model sample calculation (figure 2-3).

Methodology

In general, actuated phase lengths are estimated using the structure illustrated in

figure 2-11. The NCHRP model specifies that the length of an actuated phase can be

estimated by summing the queue service time (gs), the green extension time (ge), and the

intergreen (yellow plus all red) time. Note that the green extension time should not be

confused with the extension of effective green (EEG) parameter, which is applied by

numerous deterministic traffic models. Although figure 2-11 does not illustrate start-up

lost time, this parameter affects the phase time as well. According to the HCM

terminology, queue service time begins where start-up lost time ends. However, in figure

2-11 and in other parts of this paper, queue service time includes start-up lost time.


1J


10 10 10 70
14 14 14 58








- --Actuated Phase Duration-


Figure 2-11: Individual Phase Length Structure within the NCHRP Model


Initial timing plan: The NCHRP model requires an initial timing plan in order to

perform calculations. This initial timing plan makes it possible to determine the effective

red time, and thus the expected initial queue, that is experienced by each actuated phase.

Subsequently, the model is able to appropriately adjust the phase times in response to the

differing characteristics of each phase, such as traffic volume demand and the actuated

control parameters.

It is important to note that differing initial timing plans should not prevent the

model from computing the same final solution each time. Only the input parameters

affecting the model should impact the final solution; however, an initial timing plan that

is close to the final solution results in fewer model iterations and faster running times for

the computer program.

Queue service time: The queue service time for each phase is calculated using

the queue accumulation polygon (QAP). The QAP concept is robust, reliable, and well-

documented in the Highway Capacity Manual [Transportation Research Board, 1997]


Queue Service Time


Green Extension Time

Intergreen Time







and in other parts of the literature. The shape of the polygon is affected by several

relevant parameters affecting vehicle queuing and delay, including traffic volume

arrivals, saturation flow rate, effective red time, and effective green time. Figure 2-12

illustrates a sample QAP.


SQueue Ser

Cu




0
o
TRed Green


Time (seconds)


vice Time


Ext. Time


Figure 2-12: Sample Queue Accumulation Polygon



Figure 2-12 illustrates a polygon in the shape of a triangle, which implies that the

rate of vehicle arrivals on red and the rate of vehicle departures on green are both

constant, uniform rates. Unless traffic volume is very heavy, the slope of the left-hand

side is not expected to be as steep as the slope of the right hand side, because when a

queue is present, the rate of vehicle departures is very high (i.e., the saturation flow rate).

The shape of the polygon is useful in determining queue service time among other things.

The shape of the polygon can become complex in response to field conditions causing


MWOMEMMNOW







non-uniform arrivals or departures, allowing queue service time to be computed

accurately under complex conditions.

The HCM discussion lists a formula for computing queue service time. This

formula (2-1) is an algebraic interpretation of the queue accumulation polygon, targeted

at computing queue service time.


qrr
gT =fq q.) (2-1)


where,
q,, qg = red arrival rate (veh/s) and green arrival rate, veh/s, respectively,
r = effective red time, s,
s = saturation flow rate, veh/s, and
fq = queue calibration factor


fq = 1.08-0.1imum actual green (2-2)
maximum green


Green extension time: The queue accumulation polygon is not as useful in

determining the green extension time. Figure 2-12 illustrates that green extension time

takes place beyond the polygon boundaries, and cannot be directly computed from the

shape of the polygon. The HCM appendix states that green extension time for each phase

can be calculated using equations developed by Akcelik [1993, 1994].


e (eo+to-A) 1
g, =- (2-3)



where
eo = unit extension time setting
to = time during which the detector is occupied by a passing vehicle








to d L) (2-4)


where
Lv = vehicle length, assumed to be 5.5 m
Ld = detector length, DL, m,
v = vehicle approach speed, SP km/h
A = minimum arrival (intra-bunch) headway, s,
= proportion of free (unbunched) vehicles, and
= a parameter calculated as:


A 1= (2-5)
1- Aq

where q is the total arrival flow, veh/s for all lane groups that actuate the phase

under consideration. Akcelik [1999] has also developed formulas for computing actuated

phase degrees of saturation. These formulas that compute degree of saturation will be

presented later on in this chapter, but should not be confused with Akcelik's green

extension time formulas above, which are an integral part of the NCHRP model.

Actuated phase lengths: The phase length is computed as the sum of the queue

service time, the green extension time, and the yellow plus all red time. Yellow and all-

red times are, of course, given parameter values that do not require calculation.

Subsequently, the estimated average phase length is subject to the constraints of the

associated minimum green, maximum green, and force-off settings. If the estimated

phase length is lower than the minimum green time, it is set equal to the minimum green

time. If the estimated phase length is higher than the maximum green value created by

the force-off, it is set equal to that maximum green time.

Overall timing plan: The new set of estimated phase lengths associated with any

given intersection may not sum to the background cycle length. This is not an issue

under isolated intersection conditions, where the cycle length is simply recalculated as







the sum of the individual phase lengths. Under coordinated conditions, adjustments are

necessary to conform the new solution to the background cycle length. If an estimated

phase time indicates phase termination prior to reaching the force-off setting, then the

unused green time must be reassigned within the cycle.

Assignment of unused green time is performed in accordance with the iterative

computational structure described in the HCM guidelines. If an estimated phase length is

lower than its original phase length from the initial timing plan, its new value is set equal

to the midpoint between those two values. The other half of the slack time is then

donated to the coordinated phase. For example, suppose the initial timing plan contains

a 15 second actuated phase and a 45 second non-actuated phase. If the actuated phase is

estimated as 9 seconds by the NCHRP model, then donating half of the slack time

(instead of all of it) to the coordinated phase results in a 12-second actuated phase time

and a 48-second non-actuated phase time for the second iteration. Donating half of the

slack time to the coordinated phase, instead of donating all of the slack time, may

increase the probability of convergence within the iterative model structure.

Iteration and convergence: After obtaining the overall timing plan, the new

design must be tested for convergence. This is necessary because when the overall

timing plan changes, it causes flow patterns to change throughout the analysis. Changing

flow patterns result in changing phase lengths, and vice versa. This iterative process can

be terminated when the timing plan on any iteration is observed to be identical to the one

from any previous iteration. For example, if the timing plan in iteration 5 were identical

to the one from iteration 3 or 4:








Table 2-2: NCHRP Model Intermediate Outputs


Iteration 1
Critlink Start MnG Fq Gs Ge Y+R Split Max Min
106 0 4 .98 6.38 4.58 2 16 20 6
0 20 4 1 0 0 2 42 72 30
102 50 4 .98 6.38 4.58 2 16 20 6
103 70 4 .98 6.15 4.58 2 16 20 6



Sample calculation

A sample calculation is presented here to demonstrate an application of the

NCHRP model. The initial timing plan (20 30 20 20) in iteration 1 reflects the same

sample calculation conditions from figure 2-3, which was used earlier to demonstrate the

existing model within TRANSYT-7F.

Individual phase times: Intermediate outputs provide details on how individual

phase lengths are estimated. Consider the intermediate output from iteration 1:


Table 2-3: NCHRP Model Iterations of Overall Timing Plan


The start time within the cycle for north/south left-turn phase 3 (link 102) is time

50. Indeed, the search for a zero-length queue begins at the phase starting time. For

phase 3, a zero-length queue must have been found after 6.38 seconds, because the queue


Iteration Phase Times
1 12 20 20 24 9 40
2 10 15 18 22 8 52
3 9 12 18 22 8 56
4 8 12 18 22 8 57

Convergence has been achieved







service time (gs) is reported as 6.38 seconds. The green extension time (ge) for phase 3 is

reported as 4.58 seconds. This value was computed using Akcelik's formula. Yellow and

all-red times for phase 3 are given for each phase as 2 and 0 seconds, respectively.

Therefore, the actuated phase time for phase 3 in this iteration is computed as gs + ge +

yellow + all-red = 6.38 + 4.58 + 2 + 0 = 13 seconds (approximately). However, in the

output file generated by the experimental version of TRANSYT-7F, "Split" is reported as

16 seconds for phase 3 in iteration 1. This is because half of the unused green time was

donated to the non-actuated phase, in accordance with the NCHRP model procedures.

The estimated phase time of 16 seconds for phase 3 does not exceed the force-off

time of 20 seconds and does not fall below the minimum phase time, reported in the

output file as 6 seconds. Therefore, the estimated phase time does not violate either the

minimum or the maximum constraints, and does not need to be readjusted prior to the

next iteration.

Overall timing plan: After determining the each of the individual phase times in

this manner, it is necessary to derive the overall timing plan to be used in the next

iteration. The phase time for phase 3 was computed as 13 seconds. The NCHRP model

calls for donation of half of the slack time. Because the left-turn phase lasted 20 seconds

in the first iteration, it is reduced to 16 seconds in the second iteration, and 4 seconds are

donated to the coordinated phase. Table 2-4 shows that in the first iteration, a total of 12

seconds is donated to the coordinated phase from the three actuated phases.

Thus, green times for the individual phases are reassigned in this manner until a

brand-new timing plan has been established for use in the second iteration. At this point,

the process would terminate if the brand-new timing plan were identical to any timing







plan from a previous iteration. In this case, the overall timing plan has changed and will

be used in the second iteration. The new design is used to assist in determining the

timing plan for the third iteration, and so on. In this case, convergence has been achieved

after iteration number 7. The average phase times listed in the final line (14 48 14 14)

are the ones that are expected to occur, given the input parameter values.



Table 2-4: NCHRP Model Timing Plan Iterations




Iteration Phase Durations
1 20 30 20 20
2 16 42 16 16
3 15 47 14 14
4 14 49 14 13
5 14 48 14 14
6 14 49 14 13
7 14 48 14 14



Existing model: Recall that the existing model for traffic-actuated control within

TRANSYT-7F was also applied to analyze conditions from the sample calculation input

file. The table 2-5 output reveals that phase times estimated by the existing model (8 66

8 8), are different than the ones produced by the NCHRP model (14 48 14 14).

Specific shortcomings

The NCHRP model is constrained by certain simplifying assumptions The

equations for green extension time listed earlier assume that detectors operate in the

presence mode, and assume that detectors are installed at the stop line. Passage detectors,

or detectors of any type that are not installed at the stop line, are not taken into account








by the formula for green extension time. In addition, computer execution time for the

NCHRP model exceeds that of the existing model by many orders of magnitude, since

numerous iterations are required.




Table 2-5: Existing Model Timing Plan for NCHRP Sample Problem



--------------------------------------------
Intersection 1 Actuated Splits Estimated
--------------------------------------------

Interval Number : 1 2 3 4 5 6 7 8

Intvl Length(sec): 6.0 2.0 64.0 2.0 6.0 2.0 6.0 2.0
Intvl Length (%) 7 2 71 2 7 2 7 2

Pin Settings (%) 100/0 7 9 80 82 89 91 98

Phase Start (No.): 1 AC T 2 NA P 3 AC T 4 ACT

Interval Type : V Y V Y V Y V Y

Splits (sec): 8 66 8 8




NCHRP model summary

The NCHRP model has the potential for improved accuracy over the existing

model. It accounts for numerous elements that affect phase lengths, including actuated

signal settings and detector layout. By varying these input conditions during testing, it is

possible to show that the NCHRP model produces more accurate results than the existing

model. Test results such as this are presented later on in this paper.

Iterative Target Degree of Saturation Model

Appendix II of the 1997 HCM states that there are two methods of determining

the required green time given the length of the previous red. One of these methods is the

NCHRP model, as described earlier The second method describes the general procedure








for computing phase times as a function of the target degree of saturation. The existing

model within TRANSYT-7F, also described earlier, employs this strategy. However,

Akcelik [1999] has developed a unique model that combines these two strategies.

Earlier in this chapter it was stated that one of the specific shortcomings of the

TRANSYT-7F existing model is its inability to respond appropriately to changes in

traffic-actuated control parameters. Akcelik's model avoids this shortcoming to some

extent by using special equations to compute the target degree of saturation. The

equations specify that target degree of saturation is affected by the values of certain

actuated control parameters, in addition to a couple of other relevant parameters.

Akcelik's model also involves elements of the NCHRP model. The NCHRP

model procedure is iterative because of the circular dependency between individual

actuated phase times. A change in phase length 'A' has an impact on the effective red

time experienced by subsequent phase 'B'. This affects the average queue length at the

beginning of phase 'B', which affects phase length 'B', possibly affecting the effective red

time experienced by phase 'A', etc. Thus, the circular dependency between actuated

phase times is recognized by dynamic changes in the queue service times.

In Akcelik's model, the circular dependency between actuated phase times is

recognized by dynamic changes in the target degree of saturation Two formulas are

provided for calculating the target degree of saturation. The first formula is intended for

use with initial calculations, when the effective red time is not known:


Xa = 1.5y05eh-o (2-6)


subject to 0.40 <= xa <= 0.95
where,







xa = target degree of saturation for actuated signals
y = flow ratio (v/s)
eh = effective headway (seconds)

The second formula is intended for use with subsequent iterations, when the

effective red time is known:


x = 0.78y05eh-0 018 (2-7)


subject to 0.40 <= xa <= 0.95
where,
r = effective red time (seconds)



eh = 3.6(L, +L) (2-8)
eh = e +tu +---e-
Vac


where,
eh = effective headway (seconds)
es = gap setting (seconds)
tou = detector occupancy time (seconds per vehicle)
Lv = average vehicle length (meters per vehicle)
Lp = effective detection zone length (meters)
vac = approach speed (km per hour)

Effective headway setting is a function of detector length and vehicle length, in

addition to the gap setting. Thus, the target degree of saturation generated by this method

is responsive to physical factors as well as signal settings. Since flow ratio and effective

red time are also taken into consideration through the first two formulas, target degrees of

saturation are appropriately sensitive to volume demand on the subject movement, in

addition to phase lengths of the other movements. On the surface this appears to be an

ideal candidate for upgrading the existing model without requiring substantial changes to

the existing degree of saturation strategy. Instead of using a default value or a user input

value for the target degree of saturation, this formula could be used to intelligently







predict degrees of saturation in response to numerous relevant parameters. However,

earlier discussion on the existing model pointed out possible pitfalls of the target degree

of saturation strategy. Specifically, there is no clear-cut way for revising the target

degree of saturation strategy to account for added complexities such as protected-

permitted left-turn phasing, or queue spillback.

In order to view a sample calculation according to the Akcelik's model, it is only

necessary to review the earlier sample calculation for the existing model within

TRANSYT-7F. Of course, the one exception to this is that target degrees of saturation

for each phase would be calculated in advance via Akcelik's formulas, instead of using a

default value or a user input value.

Modified NCHRP Percentile Joint Poisson Probability Model

Husch [1996] describes a procedure for estimating actuated phase times that is

similar to the NCHRP model. It utilizes the queue service time green extension time

strategy for calculating actuated phase times. However, Husch's model actually

computes five hypothetical phase times, based on the 10th, 30t, 50th, 70th, and 90t

Poisson percentile versions of the average traffic volume. Subsequently, a volume-

weighted average phase time is computed, based on the five hypothetical phase times. If

any one of the five phase times violates the minimum or maximum phase time

requirements, the average phase time can be adjusted accordingly. If the arrival rate on

red for any one of the five hypothetical volumes is less than 0.69 vehicles, then the model

assumes phase skipping (phase time = 0 seconds) for that volume scenario, based on a 0.5

Poisson probability of zero arrivals. Beyond this, the only clear difference between

Husch's model and the NCHRP model lies in the calculation of green extension time.







Queue service time

Husch's queue service time formula is listed as equation (2-9) below.



Tq =T, + x (Y, +R+T) (2-9)
D-A (2-9)


where,
Tq = queue service time (seconds)
T, = start-up lost time (seconds)
A = arrival rate (vehicles per hour)
D = saturation flow rate (vehicles per hour)
R = actual red time (seconds)
Yu = unused yellow time (seconds)

This is essentially identical to the NCHRP model's formula for queue service

time, presented earlier in this chapter as equation (2-1):


f (qr2-
= f s-q)(2-1)



Although there are some apparent differences in the formulas, these differences

are mostly cosmetic, and would not produce any difference within the overall results.

The two formulas are essentially identical because the term (Yu + R + T,) is the same as

effective red (r), arrival rate A is the same as arrival rate q, and departure rate D is the

same as saturation flow rate s. Husch's formula contains start-up lost time (T,), which is

not listed in the NCHRP queue service time formula. However, NCHRP procedures

stipulate that start-up lost time must be added to the queue service time and green

extension time. The question of whether to define start-up lost time as a separate entity,

or as part of the queue service time, is purely semantic and would not affect results.







Some differences are visible that could potentially introduce a bias into the

results. The NCHRP formula contains two variables, qg and qr, to represent vehicle

arrival rates on green and red, respectively. Husch's formula contains only one variable,

A, to represent the arrival rate. In addition, Husch's formula does not implement the

queue calibration factor, fq, which accounts for stochastic behavior. Therefore, in

situations where the arrival rate on green differs from the arrival rate on red, or in

comparing the results to those from stochastic simulation, the NCHRP formula would

presumably produce better correlation.

Green extension time

Husch's green extension time model is completely different than the NCHRP

green extension time model (Akcelik's formula). Husch's model stipulates that once the

queue has been serviced, phase termination via gap-out occurs when there is at least a 0.5

Poisson probability of zero arrivals. The Poisson calculations are performed for each

second within the cycle, following the queue service time. For example, given a flow

rate of 500 vehicles per hour, the Poisson probability of zero arrivals in the second that

immediately follows queue service time is:

(500
P(0)= e 3600 = 0.87


Given a gap setting of 3 seconds, the joint probability of three consecutive

seconds of zero arrivals is:


P(0,0,0)= 0.87 x 0.87 x 0.87 = 0.66


Since the probability of three consecutive zero arrivals is greater than 0.5, an

immediate gap is assumed, and the green extension time is equal to 3 seconds. Under a







different set of input conditions, if an immediate gap were not found, then the

determination of whether a greater than 0.5 probability of gap-out occurs on subsequent

seconds changes slightly.

Table 2-6 demonstrates the relationship between traffic volume and gap setting.

This model computes an effective gap setting (GapEff) as a function of the actual gap

setting and the detector layout. This allows phase times to be computed under various

detector configurations. However, for standard presence detectors installed at the stop

line, the effective gap setting would still be equal to the actual gap setting. In table 2-6, a

cell value of zero indicates that the phase was not extended, and that the green extension

time is equal to the gap setting.

Analysis

Although the volume-weighting approach may be useful in calculating an

accurate average phase time, the individual phase times calculated for any given volume

may be underestimated by Husch's model. First, by omitting the queue calibration factor,

fq, the queue service time model is unable to increase phase times in response to

stochastic effects. Second, by assuming phase termination whenever there is a better than

50% chance of gap-out, the green extension time model is unable to increase phase times

in response to vehicle extensions of the phase. In other words, if there were a 60 percent

chance of gap-out after 3 seconds, a 20 percent chance of gap-out after 6 seconds, and a

20 percent chance of max-out after 9 seconds, this model would nevertheless compute a

green extension time of 3 seconds. However, the appropriate green extension time in this

scenario, considering each possible outcome, would actually be:


g, = (0.6 x 3)+(0.2 x 6)+ (0.2 x 9)= 4.8 seconds








Table 2-6: Husch's Green Extension Time Model Matrix


Volume GapEff= 2 GapEff= 3 GapEff= 4 GapEff= 5 GapEff= 6

(vph)

500 0 0 0 1 1

700 0 0 1 2 3

1000 0 1 2 4 6

1500 1 3 6 10 17

2000 2 5 12 23 49

2500 3 9 22 48 101



The mathematics of this model make it appear as though it would tend to

underestimate actuated phase lengths, and subsequently overestimate green time available

on the coordinated, non-actuated phase. Nevertheless, more detailed analysis and testing

will be conducted on Husch's green extension time model later on in this study, in order

to confirm these appearances.

Other aspects of Husch's overall phase time model need not be tested for the

purposes of this study. The queue service time model is no different than that of the

NCHRP, except that Husch's model does not incorporate the queue calibration factor and

has fewer variables to describe the arrival rate in detail. The technique of performing

calculations on five different Poisson percentile arrival rates seems only appropriate for

external links, or at isolated intersections. The assumption of a Poisson distribution







would invalidate the results on internal actuated links with a nearby upstream signal,

where vehicle arrivals are clearly non-random.

EVIPAS Program

Similar to TRANSYT-7F, the EVIPAS program was developed for the purpose of

traffic signal timing optimization. The primary differences between the two programs are

as follows. The primary feature of EVIPAS is that it was originally designed to optimize

traffic-actuated signal settings such as the maximum green and the gap setting. The

primary limitation of EVIPAS is that it is only capable of analyzing isolated intersections.

The following description of the program appears in a paper titled "Design and

Optimization Strategies for Traffic-Actuated Signal Timing Parameters" [Hale, 1995]:

EVIPAS (Enhanced Value Iteration Program for Actuated Signals) is a program

that has the ability to explicitly simulate traffic-actuated control. Its unique

characteristic is the ability to optimize pre-timed or traffic-actuated signal settings

by performing large quantities of iterative simulation runs. EVIPAS performs

event-based simulations (the events being green extensions or green terminations)

of an isolated intersection [Halati, 1992]. Since the simulations are event-based,

they would tend to have much faster run times than individual CORSIM

microscopic simulation runs for identical conditions. However, EVIPAS is only

capable of modeling a single, isolated intersection. CORSIM and TRANSYT-7F

have the ability to model arterials or networks with multiple intersections.

EVIPAS performs the iterative simulation runs while attempting to minimize

internally calculated vehicle delay. Univariate and gradient search techniques are

used to find the optimal signal settings for an intersection with numerous input







field characteristics. The user can request to optimize any of the available traffic-

actuated signal settings for a given controller. The user can also request to hold

constant any of the signal settings in any phase and to optimize the others. The

reduced run time for a single simulation run allows the optimization routine to

perform hundreds or thousands of iterative simulation runs in a reasonable

amount of time.

The EVIPAS program is unique to this study in the sense that it belongs within all

three major categories of actuated control models in the literature (phase time estimation,

delay estimation, and control parameter design/optimization). In the context of this

literature review section on phase time estimation, EVIPAS appears to be an attractive

candidate model for inclusion into, or evaluation of, TRANSYT-7F. It not only reports

average phase times as outputs, but it has the ability to explicitly simulate actuated

control with reasonable computer execution time. However, the current structure of

EVIPAS, which assumes isolated operations, does not allow a background cycle length to

be applied during the analysis. This existing limitation makes the program less useful in

the context of evaluating or enhancing TRANSYT-7F network analysis of actuated

control. Hopefully future versions of EVIPAS will have the added capability of

optimizing traffic-actuated signal settings when a background cycle length is in effect.

CORSIM Program

The CORSIM program explicitly simulates traffic-actuated control. The same

logic employed by actuated controller hardware in the field has been embedded within

CORSIM. Therefore, CORSIM can be used as a tool in evaluating the candidate models

for improvement of TRANSYT-7F performance. Unlike TRANSYT-7F, CORSIM (once







known as TRAF-NETSIM or NETSIM) was not developed for the purpose of signal

timing optimization. It was meant to be an evaluation tool that could simulate a wide

variety of traffic conditions.

Like TRANSYT-7F, the NETSIM component of CORSIM is a relatively old

program that has earned a certain degree of recognition and acceptance within the

transportation profession. The FRESIM component of CORSIM, used for simulating

freeway links, is relatively newer. Since CORSIM was meant to be an evaluation tool, a

fair amount of research has been done involving comparisons between its results and

observed field data. One example of such comparisons involving field-measured traffic-

actuated phase times is illustrated in figure 2-13 [Courage et al., 1996]. The realism of

simulated traffic-actuated phase times is important in the context of this study.


60
I 2= 0.96 (256 ob~srvolons)
D / =
50-


i -ir Through Phases
I- Q-- 0----- --

L 7

bi. Lefi L-lurn Phases
10

C o 7,00 AM :O0 PMu

0 10 20 30 40 50 60
Phose Time from Feld Dolo (sec)


Figure 2-13: Traffic-Actuated Phase Times CORSIM vs. Field Measured







The following description of the program appears in the CORSIM User's Manual

[ITT Systems & Sciences, 1998]:

CORSIM applies interval-based simulation to describe traffic operations. Each

vehicle is a distinct object that is moved every second. Each variable control

device (such as traffic signals) and each event are updated every second. In

addition, each vehicle is identified by category (auto, carpool, truck, or bus) and

by type. Up to 9 different types of vehicles (with different operating and

performance characteristics) can be specified, thus defining the four categories of

the vehicle fleet. Furthermore, a "driver behavioral characteristic" (passive or

aggressive) is assigned to each vehicle. Its kinematic properties (speed and

acceleration) as well as its status (queued or moving) are determined. Turn

movements are assigned stochastically, asare free-flow speeds, queue discharge

headways, and other behavioral attributes. As a result, each vehicle's behavior

can be simulated in a manner reflecting real-world processes.

Each time a vehicle is moved, its position (both lateral and longitudinal) on the

link and its relationship to other vehicles nearby are recalculated, as are its speed,

acceleration, and status. Actuated signal control and interaction between cars and

buses are explicitly modeled.

Vehicles are moved according to car-following logic, response to traffic control

devices, and response to other demands. For example, buses must service

passengers at bus stops (stations); therefore, their movements differ from those of

private vehicles. Congestion can result in queues that extend throughout the

length of a link and block the upstream intersection, thus impeding traffic flow.







In addition, pedestrian traffic can delay turning vehicles at intersections.

The above description of CORSIM highlights some of the fundamental

differences between it and TRANSYT-7F. Unlike TRANSYT-7F, which is mesoscopic,

CORSIM is a microscopic model in which "each vehicle is a distinct object" [ITT

Systems & Sciences, 1998]. Moreover, CORSIM is a stochastic model: "Turn

movements are assigned stochastically, as are free-flow speeds, queue discharge

headways, and other behavioral attributes" [ITT Systems & Sciences, 1998]. The

detailed nature of CORSIM also leads to significant input data requirements and

relatively long execution times on the computer.

Since it recognizes actuated control parameters as inputs and produces phase

times as outputs, CORSIM does meet the minimum requirements as a model that may

improve TRANSYT-7F performance. The execution time of CORSIM prevents

simultaneous processing with TRANSYT-7F. As realistic as CORSIM is, it should at

least be used as a key evaluation tool in this study. It can be used to evaluate the

candidate models for improvement of TRANSYT-7F performance.

The model testing experiments in chapter 4 demonstrate that variation of relevant

input parameters within CORSIM tends to cause the appropriate changes in the actuated

phase times. Variation of the same input parameters within TRANSYT-7F does not

cause the appropriate changes in the actuated phase times, under the existing model.

When the same input conditions are specified within TRANSYT-7F, comparisons

between the two programs become possible.

Figure 1-1 from Chapter 1 illustrates mediocre correlation of actuated phase times

calculated by CORSIM and the existing model within TRANSYT-7F. Similar







experiments later on in this study should indicate that better correlation is possible by

implementing upgraded sub-models for actuated control within TRANSYT-7F. The

appendix describes techniques for calibrating TRANSYT-7F and CORSIM to achieve

better general agreement between the two programs; however, calibration efforts are not

capable of significantly improving actuated phase time estimates from the oversimplified

TRANSYT-7F existing model.

Phase Time Estimation Summary

To this point, the literature review has focused on models with the ability to

estimate average phase times under traffic-actuated control. In the context of this study,

these models are important to consider while attempting to develop an improved

treatment of actuated control within TRANSYT-7F. The next two sections of literature

review focus on the other classes of actuated control models, namely vehicle delay

estimation and control parameter design and optimization. These two sections are useful

for gaining perspective on the overall study; however, the upcoming models will not be

immediately applicable for developing an improved model as described in the upcoming

chapters.



Vehicle Delay Estimation



In the literature, models that calculate vehicle delay on an actuated phase have the

tendency to predict better performance for that phase, compared to a non-actuated or pre-

timed phase of equal duration. This is understandable because an actuated phase has a

lower probability of temporary oversaturation, due to its ability to respond to variations in







traffic flow. These models in the literature that calculate vehicle delay on actuated

phases will not, in the context of this study, be candidates for improvement of

TRANSYT-7F performance. However, in order to better understand the candidate

models for estimating phase times, it may be useful to understand how these delay

calculators work. In fact, TRANSYT-7F currently implements one of these models for

calculating vehicle delay on actuated phases. It currently implements the 1997 HCM

delay equation [Transportation Research Board, 1997].

HCM Actuated Delay Model

The Highway Capacity Manual (HCM) was written for the purpose of evaluating

the performance of various highway facilities. Similar to CORSIM, it was originally

designed to be an evaluation tool, having no algorithms directly associated with design or

optimization. Unlike the computer programs mentioned in this chapter, the HCM has no

capability for simulating the flow of traffic within a simulated intersection or network.

Rather, it uses various tables and equations to estimate the capacity of a given facility;

although in some cases simulation programs may have been used to assist in developing

certain tables and equations. It also reports the associated "level of service" along with

other measures of effectiveness for the given facility, based on user inputs and

intermediate computations. Table 2-7 [Transportation Research Board, 1997] is an

example of one of these tables.

The HCM has been revised and published several times over the past few

decades. At the time of this writing, the next update (HCM 2000) is scheduled to be

published in October of the year 2000. The manual is a true benchmark within the

transportation profession, and has earned a high degree of recognition Although the








HCM is a manual or document, there are numerous software packages that incorporate

portions of its procedures, including TRANSYT-7F. Delay equations are implemented

within multiple HCM procedures, including the one for signalized intersections.



Table 2-7: HCM Level of Service Criteria for Signalized Intersections


Level of Service Control Delay / Vehicle (sec)
A 0 10
B 10 20
C 20 35
D 35 55
E 55 80
F 80 +



The current (1997) delay model for signalized intersections begins with a large

equation, having three "terms". These three terms contain numerous individual variables

that are affected by many other tables, equations, and sub-models within the procedure.

The first term of the delay equation is used to calculate uniform delay. Generally

speaking, uniform delay can be calculated by measuring the area inside the queue

accumulation polygon (QAP) illustrated earlier in figure 2-12. Conceptually, this is the

vehicle delay that would occur if traffic flow were not stochastic, that is; identical queues

and green times on each cycle, identical performance by each driver and vehicle, etc.

Therefore, the first term of the delay equation is not responsive to actuated control, which

is a stochastic process. Uniform delay is typically unchanged when changing between

actuated and non-actuated phase definitions, provided other inputs are held constant.

The third term of the delay equation is used to calculate residual delay. This only

becomes applicable when queues of unserved (by the previous green phase) vehicles are

present at the beginning of the analysis. When conditions are temporarily oversaturated,







actuated phases are typically driven to their maximum green time on each cycle, and thus

behave like non-actuated phases. Therefore, the third term of the delay equation is not

responsive to actuated control. Residual delay is typically unchanged when changing

between actuated and non-actuated phase definitions, provided that all other input

conditions are held constant.

The second term of the delay equation is used to calculate incremental delay. The

HCM states that incremental delay occurs "due to non-uniform arrivals and temporary

cycle failures (random delay) as well as that caused by sustained periods of

oversaturation oversaturationn delay)." Because traffic-actuated control is effective at

reducing the probability of temporary cycle failures, the second term of the delay

equation is indeed responsive to this. Incremental delay typically decreases when

changing between actuated and non-actuated phase definitions, provided that all other

input conditions are held constant. This delay term is listed as equation (2-10).



8kl-X (2-10)
d2 = 900T (X-1)+ -)2 kI
cT


where
T = duration of analysis period, hours;
k = incremental delay factors that is dependent on controller settings;
I = upstream filtering/metering adjustment factor;
c = lane group capacity, vph;
X = lane group v/c ratio, or degree of saturation.

TRANSYT-7F currently implements the 1997 HCM delay equation. However,

performance of the traffic flow simulation model has an impact on the estimated delay,

because the values of several variables within the equation are computed based on the

simulation results. The values of the other variables are obtained directly from user








input. The end result is that TRANSYT-7F usually computes the same vehicle delay as

other programs implementing the HCM procedures. Differences in estimated delay will

sometimes be introduced due to the differences within other sub-models. For example,

TRANSYT-7F by default applies an Australian model to compute permitted left-turn

capacities, whereas the HCM signalized intersection procedures contain their own unique

permitted left-turn movement model. All in all, TRANSYT-7F is considered up-to-date

in the way that it calculates vehicle delay, thanks to the HCM delay equation.

It so happens that one of the variables that has a huge impact on the results of the

delay equation is the average phase time. This underscores the importance of upgrading

the actuated phase time calculation methodology that is currently implemented by

TRANSYT-7F. Improvements to the accuracy of phase time calculation will

automatically improve the accuracy of vehicle delay calculation, without even changing

the way vehicle delay is calculated.

Volume-Weighted Average

In order to calculate vehicle delay at actuated signals, Husch [1996] recommends

implementing the delay equation five times in a row based on five hypothetical traffic

volumes, and then using a volume-weighted average to calculate the overall average

delay. The hypothetical traffic volumes are estimated by assuming random Poisson

arrivals that are often observed on the minor street, and then calculating the expected

10th, 30th, 50th, 70th, and 90th percentile volumes. This allows for some actuated

control related adjustments, depending on whether some of these volume levels would

clearly cause the phase length to violate the minimum or maximum phase times. The

equation for calculating the volume-weighted average is listed below:










D DIO*VIO+D30*V30+D50*V50+D70*V70+D90*V90 (2-11)
V10 +V30+V50+V70+V90


CORSIM and EVIPAS Programs

CORSIM computes and reports three types of vehicle delay. Instead of using an

equation to estimate delay, it is computed directly from simulation. Total delay is

determined by CORSIM as the difference between actual travel time and the travel time

if constantly moving at the free flow speed. Queue delay is accumulated for each second

when a vehicle has an acceleration of less than 2 feet per second squared, and a speed of

less than 3 feet per second. Queue delay is accumulated every other second when a

vehicle has an acceleration of less than 2 feet per second squared, and a speed between 3

feet per second and 9 feet per second. Stop delay is accumulated for each second when a

vehicle has a speed of less than or equal to 3 feet per second.

Like CORSIM, EVIPAS computes delay directly from simulation. Exact

measurement criteria similar to those listed above for CORSIM are unknown for

EVIPAS. EVIPAS is therefore mentioned here so that all known models for calculating

traffic-actuated vehicle delay are listed in this chapter, and to document the fact that

EVIPAS is not known to use a separate analytical model for calculating delay, as does

TRANSYT-7F.

Vehicle Delay Estimation Summary

This section of literature review has focused on models with the ability to

estimate vehicle delay under traffic-actuated control. Improved vehicle delay estimation

is not the direct objective of this study. It is important to note that an improved







methodology for calculation of actuated phase times should automatically result in better

estimates of delay and other measures of effectiveness. The upcoming final section of

literature review focuses on actuated control models for control parameter design and

optimization. Again, this section is useful for gaining perspective on the overall study;

however, the upcoming models will not be immediately applicable for developing an

improved model as described in the upcoming chapters.



Control Parameter Design and Optimization



As mentioned earlier in this chapter, the requirements of an improved model

include the ability to estimate average actuated phase lengths as outputs. Actuated phase

lengths cannot be directly designed or optimized. They must instead be calculated as a

function of numerous other parameters, some of which are indeed subject to design and

optimization.

The models presented in this subsection were instead developed to design

actuated control parameter values as outputs. The possibility exists that TRANSYT-7F

could someday assist in directly designing actuated signal timing parameters. However,

that is not the purpose of this study. These models presented in this subsection may

provide a frame of reference. Although the overall objective of this study is to provide an

improved methodology for calculation of actuated phase times, this methodology may

result in a new facility for designing actuated control parameters within TRANSYT-7F.







Minimum Green Design

Some traffic-actuated signal settings, including the minimum green, cannot

technically be optimized. The minimum green time should be set to a value that

accommodates pedestrian traffic and driver expectations. Regardless of controller type,

the value of the minimum green is generally at least 5 seconds for left-turn phases and 10

seconds for through phases, just to satisfy driver expectancy. The minimum green is

increased and designed as a function of walking speed if pedestrians would require the

extra time for crossing the intersection. These practices illustrate that design of the

minimum green setting is governed by safety considerations.

Gap Setting Design

Engineering judgment is necessary in designing the gap setting (a.k.a. "unit

extension"). If the driver of a queued vehicle is not paying attention when the queue

begins moving, the detector may sense a gap and terminate the phase prematurely. A

low-value gap setting can lead to premature phase terminations and excessive delays on

an actuated phase unless the drivers are very attentive. On the other hand, a high-value

gap setting can lead to wasted green time on the actuated phase, leading to excessive

delays on the other phases. Gap settings can thus be improper if they are too low, or too

high.

Several methods for design of the gap setting exist in the literature. Most

methods are jurisdiction-specific recommendations of a certain value or a narrow range

within x and y seconds. One method [Courage and Luh, 1989] recommends gap settings

based on a statistical analysis that contains approximations. It assumes that a phase

should be terminated when it may be concluded with 95 percent confidence that the








current flow rate has dropped below 80 percent of the saturation flow rate. EVIPAS was

designed to optimize the gap setting, but this feature may be inappropriate from a

practical standpoint, since the program contains no methodologies for modeling

inattentive drivers.

Computer programs such as CORSIM, EVIPAS, and TRANSYT-7F typically do

not model inattentive drivers or premature phase termination. The engineer should thus

select a gap setting with the prospect of premature phase termination in mind, and then

define that value in the programs, realizing that the models will not simulate inattentive

drivers.

Maximum Green Design and Optimization

Numerous design and optimization methods for maximum green exist in the

literature. They include a mixture of charts, programs, graphs, tables, and guidelines.

Each one is a function of a different set of field variables.

The method for design of the maximum green setting described in the

Methodology for Optimizing Signal Timing (MOST) manual [Courage and Wallace,

1991] can be applied through the SOAP program. The equations used by SOAP to

calculate its maximum phase times involve computation of a traffic-actuated cycle length

based on a user-specified target volume-to-capacity (v/c) ratio, and calculation of the

phase times to be proportional to the critical flow ratios for each phase. This method is

similar to the existing model for traffic-actuated control within TRANSYT-7F.

The method developed by Lin [1985] normally performs calculation of the

maximum green setting as a function of the peak hour factor and the optimal pre-timed

green setting. However, this method also incorporates compensation for the extra time







that is required for exclusive right-turn lanes. The formulas recommended by

Skabardonis [1988] and modified by Fambro et al. [1992] are sensitive to the volume-to-

capacity ratio, and recognize the impact of oversaturation on the design of the maximum

green setting. Apart from their individual reference sources, the equations associated

with these techniques for maximum green and gap setting design are compiled in a paper

titled "Design and Optimization Strategies for Traffic-Actuated Signal Timing

Parameters" [Hale, 1995].

Detector Configuration Design

Appropriate detector configuration design is a function of numerous

characteristics. Presence detectors are typically installed near the stop line in order to

detect the first vehicle in queue (see figure 2-14). Detector length specification is another

engineering judgment call. Detector lengths that are too short increase the risk of

vehicles going undetected, and increase the risk of premature phase termination.

Detectors that are too long become expensive to purchase, install, and maintain. Also, if

premature phase termination does not occur, longer detectors may increase vehicle delay.

Multiple detectors within the same lane can affect traffic performance.

Evidence [Cribbins, 1975] [Lin, 1985] supports the intuitive notion that presence

detectors that are too long lead to wasted green time and increased delay. In Florida,

presence detectors are typically 30 feet long. Orcutt [1993] recommends 40-foot

presence detectors, but adds that 60 foot detectors are preferable when approach speeds

exceed 35 mph. Passage or pulse detectors are recommended if all traffic to be detected

will flow freely between the detector and the intersection. Because they are much

smaller than presence detectors, they are generally less expensive to install and maintain.








Detector length is not the primary design consideration as with presence detectors.

Instead, detector setback is. As illustrated in figure 2-14, setback is the distance between

the stop line and the detector.


Figure 2-14: Sample Detector Layout or Configuration


Several sources [Kell and Fullerton, 1991] [Lin, 1985] [Tarnoff and Parsonson,

1981] recommend that setback should be designed based on safe stopping distance,

which is a function of approach speed. The main purpose is to avoid the dilemma zone in

which a vehicle can neither pass through the intersection nor stop before the stop line

[Lin, 1994]. Bonneson and McCoy [1993] propose the alternative strategy of carrying

the last clearing vehicle only through the indecision zone (rather than into the

intersection) upon gap-out. Other sources [Bonneson and McCoy, 1993] [Fambro et al.,

1992] describe the added benefit of using multiple advance loops in the detector design.


Detector Length (Presence)

< ~>"""""""""


Detector Scbhack (Passainc or Pulse)


~s~ar~laaa~a~ao~aaooaooolraoaao~







Coordination Setting Design

Certain traffic-actuated signals settings, such as the yield point, force-off, and

permissive period settings, are applicable only in coordinated, actuated systems.

However, some models recommend optimal values using the terminology of splits and

offsets. The EVIPAS simulation-based optimization model, as well as other analytical

design techniques, can recommend maximum green and gap setting values, but not

coordination settings. As such, an additional analysis phase is sometimes recommended

in the literature in order to obtain these settings. Skabardonis [1988], Courage [1989],

Khatib and Coffelt [1999] have written guidelines and developed software packages

associated with selection of coordination settings for actuated systems. The CORSIM

Users Guide [ITT Systems and Sciences Inc., 1998] also contains guidelines for selection

of coordination settings, though explained in the context of the CORSIM program.

Control Parameter Design and Optimization Summary

The control parameter design and optimization models in this subsection were

presented primarily for informational purposes. In the context of this study, it is helpful

to know that these models will not be immediate candidates for improvement of

TRANSYT-7F performance, even though they exist in the literature as models for

actuated control. Some of the concepts involving the individual traffic-actuated signal

timing parameters were also discussed, which may be helpful as a review for the reader.

Also, if it is ever decided that TRANSYT-7F could be enhanced in order to design or

recommend traffic-actuated control parameter values, the models mentioned in this

subsection may prove useful.







Chapter Two Summary



Many of the realistic components within these models for traffic-actuated control

are not taken into consideration within the current methodology of TRANSYT-7F.

However, not all of the available models in the literature for actuated control are able to

meet the minimum requirements for improvement of TRANSYT-7F performance.

The following models do not meet the minimum requirements:

Existing Model within TRANSYT-7F

CORSIM

EVIPAS

Husch's Queue Service Time and Percentile Models

Vehicle Delay Estimation Models

Control Parameter Design and Optimization Models

The existing model within TRANSYT-7F is not ideal because it is oversimplified,

which compromises the accuracy of actuated phase times. CORSIM and EVIPAS

provide good treatment of actuated control, but from a practical standpoint, they are not

good candidates for implementation in conjunction with TRANSYT-7F. Husch's queue

service time model is essentially identical to the NCHRP queue service time model, and

the percentile computation of actuated phase times is not ideal for internal links where

random arrivals cannot be assumed. Finally, all vehicle delay estimation models, and all

control parameter design and optimization models, do not meet the minimum requirement

for this study associated with improved accuracy in calculating actuated phase times.







The following models do meet the minimum requirements for improvement of

TRANSYT-7F performance:

NCHRP Model

Iterative Target Degree of Saturation Model

Joint Poisson Probability Green Extension Time Model

These models were examined and tested further, and these results are documented

in the upcoming chapters.


















CHAPTER 3
MODEL DEVELOPMENT



This chapter describes the development of new models during the course of this

study. An experimental version of TRANSYT-7F was developed in order to implement

the new models, which address some of the existing deficiencies in estimating actuated

phase times. Specific shortcomings of the target degree of saturation strategy, employed

by multiple models from the literature, were discussed at length in chapter 2. Therefore,

an ideal model for improvement of TRANSYT-7F performance should not adopt this

strategy.

The queue service time green extension time strategy, employed by multiple

models from the literature, seems to be the most viable strategy. Thanks to the queue

accumulation polygon (QAP) concept, which is well-documented within the Highway

Capacity Manual and other sources, queue service time is readily and accurately

calculated. Indeed, an actuated phase is not capable of gapping out in the midst of the

queue service time, so this structure prevents modeling blunders. In addition, if the

queue service time exceeds the maximum green time, max-out is the obvious result.

Finally, taking queue service time out of the mix allows for more







accurate estimation of green extension time. Therefore, the queue service time green

extension time strategy will be pursued at this time.



Queue Service Time



In the literature, queue service time is computed by equations that are algebraic

interpretations of the queue accumulation polygon. As mentioned in chapter 2, the QAP

concept is flexible enough to adapt to complexities from the field that would alter vehicle

arrival or departure rates. Here again is the queue service time equation (2-1) from the

NCHRP model, initially introduced in chapter 2:


qrr
g (s-q,) (2-1)


where,
qr, qg = red arrival rate (veh/s) and green arrival rate, veh/s, respectively,
r = effective red time, s,
s = saturation flow rate, veh/s, and
fq = queue calibration factor


f, = 1.08-0. tual green (2-2)
Maximum green)


Permitted Left-Turn Effects

One advantage of the queue service time approach involves the modeling of

permitted left-turns. Typically permitted-only left-turn phases, in which only a green ball

is displayed by the signal in the field, are not actuated because the length of the phase is

designed to handle through movement traffic. However, protected-permitted left-turn








phases, in which a green arrow followed by a solid green is displayed in the field, are

frequently actuated.

It is more complicated to estimate actuated phase times for the protected portion

of a protected-permitted phase. The results are dependent on how much traffic is served

during the permitted portion of the phase. If the opposing movement has heavy traffic

and few left-turns are served during the permitted portion of the phase, then the actuated

phase time may be nearly equal to what it would be under protected-only phasing. If the

opposing movement has light traffic and many left-turns are served during the permitted

portion, then the actuated phase time may be nearly equal to the minimum phase time,

because the queues are so small during the protected portion. The queue accumulation

polygon (QAP) illustrated in figure 3-1 shows that the queue length accumulated during

the permitted portion directly affects the subsequent queue service time.


Figure 3-1: Queue Accumulation Polygon (QAP) for Protected-Permitted Phasing


Gs?
Protected Portion Permitted Portion







The queue service time models are appropriately sensitive to how many vehicles

were served during the permitted portion of the phase. Multiple QAPs from the HCM

guidelines illustrate how the queue at the beginning of the protected portion of the phase

can be adjusted to reflect the number of vehicles served during the permitted portion of

the phase.

Whereas deficiencies of the existing literature models were initially introduced in

chapter 2, additional technical details regarding these deficiencies are supplied within

chapters 3 and 4. For example, chapter 2 states that permitted left-turn effects (on

actuated phase times) are one category of operational characteristic effects that are

difficult to quantify without using simulation. The existing model within TRANSYT-7F

for calculating actuated phase times is inadequate because it does not attempt to estimate

protected portion actuated phase times for protected-permitted phases. Instead such

phases are currently set to their minimum phase times automatically, as if all traffic was

served during the permitted portion of the phase. No known methodology is available for

automatically adjusting the (protected portion) actuated phase target degree saturation in

response to how much traffic was served during the permitted portion of the phase.

In order to rectify this model in its existing form, it would be necessary to readjust

target degrees of saturation, based on the amount of traffic served during the permitted

portion of the phase. Because phase times must be known prior to simulation, and

because the amount of traffic served in the permitted portion is determined during

simulation, an iterative target degree of saturation structure is required, similar to

Akcelik's model from chapter 2.








If permitted left-turn effects were the only complexity affecting the actuated

phase model, then the target degree of saturation strategy could possibly be updated as

described by Akcelik. Perhaps there would be no obvious disadvantages relative to the

queue service time green extension time models; however, there are other

complexities that further hinder this strategy, such as progression and spillback.

Progression and Spillback Effects

Unfortunately, the equations that interpret the QAP to compute queue service time

are not flexible enough. They are oversimplified, and unable to interpret complex QAPs

that are likely to occur due to network-wide interaction effects. The NCHRP queue

service time equation implements two separate arrival rates, and one unique departure

rate. The arrival rates are divided into two quantities: arrivals on red, and arrivals on

green. The departure rate is the saturation flow rate. However, when analyzing a single

system having multiple intersections, arrival rates and departure rates are unpredictable

enough such that three variables are not adequate for calculating the correct results.

For example, consider having only one variable to describe arrivals on green.

This means that only one arrival rate on green can be modeled. However, non-uniform

arrival rates on green will occur when a nearby upstream signal is present. Even if the

average arrival rate on green is specified correctly, progression effects (non-uniform

arrivals) can change the queue service time.

Figure 3-2 illustrates an example of progression effects on queue service time.

The slope of the queue accumulation polygon's right side is affected by a constantly

changing arrival rate. Although 200 vehicles per hour are expected during the green

phase, good progression from the upstream signal causes vehicles to arrive after the








queue has been serviced. In this case, progression effects allow the average queue

service time to decrease from 12.6 seconds to 10.6 seconds. However, the formula would

still predict a queue service time of 12.6 seconds in this case. One variable is not enough

to account for progression effects. Ideally, the arrival rate during each second should be

known in order to calculate the correct queue service time.


Figure 3-2: QAP Depiction of Good Progression Decreasing the Queue Service Time



The formula is additionally constrained to having only one variable to describe

departure rates. This means that only one departure rate can be modeled for each

movement. However, non-uniform departure rates will sometimes occur when a nearby

downstream signal is present. Even if the average departure rate is specified correctly,

spillback effects (non-uniform departure rates) can change the queue service time.


Queue Service Time
-C >


Red







Figure 3-3 illustrates an example of spillback effects on queue service time. The

slope of the queue accumulation polygon's right side is affected by a constantly changing

departure rate. Although 3515 vehicle departures per hour are expected when serving

queues, spillback from the downstream signal decreases the departure rate and increases

the queue service time. In this case, spillback effects allow the average queue service

time to increase from 15.6 seconds to 24.4 seconds. However, the formula would still

predict a queue service time of 15.6 seconds in this case. One variable is not enough to

account for spillback effects. Ideally, the departure rate during each second should be

known in order to calculate the correct queue service time.


Figure 3-3: QAP Depiction of Spillback Increasing the Queue Service Time



Queue Service Times from the Program

Fortunately, TRANSYT-7F continuously tabulates uniform or non-uniform

arrival rates, departure rates, and queue lengths during each step of analysis and


Queue Service Time


Time (seconds)







throughout the network. On external links with no nearby upstream signal, queue service

times computed by TRANSYT-7F and the NCHRP formula are identical, barring any

differences introduced by permitted left-turn movement models. However, TRANSYT-

7F has the added capability to adjust queue service times in response to traffic flow from

upstream signals, and spillback from downstream signals. Queue service time should

therefore be extracted directly from the results of TRANSYT-7F step-wise simulation.

This will allow queue service times and actuated phase times to be automatically

responsive to progression and spillback effects, in addition to permitted left-turn effects.



Green Extension Time



A perceived deficiency of existing models in the literature for computing green

extension time is the assumption of random vehicle arrivals. It is true that the assumption

of random arrivals is reasonable on external links having no upstream signal nearby.

However, many practitioners continue to conduct analyses with the assumption of

uniform arrivals on external links. More importantly, an ideal green extension time

model would not assume any specific pattern of vehicle arrivals, especially since

platooned arrivals are expected on internal links having a nearby upstream signal.

Rather, an ideal model would intelligently compute green extension times as a function of

any possible pattern of vehicle arrivals. Here again is the green extension time equation

(2-3) from the NCHRP model, initially introduced in chapter 2:


e A(eo+tr-A) 1
g5e (2-3)
(pq A'







where
eo = unit extension time setting
to = time during which the detector is occupied by a passing vehicle


to = (Ld + L) (2-4)
v

where
Lv = vehicle length, assumed to be 5.5 m
Ld = detector length, DL, m,
v = vehicle approach speed, SP km/h
A = minimum arrival (intra-bunch) headway, s,
= proportion of free (unbunched) vehicles, and
= a parameter calculated as:


1= q (2-5)
1- Aq

where q is the total arrival flow, veh/s for all lane groups that actuate the phase

under consideration.

This equation noticeably implements one unique arrival rate (q). This means that

only one arrival rate on green can be modeled; however, when analyzing a single system

having multiple intersections, arrival rates are unpredictable enough such that one

variable is not adequate for calculating the correct results. Non-uniform and non-random

arrival rates on green will occur when a nearby upstream signal is present. Even if the

average arrival rate on green is specified correctly, progression effects (non-uniform,

non-random arrival rates) can change the green extension time.

Figure 3-4 illustrates an example of progression effects on green extension time.

The histogram represents a constantly changing arrival rate. Although 200 vehicles per

hour are expected during the green phase, good progression from the upstream signal

causes vehicles to arrive after the queue has been serviced. In this case, progression








effects cause the average green extension time to increase from approximately 3 seconds

to more than 5 seconds. However, the formula would still predict the same green

extension time in both cases by assuming the average arrival rate of 200 vehicles per hour

(illustrated by the superimposed dashed line). One variable is not enough to account for

progression effects. Ideally, the arrival rate during each second should be known in order

to calculate the correct green extension time.


Figure 3-4: Example of Good Progression Increasing the Green Extension Time



Prototype Green Extension Time Model Using Applied Probability and Flow Profile

As mentioned earlier in this chapter, the TRANSYT-7F program continuously

tabulates the arrival rate, departure rate, and queue length during each step of simulation

and throughout the network. Knowledge of the network-wide arrival rate, or flow profile,

should be useful in computing green extension time. However, the flow profile does not


0 Green Extension Time

C Queue Service Time |-



200 -----...... .. .. ... .. ..... .
.. .. .. .. .
.. .... ...* .. ... .. .. .. .... ...
... .....Cj
2 0 0 ---- --- -- ---- ---- ---- _.. .... ...


Time (seconds)







automatically reveal the correct green extension time, in the way that queue profiles

reveal the correct queue service time. The only way to explicitly compute green

extension time is through microscopic simulation employed by programs like CORSIM.

These programs simulate individual vehicles rolling over detectors and thus are able to

know exactly when gap-out occurs. The TRANSYT-7F flow profile information allows

the opportunity to calculate the maximum likelihood green extension time, which should

be a better estimate than is possible using any model that assumes uniform or random

arrivals. A new model was developed to compute the most probable location of gap-out

and thus the overall green extension time, based on the TRANSYT-7F flow profile.

Methodology and sample calculation #1

A sample calculation illustrates the methodology of this prototype model. Figure

3-5 illustrates an actual simulated flow profile for an actuated left-turn phase having a

nearby upstream signal. Although the average flow rate is 200 vehicles per hour, arrival

rates much higher than this are occurring during a certain part of the 100-second cycle,

due to progression effects. Note that flow intensity would be affected by multiple links in

the case of a shared lane. Although figure 3-5 does not show this, the left-turn phase

begins at step 92 towards the right-hand side of the histogram in this example. The force-

off time for this phase occurs at step 29 towards the left-hand side of the histogram.

In order to estimate the green extension time, it is only necessary to scrutinize the

flow profile after the queue service time and until the force-off time. Figure 3-6

illustrates this abbreviated flow profile that can be used for green extension time

calculations. Looking at this flow profile, the flow rate occurring immediately after

queue discharge is clearly higher than the 200 vph average. In fact, the average flow rate








1000.


Time (seconds)


Figure 3-5: Sample Calculation Internal Link Flow Profile


900
800
700
600
4-.
300 ---..

200
100
0
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
Time Step (seconds)



Figure 3-6: Sample Calculation Internal Link Flow Profile (Abbreviated)


poll.
I logo.
....... ..... .
.
up I ft I U1.0111


1


I


II







in this range is 380 vph. Therefore, a higher-than-average green extension time is

expected.

The first step of the prototype model involves calculating the probability of zero

vehicle arrivals during each second within the abbreviated flow profile. The Poisson

distribution is used to calculate the probability of zero arrivals during each second.

However, instead of using the average hourly traffic volume in the calculations, each

individual flow rate at each individual simulation step is used to calculate numerous

individual probabilities. For example, the probability of zero arrivals at step 3

immediately following queue discharge, is:

P(0)= e-727/3600 0.82


The second step of applying the prototype model involves calculating the

probability of consecutive simulation steps having zero vehicle arrivals within the

abbreviated flow profile. It is known that if zero arrivals take place on enough

consecutive steps, the phase will terminate via gap-out. Assuming a gap setting of 3

seconds, phase termination will occur if three consecutive steps have zero arrivals. For

example, the probability of three consecutive steps with zero arrivals at step 5

immediately following queue discharge, is:


P(0,0,0)= 0.82 x 0.81 x 0.82 ; 0.54


The third step of applying the prototype model involves calculating the

probability of gap-out within the abbreviated flow profile. At step 5, the probability of

gap-out is actually equal to the probability of consecutive zero arrivals at steps 3, 4, and

5. However, at step 8, the probability of gap-out is not exactly equal to the probability of







consecutive zero arrivals at steps 6, 7, and 8. It is known that there is only a 1 0.54 =

0.46 probability of not gapping out at step 5. Therefore, the probability of gap-out at step

8 is:

P(gap out)= 0.46 x (0.84x 0.86 x 0.87)q 0.29


The fourth step of applying the prototype model involves calculating the

probability of max-out within the abbreviated flow profile. The probability of max-out is

actually equal to one minus the summation of all gap-out probabilities:


P(max out) = 1- P(gap out)


The fifth step of applying the prototype model involves calculating time step

weighted averages. In this sample calculation, there was a 0.54 probability of phase

termination at step 5. Therefore, the time step weighted average here is:

T(step 5)= 0.54 x 5 ; 2.7


The sixth step of applying the prototype model involves calculating the average

phase time by summing the time step weighted averages:

PhaseTime = I T(step)


Table 3-1 lists the entire set of values in the sample calculation. After summing

the time step weighted averages, the final answer is time step 7.1 as the location of phase

termination. Because the queue service time ended at step 2, the green extension time is

5.1 seconds. The Poisson distribution is not the only method available to calculate P(0).

For 200 vph (an arrival every 18 seconds on average), the uniform P(0) would be 1/18, or








0.055. However, this method would only change the answer by one tenth of a second in

table 3-1. Note that the probability of immediate gap-out was 54%. Oddly, Husch's

green extension time model specifies immediate gap-out due to the value above 50%,

even though the 46% chance of extension results in a 2.1 second increase (ge = 5.1 vs. 3).

Also note that green extension times are potentially affected by the maximum green

setting. Green extension time decreases to 4.4 seconds if the maximum occurs at step 8,

because all of the remaining weighted average values would be rolled into step 8.


Table 3-1: Prototype Model Sample Calculation of Green Extension Time

Time Flow Rate P(0) P(0,0,0) P(gap) P Weighted
Step (vph) cumulative Average

3 727 0.82
4 765 0.81
5 702 0.82 0.54 0.540 2.700
6 623 0.84
7 558 0.86
8 506 0.87 0.63 0.288 0.83 2.303
9 464 0.88
10 430 0.89
11 402 0.89 0.70 0.120 0.95 1.321
12 383 0.90
13 367 0.90
14 354 0.91 0.74 0.038 0.99 0.536
15 345 0.91
16 337 0.91
17 331 0.91 0.75 0.010 1.00 0.176
18 323 0.91
19 311 0.92
20 297 0.92 0.77 0.003 1.00 0.052
21 282 0.92
22 266 0.93
23 251 0.93 0.80 0.001 1.00 0.014
24 237 0.94
25 223 0.94
26 211 0.94 0.83 0.000 1.00 0.003
27 198 0.95
28 186 0.95
29 175 0.95 0.000 0.001

7.107







Another observation is that green extension time calculations begin at an integer

step number such as step 3 because TRANSYT-7F tabulates the flow profile by integer

step sizes. Although queue service time is actually a real number and the green extension

time actually begins at time step 2.6, the approximation of beginning the green extension

time calculations at step 3 should have negligible impact on the result (5.1 seconds). In

other words, there are so many calculations within the flow profile, that beginning the

green extension time calculations at step 2 or step 3 would probably produce the same

answer (5.1 seconds).

Sample calculation #2

In order to better understand the prototype model, another sample calculation can

be demonstrated in which changes to progression cause changes in the green extension

time. In this sample calculation, all conditions except for one are identical to those from

the previous sample calculation. The one difference is the offset design, which changes

the observed traffic patterns on the arterial street. Figure 3-7 illustrates the updated flow

profile for the actuated left-turn phase having a nearby upstream signal.

Comparing the figure 3-7 flow profile with the original flow profile from figure 3-

5, the shape and intensity of the platoon is similar. However, with the new offset design,

the platoon arrives 5 seconds earlier at step 84. Again, to estimate the green extension

time, it is only necessary to scrutinize the flow profile after the queue service time and

until the force-off time. Figure 3-8 illustrates the updated abbreviated flow profile that

can be used for green extension time calculations.

The queue service time ends at step 12, and the force-off time occurs at step 37.

Looking at this flow profile, the flow rate occurring immediately after queue discharge is



































Figure 3-7: Sample Calculation #2 Internal Link Flow Profile


180
160
140
120 .
100
80 -
60 -
LL
40
20
0
0 L ,, s


Time Step (seconds)




Figure 3-8: Sample Calculation Internal Link Flow Profile (Abbreviated)


1200


1000


- 800


cu 600


0o 400
LL

200


0


O- () CO r- oD L) J- co Cj V- O
C CO) q n CD e- cO o) 0








clearly lower than the 200 vph average. In fact, the average flow rate in this range is 84

vph. Therefore, a lower-than-average green extension time is expected. Table 3-2 lists

the entire set of values in the second sample calculation.


Table 3-2:


Prototype Model Sample Calculation #2 of Green Extension Time


P(0,0,0) P(gap)


Time
Step

13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37


P
cumulative


0.88


Flow Rate
(vph)

156
149
142
136
131
125
119
114
108
101
101
109
103
88
74
63
53
45
38
33
28
23
20
17
14


P(0)


0.96
0.96
0.96
0.96
0.96
0.97
0.97
0.97
0.97
0.97
0.97
0.97
0.97
0.98
0.98
0.98
0.99
0.99
0.99
0.99
0.99
0.99
0.99
1.00
1.00


After summing the time step weighted averages, the final answer is time step 15.4

as the location of phase termination. Because the queue service time ended at step 12, the

green extension time is 3.4 seconds. The sample calculation demonstrates that when

progression becomes worse, the prototype model responds logically by calculating a


0.88


0.90


0.91


0.92


0.93


0.96


0.97


0.98


0.108


0.011


0.001


0.000


0.000


0.000


0.000


0.99


1.00


1.00


1.00


1.00


1.00


1.00


Weighted
Average


13.200


1.937


0.236


0.025


0.002


0.000


0.000


0.000
0.000

15.401








lower green extension time. This means that because the traffic flow pattern is light

following queue discharge, there is a lower probability of the phase being extended. By

comparison, the NCHRP model would not have recognized progression effects. It would

have calculated the same green extension time in both scenarios.

Prototype Green Extension Time Model Based on Uniform Vehicle Arrivals

Another prototype model was developed during the course of this study as an

alternative to the existing models from the literature designed with random arrivals in

mind. This model carries with it the basic assumption of uniform vehicle arrivals. The

model is simple because when vehicle arrivals may be assumed to be perfectly uniform,

there are only two green extension times that are physically possible. After computing a

weighted average based on these two possible green extension times, the result is an

overall estimate for the average green extension time.

When perfectly uniform arrivals are in effect, the two physically possible green

extension times can be described as follows. The first possibility is that no vehicle

arrives during the gap setting interval immediately following queue discharge. When this

occurs, the green extension time is equal to the gap setting. The second possibility is that

one vehicle arrives during the gap setting interval immediately following queue

discharge. When this occurs, the green extension time is equal to 1.5 times the gap

setting. If a vehicle extends the phase once, no additional extensions are possible because

the inter-arrival time between vehicles will be larger than the gap setting. Assuming that

one vehicle does extend the phase, it must arrive sometime within the gap setting interval,

or on average halfway through the gap interval. After that, the phase will be extended by

exactly 1 additional gap time.







Sample calculation

A sample calculation is useful for understanding the logic here. Suppose that the

traffic volume demand is 600 vehicles per hour per lane. Assuming uniform arrivals, this

translates into one vehicle arrival every six seconds. Given a gap setting of two seconds,

there would be a 0.33 probability of a vehicle arrival within the gap interval, and a 0.67

probability of no vehicle arrival within the gap interval. Also, if a vehicle does arrive

within the gap interval, then on average it will arrive halfway through the gap interval, or

after 1 second in this case. In addition, a vehicle extension after 1 second automatically

extends the phase by exactly 1 gap interval, or 2 seconds in this case. Therefore, there

would be a 0.33 probability that the green extension time would be equal to 1.5 2 = 3

seconds, and a 0.67 probability that the green extension time would be equal to 2

seconds. Using the weighted average, overall green extension time is estimated as:


ge = (0.33 x 3)+(0.67 x 2)- 2.33 seconds


These green extension time calculations are only valid given traffic volumes that

are sufficiently low. High traffic volumes result in low inter-arrival times that may be

lower than the gap interval. When vehicle inter-arrival times are indeed lower than the

gap interval, and uniform arrivals are in effect, the end result is that gap-out cannot occur,

physically or mathematically. In this case, the phase is assumed to terminate via max-out

or force-off. For example, a per lane volume of 1800 vehicles per hour, producing one

vehicle arrival every two seconds, would always cause max-out with gap settings of two

seconds or higher. Likewise, a per lane volume of 1200 vehicles per hour, producing one







arrival every three seconds, would always cause max-out with gap settings of three

seconds or higher.

Alternative queue service time model

Interestingly, this second prototype green extension time model concept suggests

a new and simplified calculation for queue service times. Indeed, if vehicle arrivals are

perfectly uniform in nature, and if only 0-1 vehicle extensions of the green are physically

possible, this implies that nearly all vehicles are queued while being served. Thus, the

uniform arrivals queue service time could presumably be calculated by computing the

number of vehicles served per cycle, multiplying this value by the queue discharge

headway, and then adding in the start-up lost time. Figure 3-9 illustrates the phase time

calculation under this scenario.

Figure 3-9 shows that four queued vehicles should be served on each cycle,

although the fourth vehicle joins the queue in the midst of queue service time. The phase

time of 15 seconds assumes no vehicle extensions. However, since the uniform arrivals

green extension time should actually be the weighted average of 0 and 1 extension times,

the estimated phase time would probably be something like 15.75 seconds.

When the uniform queue service times are combined with the uniform green

extension times, results may improve due to the consistency of assumptions. However,

the process of determining an average number of vehicles served per cycle, which allows

computation of uniform queue service times, is fragile. Determination of average queue

per cycle can become difficult, given numerous complications from the field, which is

why extraction of queue service times from TRANSYT-7F simulation is preferable.

Consequently, the uniform arrivals prototype model is expected to produce reliable







results under simple conditions, but may break down under complex conditions. In order

to adapt the model to complex conditions, it would be necessary to somehow adjust the

expected average queue per cycle in response to numerous factors (permitted left-turns,

spillback, etc.).


gs = Start-up Lost Time +
(#veh Headway)
= 2 + (4* 2) = 10 sec.


ge = 3 sec.
Phase Time = gs + ge + Y + R
= 10+3+2+0
= 15 sec.





Uniform Arrival Rate = 1 vehicle / 7.2 sec.





Figure 3-9: Calculating Queue Service Times with the Uniform Arrivals Assumption



The uniform arrivals prototype model may provide a good reference point during

the testing process, and could be relatively effective at isolated intersections, where

conditions tend to be less complicated. Practical advantages include better computing

speed and easy programming, since it is not necessary to obtain queue or flow profile

data from the optimization program.







Preliminary Model Comparison

Thorough testing of all candidate models is documented in chapter 4. For the

sake of understanding the two prototype models for computing green extension times,

some preliminary comparison is useful.

Model comparison under platooned arrivals

Recall that the sample calculations for the first prototype model involved an

actuated, major street left-turn phase having platooned vehicle arrivals due to a nearby

upstream signal. The traffic volume was 200 vph with a gap setting of 3 seconds. The

first prototype model had predicted green extension times of 5.1 and 3.4 seconds,

depending on the offsets and progression on the arterial street. Under these conditions,

the second prototype model would calculate a green extension time based on one vehicle

arrival every 18 seconds, and a one in six chance of an arrival during the gap interval:


g, = (0.17 x 11.5 x3)+(0.83 x3)= 3.25 seconds


Note that this green extension time would be applicable in both sample

calculations because the second prototype model does not take progression effects into

account. In addition, regardless of progression effects, the NCHRP model computes a

single green extension time (4.6 seconds), as does Husch's Poisson probability model (3

seconds). Depending on the duration of the queue service time, differences in predicted

phase times will not necessarily be equal to the differences in green extension times.

This will be illustrated by a larger set of results in chapter 4.







Model comparison under uniform arrivals

Another interesting comparison between the prototype green extension time

models occurs on external links with no nearby upstream signal. On these links, vehicle

arrivals tend to be nearly uniform in nature, or perhaps random arrivals with uniform

inter-arrival times on average. In theory, the first prototype model should be able to

calculate good results under this scenario because uniform arrivals are simply another

variation on the flow profile. Certainly the second prototype model, designed with

uniform arrivals in mind, would be expected to calculate relatively accurate green

extension times on external links, where vehicle arrivals are known to be close to uniform

in nature.

Suppose the green extension time must be calculated on an external link having

500 vehicles per hour, with a gap setting of 3 seconds. Figure 3-10 illustrates the uniform

flow profile, and table 3-3 lists all calculations from the first prototype model. In this

case the calculated green extension time is 4.5 seconds, because queue service time ends

at step 12 and gap-out occurs at step 16.5. Once again, substitution of uniform

probabilities in place of Poisson probabilities of zero arrivals at step would only change

the final answer by one tenth of a second.

Although the first prototype model calculates a green extension time of 4.5

seconds, the NCHRP model and Husch's Poisson probability model calculate 6.1 and 3

seconds respectively for the same conditions. Since the 500 vph volume generates one

arrival every 7.2 seconds, a 3-second gap results in a 3/7.2= 0.42 chance of phase

extension, the second prototype model computes:


g, = (0.42 x 1.5 x 3)+(0.58 x 3)= 3.63 seconds



































Figure 3-10: Sample Calculation External Link Flow Profile (Abbreviated)



Preliminary model comparison summary

The differences in results from the two prototype models, given uniform arrivals,

indicate that the first prototype model may be overestimating green extension times.

However, results from the NCHRP model indicate the opposite. In the absence of

additional test results, the only observation to be made on the first prototype model at this

time is that it responds appropriately to maximum green and progression effects. More

testing results are necessary to determine the accuracy of each candidate model.

Extensive testing results are presented in chapter 4.


600

500 -

> 400

a 300

o 200
u.

100



N_ No (se o nds
Time Step (seconds)








Table 3-3: Calculations of the First Prototype Model Under Uniform Arrivals


P(0,0,0) P(gap)


Time
Step

13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39


Flow Rate
(vph)

500
500
500
500
500
500
500
500
500
500
500
500
500
500
500
500
500
500
500
500
500
500
500
500
500
500
500


P Weighted
cumulative Average


P(0)


0.87
0.87
0.87
0.87
0.87
0.87
0.87
0.87
0.87
0.87
0.87
0.87
0.87
0.87
0.87
0.87
0.87
0.87
0.87
0.87
0.87
0.87
0.87
0.87
0.87
0.87
0.87


0.66


0.66


0.66


0.66


0.66


0.66


0.66


0.66


0.66


Model Implementation




Isolated Versus Coordinated Operation

Control type (isolated vs. coordinated) is expected to have a fundamental effect

on actuated phase time results. The top half of figure 3-11 illustrates the phasing

diagrams under coordinated conditions. Diagram #1 illustrates typical operation under


0.66


0.224


0.076


0.026


0.009


0.003


0.001


0.000


0.000


9.900


4.035


1.604


0.625


0.239


0.091


0.034


0.013


16.540


0.88


0.96


0.99


1.00


1.00


1.00


1.00


0.00







the conditions from the first part of experiment #1. Suppose that a certain parameter,

such as detector length, free flow speed, or vehicle length, has its value increased such

that green extension time would tend to respond by increasing as well (diagram #2).

Although this change by itself would tend to increase the average phase time, a feedback

effect exists that reduces the upcoming queue service time. This is because the effective

red time for phase #1 is equal to the length of phase #2. When the length of phase #2 is

reduced, this reduces the effective red time for phase #1, thus reducing the subsequent

queue and queue service time for phase #1 (diagram #3).

The bottom half of figure 3-11 illustrates the phasing diagrams under isolated

conditions. Diagram #1 illustrates typical operation under the conditions from the first

part of experiment #1. Suppose that a certain parameter, such as detector length, free

flow speed, or vehicle length, has its value increased such that green extension time

would tend to respond by increasing as well (diagram #2). This change tends to increase

not only the length of phase #1, but also the effective red time imposed on actuated phase

#2. This in turn increases not only the queue, queue service time, and length of phase #2,

but also the effective red time imposed on actuated phase #1 (diagram #3). At first

glance this appears to be an infinite loop, but as described in chapter 2, this process

converges reliably to a new actuated cycle length.

These results for isolated conditions are expected and documented in chapter 2

and the HCM guidelines. However, the results for coordinated conditions are interesting.

They imply that certain parameters (e.g. detector length, approach speed, vehicle length,

maximum green) which when increased would normally tend to increase the green

extension time, perhaps do not significantly increase the phase time due to the queue







COORDINATED:


< Cycle Length>
< Phase #1 > < Phase #2-


#1 1


Ge Y+R


< Phase #1 > < Phase #2-


I I


Gs Ge Y+R


< Phase #1 > < Phase #2-


I s e Y+R
Gs Ge Y+R


ISOLATED:



<- Phase #1 ----Phase #2 -->
#1
Gs Ge Y+R Gs Ge Y+R

< Cycle Length
-< Phase #1--- --- Phase #2 --

#2 I I 1 i I
Gs Ge Y+R Gs Ge Y+R

"< --Cycle Length
<--- Phase #1 < Phase #2 --

#3 I I
Gs Ge Y+R Gs Ge Y+R


Figure 3-11: Feedback Effects under Coordinated and Isolated Conditions


#2





#3


I







service time feedback effect. This begs the question of whether some parameters affect

the phase time at all. Do the queue service time and green extension time merely

redistribute themselves such that the phase time is unmovable, or do phase time shifts

occur anyway? This could be important because if certain parameters do not affect phase

time, this simplifies the problem considerably and allows for shortcuts to be taken in

modeling. Testing results related to this concept are discussed later on in chapter 4.

To summarize, fundamental differences in the actuated phase times are expected

when comparing results under different signal control types (coordinated vs. isolated).

These differences are likely caused by the queue service time green extension time

feedback effect. In the context of TRANSYT-7F and coordinated signal systems, correct

understanding and modeling of coordination behavior is a higher priority. However,

important analyses are performed on isolated intersections also. Proper understanding

and modeling of these conditions is also useful.

Early Return to Green Effects

One of the first things observed when looking at preliminary results on arterial

street performance was that some of the oversaturated actuated phase lengths were being

underestimated by the TRANSYT-7F candidate models, relative to CORSIM. Figure 3-

12 illustrates the pitfall that was occurring. CORSIM was showing that unused green

time from the first actuated phase #1 was being taken by oversaturated phase #2.

However, allocation of unused green time was originally been performed according to the

NCHRP procedure, described in chapter 2, which specifies that all unused green time will

be donated to the non-actuated phase under coordinated conditions.








ACT ACT ACT NAP
Phase #1 Phase #2 Phase #3 Phase #4

.. ... .. .. .
Incorrect
10 30 15 50


10 35 15 40 Correct




ACT = Actuated Phase
NAP = Non-Actuated Phase



Figure 3-12: Allocation of Unused Green Time under Coordinated Conditions


Before any significant testing was performed on arterial streets, the experimental

version of TRANSYT-7F was redesigned such that oversaturated actuated phases would

be able to take unused green time from prior actuated phases if necessary. Note that this

means actuated phase #1 from figure 3-12 is not able to take unused green time from the

other actuated phases because they occur later on in the cycle. If no oversaturated

actuated phase occurs following an undersaturated actuated phase, unused green time will

be utilized by the non-actuated phase.

Overlap Phasing Effects

The next obvious problem observed when looking at preliminary results on

arterial street performance was that some of the undersaturated actuated phase lengths

were being overestimated by the TRANSYT-7F candidate models. This was occurring







due to a consistent, incorrect determination of the "critical link" within actuated phases.

What is a critical link?

In experiment #1 only one link was moving during each phase. However, under

complex conditions, there will be multiple links moving in each phase. When this

happens, the basic strategy of an actuated controller dictates that the right-of-way should

be terminated after all queues have been served on all links. Therefore, the overall phase

should be terminated after the longest queue has been served, or rather after the queue

that takes the longest time to dissipate has been served. The link that happens to possess

relatively heavy traffic, resulting in a queue that takes the longest time to dissipate, is

known as the critical link.

Figure 3-13 illustrates a hypothetical phase sequence where multiple links are

moving on each phase. If the hourly traffic volume demand on each link is known, then

normally the link having the highest volume during each phase would be critical and

affect phase termination. For example, the link having 300 vph will affect when phase #1

terminates, the link having 500 vph will affect when phase #2 terminates, etc.

It may take more than knowledge of the traffic volume in order to determine the

true critical link. Suppose the 500 vph link in phase #2 actually has two lanes to use,

unlike the 400 vph link that only has one lane to use. This means the queues on the 500

vph link will dissipate twice as quickly, behaving almost like two 250 vph lanes, and the

400 vph link will then have the longest queues on average and tend to affect phase

termination.










ACT ACT ACT NAP

300 vph 500 vph







200 vph 400 vph

Phase #1 Phase #2 Phase #3 Phase #4



Figure 3-13: Sample Problem for Determination of Critical Link



In addition to number of lanes, there are numerous field conditions that can slow

down or speed up queue service time, including vertical grade, lane width, heavy vehicle

percentage, percentage of turns from a shared lane, and parking or bus maneuvers, just to

name a few. The effect of these field conditions is quantified by the saturation flow rate

(s) parameter.

The flow ratio (v/s) can be used to quantify the combined affect of volume and

saturation flow rate. This becomes a better quantity to use than volume in determining

the critical link because the queue service rate is taken into account Thus, in the early

stages of data collection for arterial streets, flow ratio was used to determine the critical

links. Unfortunately, critical link determination using this parameter can be shown to be

inadequate due to the overlap phasing effects frequently observed at actuated signals, as

illustrated in figure 3-14.









ACT ACT ACT NAP

300 vph 500 vph







200 vph 400 vph

Phase #1 Phase #2 Phase #3 Phase #4



Figure 3-14: Sample Determination of Critical Link with Overlap Phasing Effects



Figure 3-14 shows that the 200 vph actuated left-turn phase terminates earlier than

the 300 vph left-turn phase. This means that the 500 vph through movement link, which

is adjacent to the 300 vph left-turn link, gets a head start and begins to move earlier

(phase #2) than the opposing 400 vph through movement link. Assuming these links

have the same saturation flow rate, this means that even though the 500 vph link has the

highest flow ratio (v/s), its queue doesn't necessarily take longer (than the 400 vph link)

to dissipate because its vehicles begin moving earlier in the cycle. If flow ratio was the

only technique available for determining critical link, the non-critical link would

sometimes be chosen as critical by the candidate models, resulting in underestimated

phase times.

Because of the overlap phasing effects, the only way to really know which link is

critical and will extend the phase is to apply the candidate models to each candidate link




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