DEVELOPMENT OF A TRAFFIC-ACTUATED
SIGNAL TIMING PREDICTION MODEL
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENT FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
UNIVERSITY OF FLORIDA LIBRARIES
This dissertation cannot be accomplished without the assistance of many people. I
wish to express my sincerest thanks to my supervisory committee, dear friends and lovely
family who helped make it possible.
First, I would like to express my extreme gratitude to professor Kenneth G. Courage,
chairman of my supervisory committee, for giving me the opportunity to pursue my graduate
studies under his enthusiastic guidance. He not only provided me the financial assistance but
also gave me many levels of support. Every time when I face any difficulty in research, he has
always inspired me with his ingenious idea. His lofty standard has always been a source of
motivation to me. I will never forget what he has done for me during my studies.
Dr. Charles E. Wallace is the Director of Transportation Research Center. Under his
leadership, I felt very warm in my mind when I was in this big family. Although Dr. Wallace
was very busy, he always made time for me. He has provided his professional guidance to
my research and lofty standard to my dissertation. I deeply believe his comments on my
dissertation will be beneficial for my professional career. For this, I am eternally grateful.
Dr. Joseph A Wattleworth served as one of my committee member. Although he has
been retired, his assistance and personal support are sincerely appreciated.
Dr. Sherman X. Bai has been a source of inspiration and motivation. His technical
support and personal caring were really invaluable to the success of this research. He has
helped me far more than being a member of the committee. He has become a good friend of
me. I want to thank him for his professional support and true friendship.
Dr. Mang Tia served as one of my supervisory committee member after Dr. Joseph
A Wattleworth retired. His assistance in this matter is really appreciated. Without his help,
the requirement for my dissertation cannot be completed.
Dr. Anne Wyatt-Brown served as the outside member. She has been of great help
with her assistance on the improvement of my technical writing. In addition, her patient
instruction, sincere encouragement are highly appreciated.
I am indebted to Dr. Gary Long for his guidance and encouragement during my
studies although he is not on my supervisory committee. Special thanks go to William M.
Sampson, manager of McTrans Center, and Janet D. Degner, Manager of Technology
Transfer Center, for providing me financial assistance and the personal supports.
I would also like to express my gratitude to my colleagues for their assistance. I like
to thank Shiow-Min Lin, Yu-Jeh Cheng, Cheng-Tin Gan, Jer-Wei Wu, Min-Tang Li, Chian-
Chi Jiang and Randy Showers for their encouragements. I also like to extend my thanks to
David Allen, David Hale, Jim Harriott and James Kreminski for their proofreading.
Finally, I want to express my deep appreciation to my family. My parents, Chang-
Lang Lin and Li-Chen Hsu, continually supply me their unwavering love, sincere inspiration
and selfless support throughout my life. My brother, Pei-Yi Lin, and my sister, Li-Ling Lin,
continually give me their encouragements and supports. My wife and best friend, Hui-Min
Wen, is willing to share every good time and bad mood with me. Her patience and love give
me the warmest feeling and the best support to complete my research.
TABLE OF CONTENTS
LIST OF TABLES
LIST OF FIGURES ......
CHAPTER 1. INTRODUCTION .
Problem Statement. .
CHAPTER 2. BACKGROUND .
Literature Review ..
Preliminary Model Development
Simulation Models .
Arterial Considerations .
CHAPTER 3. MODEL DEVELOPMENT
Determination of Arrival Rates
Permitted Left Turn Phasing
Compound Left Turn Protection
CHAPTER 4. MODEL IMPLEMENTATION
Structure and Logic of the ACT3-48 Program .
Extension of the Development of Coordinated Operations .
CHAPTER 5. MODEL TESTING AND EVALUATION .
Fully-actuated Operation .
Coordinated Actuated Operation .
Further Evaluation of the Analytical Model .
CHAPTER 6. EXTENDED REFINEMENT OF THE ANALYTICAL MODEL
Refinement of the Analytical Model for Volume-density Operation
Refinement of the Analytical Model to Incorporate "Free Queue" Parameter
Incorporation of the Analytical Model into the HCM Chapter 9 Procedure .
CHAPTER 7. CONCLUSIONS AND RECOMMENDATIONS .
UNIFORM DELAY FORMULAS .
BIOGRAPHICAL SKETCH .
LIST OF TABLES
2-1 The iteration results and its convergence for the illustrated example.
6-1 Through-car equivalents, EL, for permitted left turns in a shared lane
with one free queue. .......
6-2 Through-car equivalents, EL1, for permitted left turns in a shared lane
with two free queues .. ......
LIST OF FIGURES
2-1 The operation of an actuated phase under significant demand .35
2-2 Dual-ring concurrent phasing scheme with assigned movements 38
2-3 The relationship among the components in the phase time .39
2-4 Queue accumulation polygon for a single protected phase .. 42
2-5 The intersection used as an example for circular dependency illustration 50
2-6 Queue accumulation polygon in the first iteration of the illustrated example .51
2-7 Iterative loops in the phase time and cycle time computation procedure 53
2-8 Phase time comparison between EVIPAS and NETSIM 56
2-9 Conceptual relationship between major street g/C and minor street demand .58
2-10 The location of studied intersection .. 59
2-11 Prediction of the major street g/C ratio based on a power model for minor
street traffic volume. ....... .61
2-12 Prediction of the major street g/C ratio based on a logarithmic model for minor
street detector occupancy .. 62
3-1 Arrival rate over a full cycle with coordinated operation 64
3-2 Queue accumulation for a single protected phase 67
3-3 Queue accumulation polygon for a permitted left turn from an exclusive lane
with opposing lane number greater than one 69
3-4 Queue accumulation polygon for a permitted left turn from an exclusive lane
with opposing lane number equal to one .. 70
3-5 Queue accumulation polygon for a permitted left turn from an exclusive lane
with sneakers .72
3-6 Queue accumulation polygon for a permitted left turn from a shared lane
(g g ). .75
3-7 Queue accumulation polygon for a permitted left turn from a shared lane
3-8 Queue Accumulation polygon for protected plus permitted LT phasing with
an exclusive LT Lane ........77
3-9 Queue Accumulation polygon for permitted plus protected LT phasing with
an exclusive LT Lane 78
4-1 Major structure of the ACT3-48 program .. 82
4-2 Case 1: Phase sequence for simple permitted turns .. 83
4-3 Case 2: Phase sequence for leading green .. 84
4-4 Case 3: Phase sequence for lagging green .. 84
4-5 Case 4: Phase sequence for leading and lagging green .. 84
4-6 Case 5: Phase sequence for LT phasing with leading green 85
4-7 Case 6: Phase sequence for leading dual left turns 85
4-8 Case 7: Phase sequence for lagging dual left turns .. 85
4-9 Case 8: Phase sequence for leading and lagging with dual left turns .. .86
5-1 Cycle length comparison for a 1.5-sec allowable gap setting 96
5-2 Cycle length comparison for a 3.0-sec allowable gap setting 97
5-3 Cycle length comparison for a 4.5-sec allowable gap setting 97
5-4 Composite cycle length computations with all gap settings .. 98
5-5 Percent of phase terminated by maximum green time for each gap setting .99
5-6 Phase time comparison between the Appendix H method and NETSIM. .101
5-7 Phase time comparison between the proposed model and NETSIM 101
5-8 Intersection configuration of Museum Road and North-south Drive on the
campus of the University of Florida 102
5-9 Phase time comparison between the analytical model and field data 104
5-10 Phase time comparison between NETSIM and field data 104
5-11 Phase time comparison between arterial street and cross street 106
5-12 Relationship of estimated phase times between NONACT and NETSIM 108
5-13 NETSIM arrival distributions for a single-link of 100-ft length 111
5-14 NETSIM arrival distributions for a single-link of 1000-ft length 111
5-15 NETSIM arrival distributions for a single-link of 2000-ft length 112
5-16 NETSIM arrival distributions for a single-link of 3000-ft length 112
5-17 Comparison of analytical and simulation model arrival distribution for
single-lane, 100-vph flow 114
5-18 Comparison of analytical and simulation model arrival distribution for
single-lane, 300-vph flow 114
5-19 Comparison of analytical and simulation model arrival distribution for
single-lane, 500-vph flow 115
5-20 Comparison of analytical and simulation model arrival distribution for
single-lane, 700-vph flow 115
5-21 Comparison of analytical and simulation model arrival distribution for
single-lane, 900-vph flow 116
5-22 Optimal NETSIM single-lane link length for various phase termination
headway settings 116
5-23 Comparison of analytical and simulation model arrival distributions for
two-lane, 200-vph flow 118
5-24 Comparison of analytical and simulation model arrival distributions for
two-lane, 600-vph flow 118
5-25 Comparison of analytical and simulation model arrival distributions for
two-lane, 1000-vph flow 119
5-26 Comparison of analytical and simulation model arrival distributions for
two-lane, 1800-vph flow 119
6-1 Variable initial feature for volume-density operation 124
6-2 Gap reduction feature for volume-density operation 125
6-3 Phase time comparison for volume-density operation with a zero detector
6-4 Phase time comparison for volume-density operation with a 150-ft detector
6-5 Phase time comparison for volume-density operation with a 300-ft detector
6-6 Phase prediction for single shared lane with free queues 142
A-i Uniform delay formula for ingle protected phase 154
A-2 Uniform delay for permitted left turns from an exclusive lane (n >1) 155
A-3 Uniform delay for permitted left turns from an exclusive lane (n,=1) .156
A-4 Uniform delay for permitted left turns from a shared lane (gq>gf) 157
A-5 Uniform delay for permitted left turns from a shared lane (gg,) 158
A-6 Uniform delay for compound left turn protection: HCM Chapter 9 Case 1 .159
A-7 Uniform delay for compound left turn protection: HCM Chapter 9 Case 2 160
A-8 Uniform delay for compound left turn protection: HCM Chapter 9 Case 3 .161
A-9 Uniform delay for compound left turn protection: HCM Chapter 9 Case 4 .162
A-10 Uniform delay for compound left turn protection: HCM Chapter 9 Case 5 163
Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
DEVELOPMENT OF A TRAFFIC-ACTUATED
SIGNAL TIMING PREDICTION MODEL
Chairman: Kenneth G. Courage
Major Department: Civil Engineering
The Highway Capacity Manual (HCM) provides a methodology in Chapter 9 to
estimate the capacity and level of service at a signalized intersection as a function of the traffic
characteristics and the signal timing. At traffic-actuated intersections, the signal timing
changes from cycle to cycle in response to traffic demand. An accurate prediction of average
phase times and cycle length is required to assess the performance of intersections controlled
by traffic-actuated signals. The current technique in Appendix II of HCM Chapter 9 for this
purpose has not been well accepted.
This dissertation describes a more comprehensive methodology and a more
satisfactory analytical model to predict traffic-actuated signal timing for both isolated and
coordinated modes. The proposed methodology and model have been verified by simulation
augmented by limited field studies. The results are very encouraging with respect to their
general reliability and their compatibility with the current HCM Chapter 9 structure. The
techniques developed in this study would provide an important contribution to the
methodology of traffic engineering for traffic-actuated signal timing prediction and improve
the analytical treatment of traffic-actuated control in the HCM Chapter 9.
The concepts of capacity and level of service (LOS) are central to the analysis of a
signalized intersection. Level of service is expressed as a letter grade from A through F that
describes the quality ofperformance of a signalized intersection from the driver's perspective.
It is evaluated based on the average stopped delay per vehicle for various movements within
the intersection. The 1985 Highway Capacity Manual (HCM)  prescribes a methodology
in Chapter 9 (Signalized Intersections) to estimate the LOS as a function of the traffic
characteristics and the signal timing.
Intersection traffic control is characterized as "pretimed" if a predetermined timing
plan is repeated cyclically or "traffic-actuated" if the operation varies from cycle to cycle in
response to information from traffic detectors on the roadway. Pretimed control is usually
appropriate for constant traffic demand, while traffic-actuated control is better suited to
variable traffic demand. Pretimed control is much easier to analyze, but traffic-actuated
control offers more in the way of performance to the motorist.
Whether an isolated actuated controlled intersection or a set of coordinated actuated
intersections, the operational performance largely depends on traffic patterns and the actuated
controller parameters to be discussed in this dissertation. A well-designed actuated control
plan that responds appropriately to traffic demand can significantly reduce delay and fuel
consumption. More advanced forms of adaptive traffic control strategies were introduced
recently, but the traffic-actuated control concepts still play a very important role today.
Because of its superiority, traffic-actuated control has become the predominant mode
throughout the U.S.A. in spite of its analytical complexity.
Many traffic-related measures at a signalized intersection, such as intersection
capacity, vehicle delay and queue length, are determined by the phase times and cycle length.
For traffic-actuated control, the phase times and corresponding cycle length vary from cycle
to cycle in response to the traffic demand. Therefore, it becomes desirable to predict the
average phase times and cycle length for traffic-actuated control which are the main inputs
in the procedure contained in the HCM Chapter 9 for the computation of intersection capacity
and vehicle delay.
Improvement of the analytical treatment of traffic-actuated control presented in the
HCM Chapter 9 is the subject of this dissertation. An enhanced analytical model will be
proposed and tested.
Capacity and delay are two major measures of effectiveness for the analysis of a
signalized intersection. The procedure contained in Chapter 9 of the HCM is used almost as
a standard to estimate the intersection capacity and vehicle delay. For traffic-actuated
operation, accurate estimates of intersection capacity and vehicle delay must rely on accurate
estimates of the signal timing. However, the primary technique, presented in an appendix to
HCM Chapter 9, to predict the signal timing for traffic-actuated operation has been the
subject of much criticism in the literature [2, 3, 4, 5, 6].
This technique is based on the simple assumption that a traffic-actuated controller will
maintain a high degree of saturation (95% in the HCM Chapter 9 procedure) on the critical
approach to each phase. It does not consider any controller parameter that influences the
signal timing in field. This has created many questions in the literature regarding the validity
of the assumption and the simplistic nature of the technique. Therefore, the main deficiency
of the technique in the appendix to HCM Chapter 9 comes from improper analytical treatment
of traffic-actuated control
Some analytical work has been done on estimating individual phase lengths for traffic-
actuated operation [2, 6, 7, 8, 9, 10], but a method for treating the entire phase sequence,
given a specified set of traffic volumes, controller parameters and detector placements, does
not exist. Simulation is currently the most reliable method for determining the signal timing.
Simulation is a powerful tool, but its application is best suited to situations that do not lend
themselves to analytical treatment. Furthermore, the signal timing prediction based on
simulation is time consuming.
Therefore, the development of a practical analytical technique to predict traffic-
actuated signal timing is very desirable. Such a technique would provide an important
contribution to the methodology of traffic engineering and improve the analytical treatment
oftraffic-actuated control in the HCM Chapter 9.
In this case, there are three major questions with the development of the traffic-
actuated signal timing prediction model The first question is whether the model can improve
the analytical treatment oftraffic-actuated control in the HCM Chapter 9 procedure on signal
timing prediction. The proposed methodology must be in a form that can be incorporated
into the HCM Chapter 9 procedure. The second one is whether the model can treat the entire
phase sequence for a specified set of traffic volumes, actuated controller parameters,
intersection configuration and detector placements. The third question is whether the model
can accurately and quickly predict the signal timing for traffic-actuated operation.
The signal timing of a traffic-actuated signal will vary from cycle to cycle in response
to traffic demand. The goal of this research is to develop an analytical model to accurately
predict the average signal timing for traffic-actuated intersection for both isolated and
coordinated modes. Although performance measures (delay, stops, queue length, fuel
consumption, etc.) are sensitive to actuated controller parameters, it is necessary to note that
this study does not include the development of an optimization methodology of the actuated
controller parameters. The specific objectives of the research are stated as follows:
1. Review the literature that deals with the subject of traffic-actuated control,
particularly related to signal timing prediction and vehicle delay estimation.
2. Develop a model to improve the analytical treatment of traffic-actuated control
in the HCM Chapter 9 on signal timing prediction and present the methodology
in a form that may be incorporated into the HCM Chapter 9 procedure.
3. Assure that the developed analytical model can predict the average phase times
and corresponding cycle length for a specified set of traffic volumes, controller
settings, intersection configuration and detector placements.
4. Test and evaluate the analytical model using simulation and limited field data to
assess its accuracy and feasibility of implementation.
This dissertation includes seven chapters that are devoted to developing an analytical
model to predict the signal timing for traffic-actuated control The first chapter provides a
general introduction to the dissertation topic, problem statement and research objectives.
The next two chapters describe the development of the proposed analytical model
Chapter 2 presents the background knowledge required for the analytical model development
and a preliminary model that deals with protected movements from exclusive lanes only.
Chapter 3 extends the methodology developed in Chapter 2 to include shared lanes, permitted
left turns and compound left turn protections (permitted plus protected phasing and protected
plus permitted phasing).
The implementation of the proposed analytical model and procedure in a computer
program to predict traffic-actuated signal timing is addressed in Chapter 4. The
computational process of this program is also presented.
The comparisons of predicted phase times between the proposed analytical model and
simulation and field data are presented in Chapter 5. An intensive evaluation is also made on
the comparison of vehicular arrivals at the stopline produced by simulation and the proposed
Chapter 6 presents several refinements of the proposed analytical model to achieve
a stronger capability on the phase time prediction. Uniform delay formulations developed in
this study for traffic-actuated control are shown in the appendix. The final conclusions and
recommendations are stated in Chapter 7.
There has been a substantial amount of research conducted on traffic-actuated control
which provides essential information for traffic-actuated operating characteristics and signal
timing prediction. This chapter first reviews past and current research on the traffic-actuated
control followed by the presentation of a preliminary model structure of phase time prediction
for fully-actuated operation. Each traffic control concept or theory that has contributed to
the model development is addressed separately. Next, two simulation models, TRAF-
NETSIM (NETSIM) and EVIPAS, which have been adopted by this study as evaluation tools
for the proposed analytical model, are introduced. Finally, a preliminary consideration of
signal timing prediction for semi-actuated traffic signal coordination is described. Further
model development and implementation for traffic-actuated signal timing prediction will be
mostly based on the background knowledge presented in this chapter.
Traffic-actuated control has been used since in the early 1930s. Whether an isolated
actuated controlled intersection or a set of coordinated actuated intersections, the operational
performance is largely determined by the traffic arrival patterns and actuated controller
parameters. The arrival patterns refers to the arrival headway distributions. The basic
actuated controller parameters include the minimum green time, maximum green time and
allowable gap settings (vehicle interval or unit extension). A well-designed actuated control
plan that responds appropriately to traffic demand can significantly reduce delay and fuel
consumption. Therefore, shortly after actuated signal control was first introduced,
researchers began to study the influence of traffic arrival patterns and departure characteristics
at a signalized intersection with traffic-actuated control Many researchers also focused on
the optimization of controller settings, detector placement, and the relationship among them.
Recently, some researchers began to develop models to predict traffic-actuated signal timing
for the purpose of more accurate capacity computation and delay estimation.
Review of past and current research is an area which definitely merits attention. There
has been a substantial amount of research conducted on traffic-actuated control which will
contribute to this dissertation.
The development of a traffic-actuated signal timing prediction model is the subject of
this study. Thus, the major emphasis ofthis literature review is on the traffic-actuated control
that particularly is related to operation characteristics, vehicle arrival headway distributions
and signal timing prediction models. The procedure contained in the HCM Chapter 9 is used
almost as a standard to analyze signalized intersection capacity and level of service, so the
literature review also covers the methodology for both capacity computation and delay
estimation. One item that needs to be reviewed carefully is a new program called EVIPAS.
The EVIPAS model is an optimization program which is able to analyze and determine the
optimal settings of controller parameters for traffic-actuated control The results of the
testing efforts on EVIPAS are report in this chapter.
The main topics of the literature review include
Traffic-actuated control definitions;
Warrants for traffic-actuated control;
Benefits and operating considerations for traffic-actuated control;
Effects of coordination and phase-skipping for traffic-actuated control;
Late-night, low-volume operation of coordinated actuated systems;
Evaluation of traffic-actuated control by simulation;
Prediction of phase times and cycle length for traffic-actuated control;
Delay models for traffic-actuated control;
Signalized intersection capacity models for traffic-actuated control; and
Overview and evaluation of "Enhancement of the Value Iteration Program for
Actuated Signals" (EVIPAS).
Traffic-actuated Control Definitions
Three basic forms oftraffic control: pretimed, fully-actuated and semi-actuated were
mentioned by Orcutt  in 1975. He indicated that pretimed control was used primarily in
the Central Business District (CBD) area, especially where a network of signals must be
coordinated. He defined actuated signals in terms of equipment that responds to actual traffic
demand of one or more movements as registered by detectors. If all movements are detected,
the operation is referred to as "fully-actuated." If detectors are installed for some, but not all,
traffic movements, the term "semi-actuated" is applied. Orcutt suggested fully-actuated
control should normally be used at isolated intersections.
Precise definitions of the basic controller types were described by the National
Electrical Manufacturers Association (NEMA) standards  in 1976. According to the
NEMA standards, the basic controllers include pretimed, semi-actuated, fuly-actuated
without volume-density features, and fully-actuated with volume-density features. In the
remainder of this dissertation, fully-actuated without volume-density features will be just
called fully-actuated control, and fully-actuated with volume-density features will be called
Warrants for Traffic-actuated Control
Warrants for selecting traffic control modes, which are very useful for practicing
engineers, have been researched since the early 1960s. Studies of delay at actuated signals
have been made for the purpose of evaluating warrants for this type of control on the basis
of the information in the 1961 edition of the Manual on Uniform Traffic Control Devices
(MUTCD). This information was expanded by the Texas Department of Highways and
Public Transportation into a graphical format. The graphical relationships were studied in
1971 by Vodrazka, Lee and Haenel , who concluded that they provide good guidelines
for selecting actuated equipment for locations where traffic volumes do not warrant pretimed
signals. The current edition of the MUTCD stops short of numerical warrants for choosing
between pretimed and traffic-actuated control, but it does suggest certain qualitative
conditions under which traffic-actuated control should be implemented.
Benefits and Operating Considerations for Traffic-actuated Control
In 1967, Gerlough and Wagner  began to compare pretimed control effectiveness
with volume-density control. They found that traffic-actuated control at higher traffic
volumes degraded performance. One of the problems cited for volume-density control was
that the duration of green for each phase was dependent on the estimated queue length at the
beginning of the phase. Difficulties with queue length estimation made this type of control
Long-loop presence detection operates by producing a vehicle call for the duration
of time that the vehicle is over the detector. This is as opposed to the mode of small-area
detector operation in which the detector outputs a pulse of less than 0.1 seconds when the
vehicle is first detected. This latter mode of operation is known as passage, pulse or count
detection. The long-loop presence detector with fully-actuated controllers in a mode known
as lane-occupancy control or loop-occupancy control (LOC). LOC operation occurs when
the controller is programmed for an initial green interval of zero. Extensions are set either
to zero or to a very low value. There is no need for a non-zero initial interval or minimum
green time because the long loops continuously register the presence of any vehicles that are
waiting, causing the controller to extend the green until the entire queue is discharged. The
result is a signal operation that responds rapidly to changes in traffic flow.
In 1970, Bang and Nilsson  compared LOC operation with small area detector
(pulse detector) operation. They concluded that delay was reduced 10 percent and stops by
6 percent under the same traffic conditions with LOC. In 1975, Cribbins and Meyer 
compared pulse and presence detectors. They concluded that the longer the length of the
presence detector on the major approach to the intersection, the longer the delay. They also
concluded that the highest intersection travel time values occurred when either long-loop
presence or pulse detectors were used on both major and minor approaches. The intersection
travel time was defined here as the average time it takes a vehicle to pass through an
intersection, whether it is stopped or slowed.
Numerous theoretical studies on traffic signal timing were conducted between 1958
and 1970. The theoretical work on pretimed control by Webster  in 1958 and Miller 
in 1963 has been applied to the computation of optimum cycle lengths as a function of vehicle
arrival rates. It has also been used for evaluating vehicle delay, intersection capacity,
probability of stops and so on. These results were also well validated through the comparison
of field data. In 1969, Newell  and Newell and Osuma  expanded the body of theory
by developing relationships for mean vehicle delay with both pretimed and actuated control
at intersections of one-way streets and intersections of two-way streets, respectively. Newell
 demonstrated that the average delay per vehicle for an actuated signal is less than that
of a pretimed signal by a factor of about three for intersections of one-way streets. Osuma
 considered intersections oftwo-way streets without turning vehicles. For the particular
traffic-actuated policy which holds the green until the queue has been discharged, the traffic-
actuated control will not perform as well as pretimed control under the following two
conditions: 1) flows are nearly equal on both approaches of a given phase and 2) the
intersection is nearly saturated.
In 1976, Staunton  summarized the work of numerous signal control researchers.
In his paper, the comparisons of delay produced by pretimed control and actuated control,
as a function of vehicle volumes, were presented. Staunton demonstrated that fully-actuated
control with 2.5-sec extensions will always be better than the best form of pretimed operation,
given optimum settings for all volumes. Longer values for the extensions can easily degrade
actuated control performance. His conclusions were based on simulation, but the details of
the detector configuration were not specified. In view of the 2.5-sec extension time, short
or passage detectors were probably used in his study. The performance estimates from
Staunton were supported by Bang .
In 1981, Tarnoffand Parsonson  compiled an extensive literature review on the
selection of the most appropriate form of traffic control for an individual intersection. Three
complementary approaches were used to evaluate controller effectiveness: 1) field data
collection using observers to manually measure vehicle volumes, stops and delay; 2)
simulation using the NETSIM model developed by the Federal Highway Administration
(FHWA) to evaluate control system performance; and 3) analytical techniques developed by
the research team and other agencies. The general conclusions from their extensive literature
review were as follows:
1. Pretimed controllers operate most effectively when the shortest possible cycle
length is used subject to the constraints ofproviding adequate intersection capacity
and minimum green times for pedestrians and vehicle clearance intervals.
2. The delay produced by fully-actuated controllers is extremely sensitive to the value
of the extension that is used. In general, shorter extensions reduce vehicle delay.
3. For small area detectors (motion or pulse detectors), at low and moderate volumes
when extensions of two or three seconds are employed, the use of the filly-
actuated controllers will reduce delays and stops over those which can be achieved
using pretimed controllers. When high traffic volumes occur both on the main
street and on the side street causing the controller to extend the green time to the
maximum on all phases, the fully-actuated controller will perform as a pretimed
controller, producing comparable measures of vehicle flow.
4. The relative effectiveness of the various control alternatives depends on the quality
of the signal timing employed. A poorly timed actuated controller will degrade
traffic performance to as great an extent as a poorly timed pretimed controller.
Through the detailed evaluation of controller performance, the conclusions by Taroff
and Parsonson  are described as follows: semi-actuated controllers produce a higher level
of stops and delays for all traffic conditions than either the fully-actuated or pretimed
controllers. However, for side street traffic volumes that are less than 20 percent of main
street volumes, there is an insignificant difference between semi-actuated and fully-actuated
controller effectiveness. Fully-actuated controllers produce significant benefits when used in
an eight-phase and dual-ring configuration over that which would be possible with a four-
phase pretimed controller.
From the simulation results on small area detectors for fully-actuated control, the
location of 150 ft produced a level of performance far superior for a 3-sec vehicle interval to
that of closer detectors for the approach speed of 35 mph. Tarnoff and Parsonson concluded
that it is appropriate to locate the detector such that the travel time is equal to the extension
time. It was also concluded that for volumes in excess of 450 vehicles per hour per lane,
additional improvement can be realized through the use ofthe added initial feature of volume-
density controller for an approach of 35 mph or higher.
They indicated that further modest gains in performance for fully-actuated control
were possible with the use of long loops and short (or zero) initial and extension settings.
This application was found to produce a performance similar to a 2-sec extension time with
a short loop. From the simulation results, they concluded that LOC was more effective than
pulse detection over a wide range of traffic volumes. LOC offered the further advantage not
reflected by the simulation results of screening out false calls caused by vehicles approaching
but not traveling through the intersection.
Volume-density controllers provide the greatest benefit at intersections with high
approach speeds where a detector setback in excess of 125 ft from the intersection requires
a variable initial green time. Tarnoff and Parsonson found that the variable initial and gap
reduction options of the volume-density control did not improve the controller's performance
over that of a filly-actuated controller unless the option is used to reduce the vehicle
extension to a value that is less than the one used for the filly-actuated controller. Thus, if
the volume-density controller is timed to provide a 3-sec passage time and a 2-sec minimum
allowable gap, its performance will be superior to that of a filly-actuated controller with a
constant 3-sec allowable gap. Noted that the above simulation results given by Tarnoffand
Parsonson do not properly account for the problem of premature termination of green due to
the variation in queue discharge headways that occur under normal operating conditions.
In 1985, Lin  studied the optimal timing settings and detector lengths for filly-
actuated signals operating in presence mode using the RAPID simulation model He
suggested the optimal maximum green for hourly flow patterns with a peaking hour factor of
1.0 was about 10 seconds longer than the corresponding optimal greens with a peaking hour
factor of 0.85, and the optimal maximum green was approximately 80 percent longer than the
corresponding optimal greens. This result was similar to the 1.5 times pretimed split
suggested by Kell and Fullerton . Lin indicated that optimal vehicle intervals were a
function of detector length and flow rate. For detectors 30,50 and 80 ft long, the use of 2-
sec, 1-sec and 0-sec vehicle intervals can lead to the best signal performance over a wide
range of operating conditions, respectively. The use of vehicle intervals greater than zero
second for detectors 80 ft or longer is not desirable unless the combined critical flow at an
intersection exceeds 1,400 vph.
In order to improve the VIPAS model, a new optimization algorithm and a new
intersection simulation were designed and programmed. The original VIPAS traffic
characteristics and vehicle generation routines were combined with these new models to
create the enhanced version called EVIPAS. In 1987, Bullen, Hummon, Bryer and Nekmat
 developed EVIPAS, a computer model for the optimal design ofa traffic-actuated signal
The EVIPAS model was designed to analyze and optimize a wide range of intersection,
phasing, and controller characteristics of an isolated, fdlly-actuated traffic signal It can
evaluate almost any phasing combination available in a two to eight-phase NEMA type
controller and similar phasing structures for a Type 170 controller. The model has been field
tested and validated.
In 1987, Messer and Chang  conducted field studies to evaluate four types of
basic fully-actuated signal control systems operating at three diamond interchanges. Two
signal phasing strategies were tested: a) three-phase and b) four-phase with two overlap.
Two small-loop (point) detection patterns (single- and multi-point) were evaluated for each
type ofphasing. They concluded that 1) single-point detection was the most cost-effective
three-phase design; and 2) multi-point detection was the more delay-effective four-phase
configuration. Four-phase control characteristically operates a longer cycle length than the
three-phase for a given traffic volume. This feature may produce higher average delays unless
the cycle increase is controlled to the extent that the internal progression features of four-
phase control can overcome this deficiency.
In 1989, Courage and Luh  developed guidelines for determining the traffic-
actuated signal control parameters which would produce the optimal operation identified by
SOAP84. They also evaluated the existing signal control parameters on an individual traffic-
actuated signal The significant conclusions are summarized as follows:
Under low volumes, the maximum green settings have little or no effect on the
performance of actuated signal controllers. Under moderate volumes, shorter maximum
greens increase the average delay considerably. Longer maximum greens, however, have no
significant effect on delay. Under high volumes, the maximum green settings become more
important. There is a setting which minimizes average delay. Other settings with longer or
shorter maximum greens will produce more average delays. The optimal maximum green
setting can be achieved by running SOAP under actuated control with an optimal saturation
level set in the BEGIN card. They indicated that the settings that are optimal at some time
may not be appropriate in other times of day.
The value of 0.95, which is the default value used in SOAP actuated control, was
suggested for multi-phase operation and a slightly higher saturation level may be desirable for
two-phase operation. For approaches with a reasonably even distribution of traffic volume
by lane, settings of 4.0, 2.0 and 1.4 seconds were recommended by the study for one, two and
three lanes as the best values for unit extension, respectively.
In the same year, Bullen  used the EVIPAS simulation and optimization model
to analyze traffic-actuated traffic signals. The variables studied were detector type, detector
placement, minimum green time and vehicle interval. The evaluation criterion was minimum
average vehicle delay. The study showed that the optimum design of a traffic-actuated signal
was specific for some variables but relatively unaffected by others. The design was critical
only for high traffic volumes. At low volumes, vehicle delay is relatively unaffected by the
design parameters studied in his paper. The most critical variable Bullen found was vehicle
interval, particularly for passage detectors, where it should be at least 4.0 seconds regardless
of detector placement and approach speed. This conclusion somewhat contradicts previous
study results. However, it should be noted that the EVIPAS model used by Bullen considered
variable queue discharge headways.
Detector configuration is essential to the success of actuated control Kell and
Fullerton  in their second edition ofthe Manual of Traffic Signal Design in 1991 indicated
the small area detector might ideally be located three or four seconds of travel time back from
the intersection, with the allowable gap set accordingly. Similar principles were proposed in
previous research by Tarnoffand Parsonson. Kell and Fullerton also indicated that, in some
states, the detectors setback were determined on the safe stopping distance. The main
purpose is to avoid the dilemma zone in which a vehicle can neither pass through the
intersection nor stop before the stopline. For long loop detectors, they indicated the concept
of loop occupancy can provide good operation when vehicle platoons are well formed. The
use of several smaller loops instead of one long loop was suggested to solve the problem of
random vehicles causing excessive green.
In 1993, Bonneson and McCoy  proposed a methodology for evaluating traffic
detector designs. They indicated that the safety and efficiency of a traffic detector design can
be determined by the probability ofmax-out and the amount of time spent waiting for gap-out
and the subsequent phase change. The stopline detector and advance loop detector with
presence and pulse mode were discussed, respectively. The methodology presented by
Bonneson and McCoy determined the optimal combination of design elements in terms of
safety (via infrequent max-out) and operations (via a short waiting time for phase change).
The design elements included detector location, detector length, vehicle speed, passage time
settings, and call extension setting). They concluded a large maximum allowable headway
will have an adverse effect on performance by increasing the max-out probability and the
length of wait for phase change.
Effects of Coordination and Phase Skipping for Traffic-actuated Control
In 1986, Jovanis and Gregor  studied the coordination of actuated arterial traffic
signal systems. In the past, all optimization methods required that each actuated signal be
converted to its nearest equivalent pretimed unit. Using bandwidth maximization as a starting
point, a new procedure was developed by Jovanis and Gregor that specifically accounts for
actuated timing flexibility. Yield points and force offs at non-critical signals are adjusted so
they just touch the edges of the through-band while critical signals are unmodified. This
method was applied to a data set describing midday traffic conditions on an urban arterial
system of six signals in central Illinois. Simulation was used to evaluate these signal timings
and compare them with corresponding pretimed alternatives. They were surprised to find out
that pretimed, coordinated control appeared superior in general to actuated coordinated
control in this experiment. They also concluded that the level of service of side streets was
much more important for pretimed than actuated strategies.
In 1989, Courage and Wallace  developed the guidelines for implementing
computerized timing designs from computer programs such as PASSER I, TRANSYT-7F
and AAP in arterial traffic control systems. The coordination of a group oftraffic-actuated
signals must be provided by some form of supervision which is synchronized to a background
cycle length with splits and offsets superimposed. Both external and internal coordination of
the local controllers were addressed.
This report focused on the external coordination of traffic signal controllers.
Permissive periods were introduced to indicate the time interval following the yield point
during which the controller is allowed to yield to cross street demand. If the computed splits
are longer than the minimum phase times, it might be possible to establish a permissive period
without further sacrifice or compromise on the rest of the sequence. The methodology of
computing permissive periods was introduced. The effect of phase-skipping due to lack of
traffic demand was also presented. The Timing Implementation Method for Actuated
Coordinated Systems (TIMACS) program was developed to perform the computations of
Since most previous studies were more specific to certain geometric and phasing
combinations, the qualitative and quantitative evaluation methodology for coordinated
actuated control needed to be fully investigated. In 1994, Chang and Koothrappally 
designed a field study to demonstrate the operational effectiveness of using coordinated,
actuated control They concluded 1) there was significant improvement, based on both delay
and number of stops, between the semi-actuated control, fully-actuated, and pretimed
coordinated timing during the study; 2) there were no significant differences in performance
among all the semi-actuated operations as long as the progression-based signal coordination
timing was developed correctly; and 3) the use of longer background cycle lengths generally
caused fewer arterial stops. However, it would generate much higher overall system delays.
Late-night, Low-volume Operation of Coordinated Actuated Systems
Coordinating the timing of adjacent signals to promote progressive traffic movement
was recognized as one of the most effective means for reducing vehicular stops, delay, fuel
consumption and exhaust emissions. Early efforts on the subject of signal control always
indicated the need to interconnect signals into a single system and to work toward maimizing
progressive movement during peak periods.
In 1990, Luh and Courage  evaluated the late-night traffic signal control strategies
for arterial systems. They stated that late-night, low-volume arterial signal control involved
a trade-off between the motorists on the artery and those on the cross street. The
conventional measures of effectiveness such as stops, delay, and fuel consumption were not
appropriate for evaluating this trade-off Luh and Courage proposed a methodology to
choose between coordination and free operation on arterial roadways controlled by semi-
actuated signals when traffic is light. The choice was made on the basis of a disutility function
that was a combination of the number of stops on the artery and the average cross-street
waiting time. The results indicated that this method provides a promising tool for late-night
arterial signal control
Evaluation of Traffic-actuated Control by Simulation
Simulation modeling has become an extremely important approach to analyzing
complex systems. After 1980, more and more simulation modeling was used in traffic
operations. In 1984, Lin and Percy  investigated the interactions between queuing
vehicles and detectors for actuated controls, which govern the initiation, extension, and
termination of a green duration. They emphasized that a model used in the simulation analysis
should be calibrated in terms of observed characteristics such as queue discharge headway,
arrival headway, the relationship between the arrival time of a queuing vehicle and the
departure time of its leading vehicle, the number of queuing vehicles in a defined area at the
onset of a green duration, and the dwell time of a vehicle on the detection area. They also
indicated, under a presence control, the chance for premature termination of a green duration
increases when detector lengths are shortened and a detector length of longer than 80 ft can
effectively eliminate the premature termination. Using long detectors, however, results in
longer dwell times and may reduce control efficiency.
Lin and Shen  also indicated that the modeling of the vehicle-detector interactions
should take into account the stochastic aspects of queuing in relation to detectors. The use
of average characteristics of departure headway could result in underestimates or
overestimates of the probabilities of premature termination of the green.
Later, Lin  evaluated the queue dissipation simulation models for analysis of
presence-mode fully-actuated signal control The queue dissipation models used in the
NETSIM program and the VIPAS program were evaluated. He indicated that both models
were capable of producing realistic departures of queuing vehicles from the detector area.
The models were rather weak, however, in representing other aspects of vehicle-detector
interactions. A major weakness of the model in NETSIM was that the simulated movements
of queuing vehicles have little to do with the discharge times generated separately from a
probability distribution. The weakness of VIPAS was that the Pitt car-following model used
in VIPAS did not provide a flexible model structure for calibration. Therefore, the outputs
of the model could not be made to conform easily and simultaneously with observed
departure, arrival and dwell characteristics of queuing vehicles.
In 1988, Chang and Williams  investigated the assumption that independent
vehicle arrivals at traffic signals, such as in the Poisson distribution, have been widely used
for modeling delay at urban intersections. The study introduced an effective yet economic
approach to estimate the degree of correlation among arriving vehicles under given conditions
and geometric characteristics. With the proposed technique, traffic professionals can easily
determine if the existing delay formulas and other traffic simulation models based on the
Poisson distribution are applicable.
The presence of high variability in traffic simulation results often leads to concern
about their reliability, and consequently precludes a rigorous evaluation of the target traffic
system's performance under various control strategies. In 1990, Chang and Kanaan 
presented the variability assessment for NETSIM. The batch-means method, which allows
the user to assess the variability of parameters, such as the average delay per vehicle, through
a single relative long run, was introduced. This study provided a good contribution to traffic
simulation users, given the large expenditures on computer simulation.
Prediction of Phase Times and Cycle Length for Traffic-actuated Control
Traffic-related phenomena at a signalized intersection, such as lane capacity, delay and
queue length are influenced by the green times (or phase times) and cycle length. For traffic-
actuated control, green split and cycle length fluctuate with respect to the traffic demand.
Consequently, it becomes desirable to predict the average phases times and cycle length. The
phase time is equal to the green time displayed plus intergreen time (clearance interval or
duration of yellow plus all-red).
In 1982, Lin  began to develop a model to estimate the average phase duration for
fully-actuated signals. The model was developed primarily on the basis of probabilistic
interactions between traffic flows and the control He assumed the arrival at the upstream
side of an intersection would be at random, so the arrival pattern in each lane was represented
by a Poisson distribution. Later, Lin and Mazdeyasna  developed delay models for semi-
actuated and fully-actuated controls that employ motion detectors and sequential phasing.
These models were based on a modified version of Webster's formula. The modifications
included the use of average cycle length, average green time, and two coefficients of
sensitivity reflecting the degree of delay sensitivity to a given combination of traffic and
control conditions. In 1992, Lin  proposed an improved method for estimating average
cycle lengths and green intervals for semi-actuated signal operations as mentioned before.
In 1994, Ak9elik [9, 10] proposed an analytical methodology for the estimation of
green times and cycle length for traffic-actuated signals based on the bunched exponential
distribution of arrival headway. The discussions in his papers were limited to the operation
of a basic actuated controller that used passage detectors and a fixed allowable gap setting.
Both fully-actuated and semi-actuated control cases were studied. A discussion of arrival
headway distributions was presented since the estimation of arrival headways is fundamental
to the modeling of actuated signal timings. The formulae were derived to estimate the green
times and cycle length based on the bunched exponential distribution of arrival headway.
The bunched arrival model was proposed by Cowan  and used extensively by
Troutbeck [42, 43, 44, 45, 46, 47] for estimating capacity and performance of roundabouts
and other unsignalized intersections. The bunched arrival model considers that the bunched
relationship between vehicles increases when the flow arrival rate increases. Since the
bunched arrival model appears to be more representative of real-life arrival patterns in
general, Akgelik used this arrival model for deriving various formulae for the analysis of
traffic-actuated signal operations. The random arrival model which uses negative exponential
or shift negative exponential distribution of arrival headway can be derived as a special case
of the bunched arrival model through simplifying assumptions about bunching characteristics
of the arrival stream. The methods given in his papers provide essential information (average
green times and cycle length) for predicting the performance characteristics (capacity, degree
of saturation, delay, queue length and stopped rate) of intersections.
Delay Models for Traffic-actuated Control
With the increase of computer software, the comparison of different traffic programs
for pretimed and actuated controls became intuitively appealing. In 1974, Nemeth and
Mekemson  compared the delay and fuel consumption between deterministic Signal
Operations Analysis Package (SOAP79) and the microscope and stochastic NETSIM
simulation for pretimed and actuated controls. They indicated that in terms of delay
prediction, SOAP79 and NETSIM were found to be entirely compatible except for the
difference in delay definitions.
In 1988, Akcelik  evaluated the 1985 HCM  delay formula for signalized
intersections. He stated that the HCM formula predicted higher delays for oversaturated
conditions. An alternative equation to the HCM formula was proposed. This formula gave
values close to the HCM formula for degrees of saturation less than 1.0, and at the same time,
was similar to the Australian, Canadian and TRANSYT formulas in producing a delay curve
asymptotic to the deterministic delay line for a degree of saturation greater than 1.0.
The signalized intersection methodology presented in the 1985 HCM  introduced
a new delay model Lin  evaluated the delay estimated by the HCM with field observed
delay in 1989. Some inconsistency existed in the delay estimation between the HCM results
and field observation. He suggested improving the progression adjustment in the HCM
procedure and using a reliable method to estimate average cycle lengths and green durations
for traffic-actuated signal operations.
In 1989, Hagen and Courage  compared the HCM  delay computations with
those performed by the SOAP84 and TRANSYT-7F Release 5. The paper focused on the
effect of the degree of saturation, the peak-hour factor, the period length on delay
computations and the treatment of left turns opposed by oncoming traffic. They indicated
that all of the models agreed closely at volume level below the saturation point. When
conditions became oversaturated, the models diverged; however, they could be made to agree
by the proper choice of parameters. The computed saturation flow rates for left turns
opposed by oncoming traffic also agreed closely. However, the treatment of protected plus
permitted left turns produced substantial differences. It was concluded that neither SOAP nor
HCM treats this case adequately.
A delay model was recommended in the HCM  for level-of-service analysis at
signalized intersections. The use of this model for the evaluation of traffic-actuated signal
operations required the knowledge of the average green times and cycle length associated
with the signal operation being analyzed. Since the method suggested in the HCM to estimate
delay of traffic-actuated signal operations was not reliable, Lin  proposed an improved
method for estimating average green times and cycle length in 1990. The method was
appropriate for semi-actuated signal operations. Lin stated that the method was sufficiently
simple and reliable. Realistic examples were used to illustrate the application of the method.
In 1993, Li, Rouphail and Akcelik  presented an approach for estimating overflow
delays for lane groups under traffic-actuated control using the 1985 HCM  delay model
format. The signal timing used in the delay model was from a cycle-by-cycle simulation
model This study was limited, however, to two-phase single-lane conditions. The results
indicated that the signal timings are much related to the controller settings, with longer
extension times producing higher cycle length. It was found that overflow delay increases
with longer extension times. Further, by applying the 1985 HCM delay formula to the
simulated signal settings, the resultant delays were much higher. This implies the need for
calibration of the second delay term to account for the actuated control effects.
Signalized Intersection Capacity Models for Traffic-actuated Control
Intersection capacity analysis is essential for measurements of most traffic control
effectiveness. The first U.S. Highway Capacity Manual (HCM) in 1950 contained a chapter
for estimating the capacities of signalized intersections. Numerous studies were undertaken
to evaluate the different aspects of signalized intersections, and many capacity methods were
developed. In 1983, May, Gedizlioglu and Tai  began the evaluation of eight available
methods for capacity and traffic-performance analysis at signalized intersections including
pretimed and actuated controls. The eight methods included the U.S. Highway Capacity
Manual method (1965), British method (1966), Swedish method (1977), Transportation
Research Board (TRB) Circular 212 planning method (1980), TRB Circular 212 operations
and design method (1980), Australian method (1981), National Cooperative Highway
Research Program (NCHRP) planning method (1982), and NCHRP operations method
(1982). They concluded that the NCHRP operations method and the Australian method were
found to be the most cost-effective.
In 1991, Prevedouros  studied the traffic measurements and capacity analysis for
actuated signal operations. He verified that the methodology in Chapter 9 of the 1985 HCM
 was not appropriate to treat the pretimed and actuated controls identically, especially
concerning the estimation of capacity and performance of existing intersections. The main
sources of error and their potential impacts were presented. He developed a comprehensive
data collection and analysis methodology to complement the procedure in the 1985 HCM.
Overview and Evaluation of EVIPAS
EVIPAS  is an optimization and simulation model for actuated, isolated
intersections. It is capable of analyzing and determining the optimal settings of controller
parameters for a wide range of geometric configurations, detector layouts, and almost any
phasing pattern available in a single or dual-ring NEMA and Type 170 controllers. It will
generate the optimized timing settings for controllers ranging from pretimed to volume-
density actuated controllers. The optimum settings of timing parameters include minimum
green time, maximum green time, unit extension, minimum gap, time before reduction, time
to reduce, variable (added) initial and maximum initial for each phase.
The value of optimal timing is defined as the timing setting which results in the
minimum "total cost." The model allows the user to define "total cost: to include a variety
of measures of effectiveness, such as delay, fuel consumption, depreciation, other vehicle
costs and emissions. The EVIPAS model allows for two modes of operation. In its
optimization mode, the model is used to obtain optimal timing settings by a multivariate
gradient search optimization module and an event-based intersection microscopic simulation.
In the simulation mode, EVIPAS allows the evaluation of a prespecified signal plan just by
For the capacity and level of service of traffic-actuated control, the performance
outputs are primarily concerned, which includes the summary of delays and signal
performance. The summary of delay table provides delay statistics for the intersection and
for each approach and lane. The summary of signal performance table shows the average
phase length and average cycle length. All above delay measures, average phase length, and
average cycle length are based on the microscopic simulation results.
Since both EVIPAS and TRAF-NETSIM are microscopic simulation models, the
phase time comparison between these two models becomes necessary. The phase times
estimated from the EVIPAS simulation model will be compared with those from NETSIM
simulation model later in this chapter.
Preliminary Model Development
The purpose of this study is to accurately predict the average phase times and
corresponding cycle length for actuated operations. The preliminary model developed in this
study is limited to through movements and left turns with "protected only" phasing from an
exclusive lane. However, this preliminary model is very useful for later development of a
complete and comprehensive model.
It is important to note that the proposed preliminary model is mainly based on the
methodology proposed by Courage and Akcelik  for evaluating the operation of a traffic-
actuated controller in their working paper NCHRP 3-48-1 for National Cooperative Highway
Research Program (NCHRP) project 3-48, "Capacity Analysis of Traffic-actuated Signals."
The proposed analytical model for predicting average phase times and corresponding
cycle length applies several traffic engineering concepts and theories. They include traffic-
actuated operation logic, dual-ring control concept, average phase time prediction for traffic-
actuated signals, queue accumulation polygon (QAP) concept, vehicle arrival headway
distribution, circular dependency relationship and sequential process. These concepts and
theories are used for both preliminary and comprehensive model development, and their
In the discussion of the preliminary model, the method in the Appendix I to HCM
Chapter 9 will initially be reviewed following the model development issues. Then, each
concept and theory used in the model development will be presented. Finally, the
computational framework proposed by Courage and Akelik  for modeling traffic-actuated
controller operations will be summarized.
Review of the Appendix II Method to HCM Chapter 9
In the HCM  Chapter 9 Appendix I methodology, an actuated signal is assumed
to be extremely efficient in its use ofthe available green time. Thus, the average cycle length
is estimated using a high critical volume over capacity ratio (v/c) which is approximately equal
to 0.95. In other words, the controller can be effective in its objective of keeping the critical
approach nearly saturated. The formula for the average cycle length may be stated as
C = L/(1-Y/X,) (2-1)
C, = the average cycle length;
L = the total lost time per cycle, ie., the sum of the lost times associated with the
starting and stopping of each critical lane group in the phase sequence;
Y = the critical flow ratio, determined as the sum of the flow ratios (v/s) for the
individual lane groups that are critical in each phase. The flow ratio for each
lane group is defined as the ratio of the traffic volume (v) to the saturation
flow rate (s); and
X, = the target degree of saturation (volume/capacity ratio or v/c ratio). A value
of 0.95 is suggested in Appendix II for traffic-actuated control
After the average cycle length has been computed, the average effective green time
(g) for each lane group I can be determined by dividing the average cycle length (C,) among
lane groups in proportion to their individual flow ratios ( (v/s) ) over target degree of
saturation (X,). The formula of average effective green time for each lane group may be
= C, [ (v/s) / X ] (2-2)
The effective green time, rather than the signal displayed green time, is usually used in signal
timing computation which is the signal displayed green time plus the intergreen time (change
interval or yellow plus all-red clearance) minus the lost time in the phase.
As mentioned before, the Appendix II method for estimating the signal timing for
actuated operation has been questioned in the literature. There are three major problems with
the Appendix I methodology:
1. The assumption that a traffic-actuated controller will maintain 95% saturation on
the critical approach to each phase has not well been accepted. Several studies
have indicated that a somewhat lower degree of saturation often results.
2. The effects of actuated design parameters such as minimum green time, maximum
green time, unit extension and detector configuration are not reflected in the
formula for average cycle length, so it is not sensitive to the above parameters.
3. The simplistic nature of this model does not provide for real-world complications
such as minimum or maximum green time setting, shared-lane permitted left turns,
left turns that are allowed to proceed on both permitted and protected phases,
phase skipping due to lack of demand, constraints imposed by coordination, etc.
In their working paper, Courage and Akgelik  indicated that the limitations of
Appendix I technique can be overcome, but not without adding considerable complexity to
the computational procedures. The HCM has traditionally dealt with "single pass" analytical
models that may be described in manual worksheets. The updated version (1994) of HCM
Chapter 9 worksheets are analytically much more complicated, however, they have retained,
with one minor exception, their "single pass" characteristics. Therefore, Courage and Ak9elik
proposed a model with a sequential process of multiple iterations to improve the model
addressed in Appendix II with "single pass."
Model Development Issues
Since the entire Chapter 9 methodology has reached the limits of single-pass
procedures, the limitations of Appendix II, as mentioned before, cannot be addressed without
resorting to complex iterative procedures. Because the limitation of the Appendix II
technique is a result of the primitive treatment of actuated control, it may only be overcome
by improving the actuated control model Thus, the model to be developed in this study must
be able to perform effective comparisons between the pretimed and traffic-actuated control
modes. The model must also be functionally capable of providing reasonable estimate of
operating characteristics (timing and performance measures) of traffic-actuated controllers
under the normal range of practical design configurations. It must be sensitive to common
variations in design parameters. The design parameters include
Actuated controller settings (minimum green time, maximum green time and
Conventional actuated vs. volume-density control strategies;
Detector configurations (length and setback);
Pedestrian timings (Walk and Flashing Don't Walk, FDW);
Left turn treatments (permitted, protected, permitted and protected, and not
Left turn phase positions (leading and lagging).
Additional input data are needed to improve the accuracy of the analysis methodology.
The information that is already required by the Chapter 9 procedure will naturally be used to
the fullest extent possible to avoid the need for new data. Most of the additional data items
are related to the operation itself The proposed model will be based on the standard eight-
phase dual-ring control concept that is more or less universally applied in the U. S. A. In this
study, a standard assignment of movements to phase is adopted. It can greatly simplify the
development and illustration of all modeling procedures without affecting the generality of
the capacity and level of service results.
It is difficult to analytically deal with the very low volume operation that typically
occurs late at night. Under this condition, the repetitive cyclical operation upon which the
analysis is based no longer applies. The effort required to develop a model for dealing
accurately with delays of a few seconds per vehicle (i.e., level of service A) is difficult to
justify. An approximation of the operating characteristics for very low volumes will generally
be acceptable from a capacity and level of service perspective.
In the literature, many analytical studies on traffic-actuated operation assume that
passage detectors are used, whereas in actual practice, presence detectors are much more
common. Passage detectors transmit a short pulse to the controller upon the arrival of each
vehicle. Presence detectors transmit a continuous signal to the controller as long as the
vehicle remains in the detection zone. For purpose of this study, variable length presence
detectors will be assumed. The operation of using passage detectors to detect vehicles may
be approximated by using short length presence detectors.
Traffic-actuated Operation Logic
Actuated operation is one kind of traffic control which uses the information collected
by detectors to determine the signal timing of an intersection. The detector type can be either
passage or presence. The main advantage of traffic-actuated control is that the traffic signal
can properly display the green times according to traffic demand. There are three types of
actuated controllers. They are semi-actuated, fully-actuated and volume-density.
The operation of the semi-actuated signal is based on the ability of the controller to
vary the length of the different phases to meet the demand on the minor approach. Maximum
and minirmm green times are set only for the minor street. Detectors are also placed only on
the minor street. On the other hand, fully-actuated controllers are suitable for an intersection
at which large fluctuations of traffic volumes exist on all approaches during the day.
Maximum and minimum green times are set for each approach. Detectors are also installed
on each approach. The volume-density control is one kind of actuated control with added
features which 1) can keep track of the number of arrivals, and 2) reduce the allowable gap
according to several rules. It is usually used at intersections with high speed approaches. For
illustration purposes on actuated control logic, a passage detector will first be assumed
because it is simple. Some basic term definitions are addressed as follows:
Initial interval is the first portion of the green phase that an actuated controller has
timed out for vehicles waiting between the detector and stopline during the green
time to go through the intersection.
Vehicle interval, also called "unit extension" or "allowable gap" is the time that the
green time is extended for each detector actuation.
Maximum green time is simply the total green time allowed to the phase.
Minimum green time is the shortest green time that can be displayed.
To avoid vehicles being trapped between the detector and stopline, it is necessary that the
vehicle interval be at least the "passage time" of a vehicle from the detector to the stopline.
Maximum Green Time
Minimum Green Ti Extension Period
trial Int.Ie. It.
Detector actuation on phase with right-of-way
SUnexpired portions of vehicle intervals
Figure 2-1. The operation of an actuated phase under significant demand.
Figure 2-1 shows the operation of an actuated phase under significant demand. Prior
to the beginning of the figure, a "call" for green had been put in by the arrival on the studied
approach. Then, the phase with right-of-way on this approach will first display the initial
interval plus one unit extension for the arrival The sum of initial interval and one unit
extension is usually called minimum green time. During the minimum green time, if an
additional vehicle arrives, as shown in Figure 2-1, a new unit extension is begun from the time
of detector actuation. The unexpired portion of the old vehicle interval with the shaded area
shown in the figure is wiped out and superseded. If vehicle actuation continues, the green
time will also be extended with the same process until the maximum green time is reached.
The total extension time after the minimum green time is referred to as the extension period.
If the traffic volume is less intense, the extension period will not reach the maximum
green time. When a vehicle interval expires without an arrival of a new vehicle (indicated by
an asterisk [*]), the green time will be terminated and the signal light will turn to yellow plus
red clearance if there is a vehicle waiting for the next subsequent phase. Since in this
illustrated example significant demand is assumed, the maximum green time is reached.
Dual-ring Control Concept
In a pretimed controller, the controller operates under a single ring sequential timing
process. Each phase is taken as an interval of time in which specified traffic movements are
serviced. Of course, it is possible to have a given movement served on more than one phase
of the sequence, and it is expected that a combination of two non-conflicting movements (two
through, two left turns or a left turn plus through) will be serviced on any one phase.
However, the vast majority of modem traffic control systems use NEMA standard
traffic-actuated controllers which employ a dual-ring concurrent timing process. By keeping
the non-conflicting phases in separate rings, it is capable of displaying them simultaneously
to optimize the combinations of movements which are displayed on each cycle. Since the
standard eight-phase dual-ring operation is more or less universally applied in the U. S. A.,
and in this study a standard assignment oftraffic movements is also based on the dual-ring
NEMA phase configuration, it is essential to be familiar with the dual-ring concurrent phasing
scheme with assigned movements. The dual-ring phasing scheme and operation logic will
be presented next.
The standard dual-ring concurrent phasing scheme using NEMA phase definition is
shown in Figure 2-2. In Figure 2-2 phases 1, 2, 3 and 4 are belong to ring 1, while phases 5,
6, 7 and 8 are belong to ring 2. A specific traffic movement is assigned to each NEMA phase
as shown at the corer of each phase box. For example, NEMA phase 2 is an eastbound
through movement and NEMA phase 7 is the southbound left turn. In a standard dual-ring
concurrent phasing scheme, east-west movements are assigned to the left side of barrier
(phases 1, 2, 5, 6), whereas north-south movements are assigned to the right side of barrier
(phases 3, 4, 7, 8). The barrier can be reversed to assign north-south movements to the left
side and east-west movements to the right side if needed.
Traffic movements for phases 1 and 2 conflict with each other. It is also true for
phases 3 & 4, 5 & 6, and 7 & 8. Since the conflicting phases on each ring are sequential, on
the side of the barrier, none of the phases within ring 1 will conflict with any of the phases
within ring 2. In such a way, non-conflicting phases can be displayed simultaneously to
optimize the combinations of movements.
An example of the dual-ring concurrent phasing scheme based on the east-west
movement in Figure 2-2 is presented as follows. The phase sequence begins with the non-
conflicting combination ofNEMA phases 1 and 5. The next phase sequence can be either the
combination of NEMA phases 1 and 6 or NEMA phases 2 and 5 according to the traffic
demand. If the demand for eastbound left turns is heavier than that of westbound left turns,
in general, the combination of phases 2 and 5 will display most of the time. Finally, NEMA
phases 2 and 6 will display.
It is a standard convention to assign the odd number to the left turn in any phase pair
(1-2, 3-4, 5-6, 7-8), and the even number to the through movement. This reflects the
popularity of leading left turn protection. When the lagging left turn protection is to be
implemented, the phase assignment may be reversed (ie., even number to the left turn).
Although any phase may be theoretically designated as the coordinated phase in each ring, it
is common to designate the phase with through movement on the left side of the barrier as
the coordinated phase. It is necessary to note that the above phasing assignments conform
to those used by the PASSER II arterial signal timing. It has also been adopted by the
WHICH program for mapping data into NETSIM.
Left Side of Barrier
( E-W Movements )
Right Side of Barrier
( N-S Movements)
Figure 2-2. Dual-ring concurrent phasing scheme with assigned movements.
Average Phase Time Prediction for Traffic-actuated Signals
The main objective of this study is to accurately predict the average phase times for
traffic-actuated signals. The average phase time includes two major portions of timing. One
is the queue service (clearance) time and the other is the extension time after queue service.
Therefore, accurate phase time predictions are mainly dependent on the accurate predictions
of both queue service times and extension times after queue service.
Before the illustration of the methodology to predict average phase times and cycle
length, some key term definitions need to be addressed first. The phase time is the signal
displayed green time (controller green time) plus the intergreen time. In the signal timing
analysis, the effective green time and the effective red time are frequently used. Therefore,
appropriate conversion of the displayed green time to an effective value is required before the
signal timing analysis.
SR G I
Phase Time -
Figure 2-3. The relationships among the components in the phase time.
The relationship among phase time (PT), displayed green time (G) and effective green
time (g) shown in Figure 2-3 is expressed as follows:
PT = G+I = t, +g = t, +gst+g, (2-3)
subject to PTm < PT < PT,=
In more detail, Equation 2-3 can be expressed as follows:
PT = t, +Go+EI = t= t+gqt+eg+I = t +g + s+ + t (2-4)
subject to PT, < PT < PT,
I = intergreen time (yellow plus all-red);
ti = lost time, which is the sum of start-up lost time, t., and end lost time, td;
gq,, G, = the queue service time (saturated portion of green), where gq, = G= ;
e., E. = the green extension time by gap change after queue service, where eg =
EI, and the total extension time, EXT, is defined as (ei+I) or (Eg+I);
ge = the effective extension time by gap change after the queue service period,
where g = e + I td; (2-5)
PTn, = the minimum phase time, PTm, = G. + I, where G. is minimum green
PT. = the maximum phase time, PT,= G + I, where G. is maximum green
Queue Accumulation Poygon (OAP) Concept
The analysis of queue accumulation polygon (QAP) is an effective way to predict the
queue service time, gq, (= G.). The QAP is a plot of the number of vehicles queued at the
stopline over the cycle. For a single protected phase which could be the through phase or the
protected left turn phase, when traffic volume does not exceed its capacity, QAP is just a
single triangle as shown in Figure 2-4. In Figure 2-4, g, stands for actual queue service time
(in this case, gq~ = g), while g, is the effective extension time after queue service. More
complex polygons occur when a movement proceeds on more than one phase.
Based on the vehicle arrival rate q, during effective red time, the accumulated queue
(Qr) before the effective green time can be estimated. The time taken to discharge the
accumulated queue can be computed simply by dividing the accumulated queue of Qr with the
net departure rate (s q) which is equal to the departure rate (s) minus the vehicle arrival rate
(q) during the effective green time. For this simple protected phase, the departure rate s is
equal to the saturation flow rate. The target v/c ratio may be considered in the peak hour
analysis. However, it must be set to 1.0 to determine the actual queue service time. In order
to determine the critical queue service time (gq) of different lane groups within the same
phase, a lane utilization factor is considered in the computation of actual queue service time
(g). In general, g, can be estimated from the following formula:
g = fu q (2-6)
fq = a queue length calibration factor  proposed by Ak9elik to allow for
variations in queue service time, where
= 1.08- 0.1 (G/ G )2 (2-7)
f = a lane utilization factor for unbalance lane usage based on the HCM Table
q, qs = q, is red arrival rate and q. (veh/sec) is green arrival rate (veh/sec);
XT = a specified target volume/capacity (v/c) ratio; and
r, s = r is red time (sec) and s is saturation flow (veh/sec).
In multi-lane cases, the saturated portion of green time should represent the time to
clear the queue in the critical lane (i.e. the longest queue for any lane) considering all lanes
of an approach in the signal phase. More complex polygons occur when a movement
proceeds on more than one phase. The computation for queue service time is mainly based
on the QAP concept.
Figure 2-4. Queue accumulation polygon for a single protected phase.
Vehicle Arrival Headway Distributions
Arrival headway distributions play a fundamental role in the estimation of green
extension time, eg (or E), at actuated signals. The bunched exponential distribution of arrival
headways was proposed by Cowan , which considers that the bunched relationship
increases among the arriving vehicles when the traffic volume increases. The free
(unbunched) vehicles are those with headways greater than the minimum headway (A), and
the proportion of free vehicles (p) represents the unbunched vehicles with randomly
distributed headways. Thus, the measurement of the proportion of free vehicles (p) depends
on the choice of minimum headway (A). The proportion of bunched vehicles in the arrival
stream is (1-p). In this arrival model, all bunched vehicles are assumed to have the same
intra-bunched headway (A). The cumulative distribution function, F(t), for this bunched
negative exponential distribution of arrival headways, representing the probability of a
headway less than t seconds, is
F(t) = 1 ype- -A) for t >A (2-8)
= 0 fort
A = minimum arrival (intra-bunch) headway (seconds);
(p = proportion of free (unbunched) vehicles; and
X = a parameter calculated as
subject to q < 0.98/A
q = total equivalent through arrival flow (vehicles/second) for all
lane groups that actuate the phase under consideration.
A detailed discussion of the application of this model on actuated control and the
results of its calibration using real-life data for single-lane and multi-lane cases are given in
Akelik and Chung . The more commonly used simple negative exponential and shifted
negative exponential models of arrival headways are special cases of the bunched exponential
model Therefore, in this study, the bunched arrival model is used to estimate the extension
time after queue clearance.
The method for estimating the green extension time, e, for an actuated controller that
uses a passage detector and a fixed gap time (unit extension) setting (e.) was described by
Akqelik . In this study, presence detectors are assumed. The headway (h) between two
consecutive vehicles is equal to the sum of the gap time (e) and the detector occupancy time
(to). Therefore, the headway, hk, that corresponds to the allowable gap time setting, e,, is
h= e. + to (2-10)
where to is the detector occupancy time given by
to = (Ld +L )/v (2-11)
Ld = effective detector length (ft);
L = vehicle length (ft); and
v = vehicle speed (ft/sec).
There is no need for the estimation of an extension time if the actual queue service
time, g, is less than the minimum effective green time, gn, or g, is greater than the maximum
effective green time, g Ifg, < g< then g willbe set to gan and ifg &> gn then g is equal
to g,. Detection of each additional vehicle between gnn and g in general, extends the
green period by an amount that is, in effect, equal to the headway time, h.. The green period
terminates when the following two conditions are satisfied.
1. the headway between two successive vehicle actuations exceeds the headway that
corresponds to the gap time setting, h > ho (gap change); or
2. the total green extension time after the expiration of minimum green time equals
the maximum extension setting. It is equivalent that g is equal to g..
During a gap change, the green period terminates after the expiration of the gap time.
Assuming that the termination time at gap change is the headway corresponding to the gap
time setting (ho = e. + to), the green extension time, eg, by gap change can be estimated from
the following formula [6, 9, 10] based on the bunched exponential headway distribution.
eg= pqq (2-12)
Once the green extension time, e, is obtained, the effective extension time, g&, is just equal
to the sum ofeg and the intergreen, I, minus the end lost time, td, as shown in Equation 2-5.
As mentioned before, the more commonly used simple negative exponential and
shifted negative exponential models of arrival headways are special cases of the bunched
exponential model. For simple negative exponential model, use
A= 0 and (p =1
(therefore X = q)
and for the shifted negative exponential model (normally used for single-lane traffic only), use
P = 1 (therefore X = q / (1- Aq)) (2-14)
These two models unrealistically assume no bunching ((p =1) for all levels of arrival flows.
The bunched model can be used either with a known (measured) value of (p, or more
generally, with a value of
relationship suggested by Akqelik and Chung  can be used for estimating the proportion
ofunbunched vehicles in the traffic stream ((p)
p = e -b (2-15)
The recommended parameter values based on the calibration of the bunched
model by Akqelik and Chung  are:
A = 1.5 seconds and b = 0.6
Multi-lane case (number of lanes =2): A = 0.5 seconds and b = 0.5
Multi-lane case (number of lanes > 2): A = 0.5 seconds and b = 0.8
Effect of Phase Skip
The minimum phase time requires more attention when the phase may be skipped due
to low traffic volume. The minimum phase time would only be valid if the controller was set
to recall each phase to the minimum time regardless of demand. On the other hand, the real
significance of the minimum phase time in an actuated controller is that a phase must be
displayed for the minimum time unless it is skipped due to lack of demand. This situation may
be addressed analytically by determining the probability of zero arrivals on the previous red
phase. Assuming a bunched arrival headway distribution, this may be computed by using the
POV = p e- A) (2-17)
POv = probability of zero arrivals during the previous red phase; and
R = previous red phase time.
So, assuming that the phase will be displayed for the minimum time, except when no vehicles
have arrived on the red, the adjusted vehicle minimum time then becomes
AVM = MnV(1 Po) (2-18)
AVM = the adjusted vehicle minimum time; and
MnV = the nominal minimum vehicle time.
The similar concept for adjusted vehicle minimum time may also be applied to compute an
adjusted pedestrian minimum time.
If the phase may be skipped due to lack of demand, the adjusted minimum phase time
is the maximum of adjusted vehicle minimum time and adjusted pedestrian minimum time.
It will be used as lower bound of the predicted phase time. When the Pov for a phase is not
zero, the estimated phase time must also be modified by multiplying the (1-Pov) factor to the
original total extension time. Therefore, the predicted phase time becomes
PT = tj +Gqs +(1 Pov) (Eg +I) (2-19)
Circular Dependency Relationship and Sequential Process
The determination of required green time using the Appendix II method is relatively
straight forward when the cycle length is given. However, traffic-actuated controllers do not
work on this principle. Instead, they determine, by a mechanical analogy, the required green
time or phase time given only the length of the previous red interval The green time or phase
time required for each phase is dependent on the green time or phase time required by the
other phases. Thus, a circular dependency relationship exists between actuated phase times.
There are two way to resolve this type of circular dependency. The first one is
simultaneous solutions of multiple equations. The second one is a sequential process
involving repeated iterations that converge toward a unique solution. Either method could
be applied to solve this dependency problem. Since the simultaneous solution will not lend
itself to the complications that must be introduced to solve the more general problem,
Courage and Akgelik  proposed and set up an iterative procedure that will apply to the
general problem. This iterative procedure is adopted in this study to predict the average
phase time for general cases, not just limited to the protected phases.
An initial set of values for all phase times must be established before the iterative
procedure may begin. With each iteration, the phase time required by each phase, given all
of the other phase times, may be determined. If the minimum phase times turn out to be
adequate for all phases, the cycle length will simply be the sum of the minimum phase times
of the critical phases. If a particular phase demands more than its minimum time, then a
longer red time will be imposed on all the other phases. This, in turn, will increase the phase
time required for the subject phase. Through a series of repeated iterations, the circular
dependency will come to an equilibrium and converge to a unique solution. When the
convergence of cycle length is reached, the final cycle length and phase times are determined.
This convergence may be demonstrated easily by using an simple example. Consider
the intersection shown in Figure 2-5. This is a trivial intersection with four identical single-
lane approaches carrying the through volume of 400 vph. A saturation flow rate of 1900
vphgpl is assumed. Each phase has assigned the following constant parameters:
Detector: 30 feet long, placed at the stopline
Intergreen time (I): 4 seconds
Lost time (t,) 3 seconds per phase
Start-up lost time (td): 2 seconds per phase
Minimum phase time: 15 seconds
Allowable gap: 3 seconds
Maximum phase time: 50 seconds
No pedestrian timing features.
No volume-density features.
N FHE1-NS SB
Figure 2-5. The intersection used as an example for circular dependency illustration.
The QAP for the first iteration in this example is shown in Figure 2-6. Initially, the
"trial time" is the nominal minimum vehicle time (15 seconds in this case) for each phase.
Although this operation has four through phases, it can actually be treated as a two-phase
operation because the northbound through phase is identical to the southbound through phase
and the eastbound through phase is the same as the westbound through phase.
Hence, the trial cycle length is equal to 15 x 2 = 30 seconds. This initial timing would
result in an effective red time of 18 seconds for each phase. The traffic volume for each
approach is 400 vehicles per hour. In other words, the arrival rate is equal to 400/3600 =
0.11 vehicles per second. Therefore, during the effective red time, the accumulated queue
can be computed as the product of arrival rate and effective red time, which is equal to 0.11
x 18 = 2 vehicles.
Required phase time
o 3 ----------i
13+5.16+8.3 16.46 see I
S13 15.16 sec 8.3 see
g Isecl I
.11 x 18 2.00 veh I
P 0.11 vps 0153 0.11
o* 1 -- 0'42 vps
z 15 + 3 18 sec
effective red r tl gg ge
0 10 20 30
Figure 2-6. Queue accumulation polygon in the first iteration of the illustrated example.
The departure rate is the saturation flow rate (1900 vehicles per hour), so the phase
can discharge (1900/3600)= 0.53 vehicles per second. Therefore, the net service rate is equal
to (0.53 0.11) = 0.42 vehicle per second. Since f is about 1.07 and f, equals 1.0, the actual
queue service time, g, taken to discharge the queue will be (1.07 2) / 0.42 = 5.16 seconds.
The extended green time, e., is 5.3 seconds and intergreen time, I, is 4 seconds. Thus, the
total extension time, EXT (= es + I), is 9.3 seconds (= 5.3 + 4) and the effective extension
time, g equals 8.3 seconds (= 5.3 + 4 1). By using Equation 2-3, the phase time, PT,
equals the sum of the lost time, tz, the queue service time, gq,, (= g, in this example) and the
effective extension time, g& which is about 16.46 seconds (= 3 + 5.16 + 8.3). By using
Equation 2-4, PT is equal to the sum oft,, gq,, (= g in this example) and EXT which is also
about 16.46 seconds (= 2 + 5.16 + 9.3). The new phase times produce a new cycle length
of (16.46 x 2) = 32.92 seconds. This will generate another version of Figure 2-6 with
different dimensions. By repeating these calculations with a new cycle length each time, the
computed cycle length will converge to within 0.1 second. Convergence for this example is
especially rapid. The process is very reliable. Table 2-1 shows the iteration result and
convergence for this trivial example.
Table 2-1. The iteration results and its convergence for the illustrated example.
Itera- Cycle Old Acc. Total Total New New Differ-
tion phase queue service time ext. time phase cycle ence
time (= t + g) (= e + I) time
(sec) (sec) (sec) (sec) (sec) (sec) (sec)
1 30.0 15.0 2.00 7.16 9.3 16.5 32.9 2.9
2 32.9 16.5 2.16 7.57 9.3 16.9 33.7 0.8
3 33.7 16.9 2.21 7.68 9.3 17.0 33.9 0.2
4 33.9 17.0 2.22 7.71 9.3 17.0 34.0 0.1
The computation framework with five worksheets proposed by Courage and Ak9elik
 for modeling traffic-actuated controller operations for simple through and protected left
turn phases is adopted by this study as the basis for more complicated and general model
development. This computation process will be introduced here. The worksheets play a very
important part in overcoming the "black box" image of a complex model such as the one in
this study. They provide a structure for presenting the results of intermediate computations
in a common form that is compatible with their proposed techniques.
Worksheet 1 is "Traffic-actuated Control Data Input". "Lane Group Data" is shown
in Worksheet 2. Worksheet 3 is "Traffic-actuated Timing Computation" and Worksheet 4
is "Required Phase Times". The last worksheet, worksheet 5, is "Extension Times Based on
Allowed Gaps". The worksheet format offered a clear and concise way to document the
information. This format is also consistent with the current HCM. While the worksheets
themselves are quite simple, the overall procedure contains iterative loops. In this research,
the worksheets proposed by Courage and Akgelik will be modified and enhanced for the
computation of more general and complicated scenarios, not just limited to simple protected
scenarios. The complete procedure involving the five worksheets is illustrated in Figure 2-7.
This figure shows the five worksheets, the main information flow path and two iterative
loops indicated as "Loop A" and "Loop B".
1. Data 2. Lane
A Adjustments SYMBOLS
5. Phase W
Extension n -
Times : Iterative Loops
Figure 2-7. Iterative loops in the phase time and cycle *..... computation procedure.
Figure 2-7. Iterative loops in the phase time and cycle time computation procedure.
Loop A. Required Time Cycle Time Adjustment: This is an external iteration
between Worksheets 3 and 4. It is required to make the phase times converge
to a stable cycle length. Worksheet 4 must also refer to Worksheet 5 if phase
time extensions are required to compute the required phase times.
Loop B. Phase Extension Time: This is an internal iteration within Worksheet 5.
It is only required when gap reduction is employed. When the allowable gap is a
function of the phase time, the phase time cannot be computed without iteration.
Simulation is one of the most powerful analysis tools available to those responsible
for the design and operation of complex process and systems. Simulation might have more
credibility because its behavior has been compared to that of a real system, or because it has
required fewer simplifying assumptions and thereby has captured more of the true
characteristics of the real system.
NETSIM, a popular and powerful microscopic traffic simulation model, has been
continually developed by the Federal Highway Administration (FHWA) for many years.
NETSIM is able to model an eight-phase, dual-ring controller explicitly, recognizing all of the
phase-specific parameters. EVIPAS is an optimization and simulation model for actuated
controlled, isolated intersections. In the simulation mode, it is also capable of providing
simulated phase times for a wide range of actuated parameter settings. Thus, both the
NETSIM and EVIPAS simulation models could be used as tools to verify the phase time
estimation from the proposed analytical model
Comparison between NETSIM and EVIPAS Simulation Results
Since both NETSIM and EVIPAS are simulation-based models, it becomes necessary
to compare the simulation results between EVIPAS and NETSIM. The current version of
NETSIM (P version 5.0) produces very detailed tables of several performance measures. It
does not, however, provide sufficient information on the operation of the controller itself in
the standard output tables. To obtain this information, it was necessary to develop a
postprocessor to extract the operational data from special files used to support the animated
graphics features ofNETSIM.
The actuated-controller data for each second of operation are recorded and stored in
a text file that is given a file name with extension of ".F45" by NETSIM. The format of
".F45" files is hard to read. After it is properly converted, a readable text file can be produced
with extension of".X45". Then, a postprocessor was developed to read the .X45 file and
produce a summary ofthe operation. Both conversion and postprocessor were combined into
a program called "NETCOP" for "NETSIM Controller Operation Postprocessor." It provides
phase-specific information such as percent skipped, percent gapout, percent maxout, average
cycle length, average phase time, adjusted cycle length and adjusted average phase time. The
"adjusted cycle length" is computed by subtracting the number of seconds of dwell (ie., the
time during which no demand was registered on any phase) from the total number of seconds
simulated before dividing by the number of cycles. The adjusted phase time is computed
according to the adjusted cycle length. Since the adjusted phase time from NETSIM can
represent the effective use of phase time, it is adopted for later phase time comparison.
Although the simulation techniques used in EVIPAS and NETSIM may differ in some
degree, theoretically, the phase time estimates for the same traffic conditions, geometric
configurations and actuated timing settings should be close. Thus, an evaluation has been
made by comparing the simulated phase times from both NETSIM and EVIPAS based on 9
hypothetical examples with traffic-actuated operations. These examples cover both two-
phase and multi-phase actuated operations. The comparison result is shown in the Figure 2-8.
In a simple regression analysis between the above two simulated phase times, a 0.96
coefficient of determination, R2, was achieved. As expected, the simulated phase times from
EVIPAS are very close to those from NETSIM simulation, which demonstrates that the
EVIPAS model has the similar effectiveness on phase time estimation as NETSIM.
I R2 = 0.96
S.......... ...............NETSIM S..... simulated Pha--- -----e Ti --e ( --ec) --
< u a
E-M S----ate---)---- ----------------
0 10 20 30 40 50 60 70
NETSIM Simulated Phase Time (aec)
Figure 2-8. Phase time comparison between EVIPAS and NETSIM.
As urban roadways become more congested, and resources available for building new
facilities become more limited, transportation professionals are exploring all possible
alternatives to improve the existing transportation systems. Fully-actuated traffic signals are
powerful for isolated intersections, but not proper for coordinated intersections. One major
area that holds great potential in reducing urban congestion is the implementation of
coordinated semi-actuated traffic signals on arterial streets. Unlike pretimed signals, semi-
actuated signals are intrinsically more intelligent and complex to implement and they provide
a better coordination than pretimed signals .
In semi-actuated operation, detectors are placed only on the minor street and
exclusive left turn lanes on the major street. No detectors are installed for the through
movements on the major street. Under this operation, once there is no detection on the minor
movements, the green will always come back to the through (coordinated) movements on the
major street. Therefore, the major benefit of using semi-actuated control is to assign unused
minor street green to the major street. This concept is fundamental to the signal timing
prediction for coordinated semi-actuated operation.
In pretimed control, the phase time of each movement is fixed, so the effective green
over cycle length ratio (g/C) for each movement is a constant. Unlike pretimed signals, the
phase time of each lane group for actuated signals does not stay constant but fluctuates from
cycle to cycle, so the g/C ratio for each movement fluctuates. Therefore, the major difference
between pretimed and traffic-actuated intersections lies in the g/C. The g/C ratio is important
because it is required for the capacity and delay computation. It is necessary to note that the
coordination for actuated signals must be provided by some form of supervision which is
synchronized to a background cycle length. Since coordinated semi-actuated control is
frequently used at intersections along an artery, the g/C ratio of the critical through-lane
group on the major street is especially important.
The true g/C ratio of each movement is difficult to access in current practice directly
from a traffic controller. Therefore, an alternative for obtaining the g/C ratio is needed. It
is found, in general, that the g/C ratio on a major street is high when the demand on minor
streets is low, and vice versa. This observation suggests the potential for using minor street
traffic demand measures to predict the major street g/C ratio. To verify the concept of the
assignment of unused minor street green to the major street, attempts have been made to
quantify the relationship between the major street g/C ratio and minor street traffic demand.
S0 Low Medium High
Minor Street Demand, x
Figure 2-9. Conceptual relationship between major street g/C and minor street demand.
Since traffic volume and detector occupancy are easy to measure with reasonable
accuracy for minor street demand, a conceptual model focusing on these two variables was
developed to predict the major street g/C ratio. As the minor street demand, x, increases
from zero, the major street g/C ratio, y, should start as a sharply decreasing function. The
rate of decrease should attenuate as x increases. The conceptual relationship between y and
x is shown in Figure 2-9.
Data from a closed loop signal system were used for the calibration of the candidate
models. The data set includes 98 intersection records generated from four coordinated semi-
actuated intersections during seven time periods along SW 34th St. in Gainesville, Florida.
A layout of the arterial system is shown in Figure 2-10. The SW 34th St. artery is a major
street, and Radio Rd., Hull Rd., SW 20th Ave. and Windmeadows are four minor streets.
Protected left turn signals exist on the major street at all four intersections.
1 Radio Rd.
2 Hull Rd.
SW 20th Ave. 3
SW 34th St.
Figure 2-10. The location of four studied intersection.
The Traffic Actuated Controller Monitor/Analyzer (TACMAN) computer package
 uses information collected by a microcomputer-based control system, the Signalized
Intersection Monitor (SIMON) , to produce hourly phase-specific descriptive information
and performance measures. The descriptive information includes traffic volume, detector
occupancy, etc., and performance measures include stops, delay and fuel consumption. The
measures used in the study pertain to the critical movements.
Statistical Analysis System (SAS)  programs were applied to perform correlation
and regression analyses. Regression techniques were used to calibrate the parameters of the
conceptual models. Regression results show that either the minor street volume or detector
occupancy can explain most of the variation in the major street g/C. Furthermore, the F and
t values indicate that both candidate models are overall significant and the coefficients in each
model are also individually statistically significant. The power model (volume model)
produced the highest adjusted R2 using the traffic volume data, while the logarithmic model
(occupancy model) was better for detector occupancy data. These two models can be
expressed as follows:
MAJG = 100(1 + 0.01 VOLUME) -3045 Adj. R2= 0.88 (2-20)
MAJG = 100 12.0954 LN(1 + OCCUPANCY) Adj. R2 = 0.91 (2-21)
MAJG = g/C ratio (%) for the major street critical through movement;
VOLUME = hourly volume for the minor street critical movement; and
OCCUPANCY = hourly detector occupancy for the minor street critical movement.
The curves for these two minor street demand measures are shown in Figures 2-11
and 2-12, respectively. As expected, the shape of both curves conforms to the described
conceptual model Although the occupancy model might be slightly better than the volume
model, the volume model may frequently be used because minor street volumes are often
known, estimated or forecast when no information is available about detector occupancy.
Based on the concept that the unused minor street green time is assigned to the major
street in coordinated semi-actuated operation, the relationship between the g/C ratio of the
critical through-lane group on a major street (major street g/C ratio) and the traffic demand
of the critical movement on minor streets (minor street demand) was quantified by the above
volume model and occupancy model In the further study, this concept will continue to be
implemented in the phase time estimation for coordinated semi-actuated operation.
50 Ii -- ,
0 100 200 300 400 500
Minor Street Traffic Volume (vph)
Figure 2-11. Prediction of the major street g/C ratio based on a power model for
minor street traffic volume.
0 5 10 15 20 25 30
Minor Street Detector Occupancy (%)
Figure 2-12. Prediction of the major street g/C ratio based on a logarithmic model for
minor street detector occupancy.
The scope of the preliminary model development presented in chapter 2 was limited
to basic through movements and protected left turn movements from an exclusive lane. This
chapter continually explores the analytical basis for extensions of the preliminary methodology
to cover permitted left turns in both shared and exclusive lanes and the complicated
compound left turn protection (Le., protected plus permitted phasing or permitted plus
Determination of Arrival Rates
In the previous analytical work, the arrival and departure rates were constant
parameters determined externally. The arrival rates were determined by the specified traffic
volumes and the departure rates were determined by the saturation flow rates. Neither
depended on the signal timing. In fully-actuated operation which is very often used at an
isolated intersection, the progression effect is not considered, therefore, the arrival type 3
(green arrival rate = red arrival rate) is appropriate. For coordinated semi-actuated operation,
since the progression effect is an important consideration, the use of different arrival types to
represent progression quality is required. The derivation of arrival rate is presented first in
this chapter for later application on coordinated semi-actuated intersections.
With arrival type 3, the arrival rate is constant over the whole cycle at q veh/sec. With
other arrival types, two different arrival rates must be computed. q, is the arrival rate on the
green phase, and q, is the arrival rate on the red phase. For a given average arrival rate, the
values of q and q, will depend on the platoon ratio, Rp, associated with the arrival type, and
the green ratio, g/C, which is a part of the timing plan. The HCM defines the platoon ratio
Rp = PC/g (3-1)
P = the probability of arrival on the green;
g = the green time for the phase; and
C = the cycle length.
Basic Continuity Relationship: qr + qgg = q(r+g)
o q = average arrival rate
Figure 3-1. Arrival rate over a full cycle with coordinated operation.
From Equation 3-1,
P = R g/C
Now, with arrival type 3, R = 1, so P = g/C, and q == q = On the other hand, if Rp 1,
then the arrival rates will be different on the red and green phases, as illustrated in Figure 3-1.
The problem is to determine q and q given q, Rp, g and C.
From Equation 3-1:
But, by definition,
qg = qR
As an extension of this derivation, the red arrival rate may be determined from the continuity
relationship shown on Figure 3-1.
qrr + qg = q(r+g)
qrr = q(r+g) (qR)g
q(r+g) (qR)g (3-3)
Permitted Left Turn Phasing
Before beginning the discussion of permitted left turn (LT) phasing, the concept of
green time determination for a protected phase is briefly reviewed first. This concept is based
on the queue accumulation polygon (QAP) shown in Figure 3-2 which was presented earlier.
It is convenient to be shown here again for the illustration. The QAP shows the number of
vehicles accumulated in a queue on a signalized approach over one cycle of operation. Each
cycle is assumed to repeat the same pattern indefinitely. The number of vehicles accumulated
at any time in the cycle may be determined as the difference between the cumulative arrivals
and departures since the start of the cycle.
The queue accumulation increases throughout the red phase at the rate ofq, veh/sec.
The maximum accumulated queue occurs at the end of the red phase, and is indicated on
Figure 3-2 as Q. During the green phase, the queue decreases at the net departure rate, (s -
q), until it has been fully serviced. The time required to service the actual queue is indicated
on Figure 3-2 is g. The green phase will continue until the occurrence of a gap in the arriving
traffic of sufficient length to cause the controller to terminate the phase. The effective
extension time is indicated on Figure 3-2 as g,. Of course, this whole process is subject to
a specified maximum phase time. An analytical model for predicting g,, g& and average phase
time, PT, was presented in the preliminary methodology. In this simple case, the queue
accumulation polygon is just a triangle. In the remainder of the cases to be discussed in this
dissertation, the QAP will assume a more complex shape.
Figure 3-2. Queue accumulation polygon for a single protected phase.
Permitted Left Turns from Exclusive Lanes
The basic QAP concept may be extended to cover a slightly difficult case in which
a permitted left turn is from an exclusive lane, yielding to oncoming traffic, instead of a
protected movement. This introduces a couple of important changes in the QAP. Since the
number of opposing lanes, np, may influence the net arrival rate during the period when the
opposing queue is being serviced, it will be considered for the permitted left turns form
opposing queue is being serviced, it will be considered for the permitted left turns form
exclusive lanes. Based on the number of opposing lanes, the QAPs for condition 1 (nW, > 1)
and condition 2 (np = 1) shown in Figures 3-3 and 3-4 are discussed, respectively.
If the number of opposing lanes is greater than one (see Figure 3-3), the queue
continues to accumulate throughout the first part of the green with the arrival rate of q, while
the opposing queue is being serviced. The time required to service the opposing queue is
indicated on Figure 3-3 as gq. There is no chance for a permitted left turner to make a
maneuver during the period ofgq. The maximum queue, indicated on Figure 3-3 as Qq, can
be computes as follows:
Qq Q +qg *gq (3-4)
If the number of opposing lane is equal to one (see Figure 3-4), the left turns from the
opposing lane do create the chance for the left turns from the exclusive left turn lane to make
maneuvers. According to the HCM Chapter 9, the adjusted saturation flow rate, s,, during
the period ofgq can be computed using the following formula:
sq = / EL2 (3-5)
sq = the permitted saturation flow rate during the period of g;
s = the protected saturation flow rate; and
E, = the left turn equivalence as determined from Equation 9-22 in the HCM.
the queue continues to accumulate throughout the period of g with the net green arrival rate
of (q sq) while the opposing queue is being serviced. The maximum queue, indicated on
Figure 3-4 as Qq, can be computes as follows:
Qq = Q + (q s,) *gq (3-6)
Thereafter, the LT vehicles will filter through the opposing traffic at a rate determined
by the opposing volume. This is indicated on Figures 3-3 and 3-4 as the permitted saturation
flow rate, Sp. The net departure rate is shown as the difference between the permitted
saturation flow rate and the green arrival rate, which is equal to (s,- q.). Fortunately, the
HCM Chapter 9 worksheets already provide the means to compute these values. The value
of gq is determined explicitly on the supplemental worksheet for permitted left turns. The
value of permitted saturation flow rate, s,, may be determined as
s, = s / EL (3-7)
s, = the permitted saturation flow rate;
s = the protected saturation flow rate; and
ELI = the left turn equivalence as determined from Figure 9-7 in the HCM.
Figure 3-3. Queue accumulation polygon for a permitted left turn from an exclusive
lane with opposing lane number greater than one.
.B Qr q sq5
I I s-
s 1 i q8
o qr Iq
Figure 3-4. Queue accumulation polygon for a permitted left turn from an exclusive
lane with opposing lane number equal to one.
Green Time Extension for Permitted Movements
The model for estimating the effective green time extension, g, assumes that the
arrivals after the queue has been serviced will be free-flowing as they cross the detector. This
will not be the case for permitted left turns. A complex stochastic model would be required
to treat this situation in detail
It should, however, be possible to use the left turn equivalence, ELI, described above
as an approximation in this situation. In other words, the equivalent through volume, VL EL,
would be used in place of the actual left turn volume, VL The green extension time must be
determined using an equivalent through volume of(VT + VLELI) in place of the actual volume
of (VT + V).
Effect of Sneakers
Sneakers are permitted LT vehicles that exit the intersection at the end of the green
phase, usually during the intergreen interval It is common to assume that a maximum of two
vehicles per cycle may be released from the queue. Sneakers are treated implicitly in the
Chapter 9 worksheets by imposing a lower limit of two vehicles per cycle on the capacity of
each exclusive LT lane with permitted movements. For purposes of this analysis, sneakers
must be recognized explicitly in the QAP. This requires the definition of some new terms:
Maximum Sneakers, Sm: The maximum number of LT vehicles released at the end
of the green phase assuming that the LT queue has not already been serviced.
Permitted phase terminal queue, Qp: The number of vehicles accumulated at the
end of the permitted phase before sneakers have been released.
Adjusted permitted phase terminal queue, Qp: The number of vehicles accumulated
at the end of the permitted phase after sneakers have been released.
Actual Sneakers, Sa: The actual number of sneakers released at the end of the green
phase. This is determined as Min (Sm, Qp).
For the purpose of illustration, the effect of sneakers on the QAP for the condition,
np > 1, is shown in Figure 3-5. This illustrates the case in which the phase is terminated by
the maximum green time before the queue of LT vehicles is completely serviced. If Qp is
greater than zero, then the maximum phase length will be displayed as a pretimed equivalent.
The adjusted permitted phase terminal queue, Qp', is equal to Qp minus Sa. If Qp is greater
than zero, then the v/c ratio for the approach will be exceeded. These parameters will be
involved in a more complex way in the analysis of compound left turn protection.
I Qr ... / Sp-qg
Figure 3-5. Queue accumulation polygon for a permitted left turn from an exclusive
lane with sneakers.
IfLT vehicles are accommodated in an exclusive lane, it is reasonable to assume that
there will be additional lanes available to handle the through traffic. It is also expected that
the detectors installed in both the through and left turn lanes will activate and extend the same
phase. Under these conditions, the queue service time, g,, for the through and LT lanes will
be different. The required phase time (RPT) is the sum of lost time (t), effective extension
time (g = g + I t, ) and the maximum value of through queue service time, g, (= g), and
left turn queue service time, gq,(= g + g,):
RPT = Max ( Through gq, Left turn g,) + t, + g (3-8)
and eg must be determined using an equivalent through volume of(VT + VLEL) in place of the
actual volume of(VT + VL).
Shared Lane Permitted Left Turns
The shared lane permitted left turn case is only slightly more complicated than the
exclusive lane permitted left turn case. The additional complication may be seen in the QAPs
shown in Figures 3-6 and 3-7. The concept of free green, g,& must be introduced here. In an
exclusive left turn lane, the first vehicle in the queue will always be an LT vehicle. However,
in a shared lane, the first vehicle could be either a through or LT vehicle. The portion of
effective green blocked by the clearance of an opposing queue is designated as gq. During the
time, an LT vehicle may be stopped by the opposing traffic, but a through vehicle will not.
Until the first left-turning vehicle arrives, however, the shared lane is unaffected by left
turners. The free green represents the average green time from the beginning of green that
will be available to move through vehicles in the shared lane. The Chapter 9 supplemental left
turn worksheets provide a method for computing gq and gf As indicated on Figures 3-6 and
3-7, there will be a net discharge rate of(s q) during the free green interval, and the queue
remaining at the end of the interval is represented as Q,
The computation for queue service time, gq, is more complicated for a shared lane
than that for an exclusive left turn lane or through lane. Basically, the gq for a shared lane
can be divided into two parts. One is the green time before the beginning of the actual queue
service time (g&), and the other one is g, itself
In Figure 3-6, since g, is greater or equal to g,, the gq, is just equal to the sum of g
and g, Note that according to the HCM Chapter 9, Q, can be computed based on the number
of the opposing lanes. The detail description for the computation of Qq is in the HCM
Chapter 9. Figure 3-7 represents the scenario that gq is less than gf. The accumulated queue,
Q, which belongs to through vehicles, will be served at a net service rate of(s qa). Assume
the time to clean all of these accumulated through vehicles is designated as &. Ifgf is less than
g, then gqg, will equal the sum ofgf and g&. On the other hand, ifgr is greater or equal to go
then g just equals g, because g, is zero for this condition. The time to clear all accumulated
through vehicles, g, may be represented by Equation 2-6. The computation for gq, may be
summarized as the following equations. If g is greater than or equal to g, the queue service
time, gq can be computed as
g& = gq + gs (3-9)
Ifgq is less than g, the formula for the computation of the queue service time, g, becomes
gst = gf + g when g,<&g (3-10)
gqst = gt when gf&g& (3-11)
The remainder of Figures 3-6 and 3-7 follows the same process as the exclusive lane
cases shown in Figure 3-3 and 3-4. The permitted movement saturation flow rate for the
shared lane must, however, be computed somewhat differently. In an exclusive LT lane, the
left turn equivalence, EL, was applied to all of the vehicles in the LT lane. In a shared lane,
it is only appropriate to apply this factor to the LT vehicles. So, s, should be computed as
sp 1 + PL(EL 1) (3-12)
PL = the proportion of left turns in the shared lane, as computed by the supplemental
worksheet for permitted left turns, and all other terms are as defined previously.
eg should be computed in the same manner as described for the exclusive LT lane case and
using an equivalent through volume of (V, + V, EI) instead of the actual volume.
o qr Qf
1 s I P-qg
Figure 3-6. Queue accumulation polygon for a permitted left turn from a shared lane
Figure 3-7. Queue accumulation polygon for a permitted left turn from a shared lane
Compound Left Turn Protection
The QAP concept may be extended to cover the case in which an LT movement
proceeds on both permitted and protected phases from an exclusive lane. One important
difference between the simple permitted LT phasing and the compound protected LT phasing
is the assignment of detectors to phases. It is assumed that detectors will be installed in all
LT lanes to ensure that LT vehicles will not face a permanent red signal. The discussion of
simple permitted LT phasing assumes that the detector in the LT lane (either shared or
exclusive) will actuate the same phase as the concurrent through traffic. On the other hand,
it is logical to assume that a protected left turn will have a detector that actuates the protected
left turn phase. This has very important implications for the analysis of compound left turn
protection. It means that LT vehicles will not extend the permitted phase. When they occupy
the detector during the permitted phase, they will simply be placing a call for their own
protected phase. In the analysis of compound left turn protection, it is necessary to make a
strong distinction between protected plus permitted (leading), and permitted plus protected
(lagging) left turn phasings. Each of these cases will be analyzed separately.
Protected Plus Permitted Phasing
The QAP for protected plus permitted phasing is presented in Figure 3-8. In Figure
3-8, it is necessary to note that if the number of opposing lanes, n,, is greater than one, s,
will be equal to zero. Keep in mind that the QAP is used for the purpose of determining the
length of the protected phase only. The length of the permitted phase will be determined by
the simple process of its corresponding through phase because there are no permitted left
turns that actuate the detector. The The most important piece of information provided by
the QAP in this case is the size of the queue accumulated at the beginning of the green arrow,
Q0. With protected plus permitted phasing, this is equal to the queue at the end of effective
red time, Q, Given %Q, the determination of green time follows the simple procedure for
SQr = Qga
QP S \Is-qg
Figure 3-8. Queue accumulation polygon for protected plus permitted LT phasing with
an exclusive LT lane.
Permitted Plus Protected Phasing
This case is illustrated in Figure 3-9, which is essentially the same as Figure 3-8,
except that the order of the phases has been reversed. It is very important to note that the
protected (green arrow) phase must be presented last in both cases, because this is the phase
whose length we are trying to determine.
Again, it is needed to know the number of vehicles accumulated at the beginning of
the green arrow phase, Q., which is equal to Q'in this case. This will raise an interesting
question. Suppose that the value of Q9 is zero. This could happen if the permitted phase was
able to accommodate all ofthe left turns. Theoretically, the protected phase should never be
called under these conditions. However, there is a stochastic element which dictates that all
of the phases will be called occasionally. In this scenario, the adjusted minimum phase time
will be used to estimate the phase time for this protected phase.
|lf Q, g,..
Figure 3-9. Queue accumulation polygon for permitted plus protected LT phasing with
an exclusive LT lane.
The analysis presented in this chapter fills the gaps left in the preliminary
methodology. The complete analytical basis for a practical computational method to predict
traffic actuated signal timing are conducted. This method should be sensitive to a wide range
of actuated controller parameters. The QAP concept is especially attractive because it can
provide a clear picture for estimating the signal timing. Another essential benefit is that it can
also provide a direct estimate of the uniform delay that is compatible with the current HCM
Chapter 9 delay model The methodology presented in this chapter will be incorporated into
the computational framework described in the preliminary model structure to develop a
complete model implementation for predicting the signal timing at a traffic-actuated signalized
intersection. The model implementation and model evaluation will be presented in the next
two chapters, respectively.
A specific analysis program, ACT3-48, was developed by Courage and Lin in this
study as a tool to implement the developed analytical model and procedure to predict the
traffic-actuated signal timing. The original worksheets have also been modified in accordance
to the analytical modelto cover all possible movements described in Chapter 3. The ACT3-
48 program can produce intermediate outputs in a format identical to the modified
worksheets. The computer program is required because the iterative nature of the procedure
makes it totally impractical for manual implementation. The program is able to evaluate the
proposed analytical models using a variety of data. In this chapter, the computer program
structure and logic are presented.
The analytical model developed in this study is for isolated mode of actuated
operation. An effective method to predict the phase times for coordinated mode of actuated
operation is to apply the analytical model for isolated mode to predict the phase times of
actuated phases and then properly assign the unused phase times to the non-actuated phases
(arterial through movements). By appropriate implementation of the analytical model for
isolated mode, a procedure has been built to predict the phase times for coordinated mode,
which will also be addressed in this chapter.
Structure and Logic of the ACT3-48 Program
The major structure of the ACT3-48 program is shown in Figure 4-1. It is not
difficult to recognize an iterative loop inside the flow chart. The iterative loop is required to
make the cycle time converge to a stable value. The program structure is divided into six
major parts: 1) Data Input, 2) Lane Group Specification, 3) Accumulated Queue
Computation, 4) Extension Time Computation, 5) Required Phase Time Computation, and
6) Cycle Time Adjustments. These six parts will be addressed separately.
The data input for the ACT3-48 program is from the WHICH program, which not
only has a user-friendly input scheme, but also provides sufficient information for actuated
operations. After the data is input, the ACT3-48 program can be executed from WHICH to
process these data and compute phase times.
In the "control specification" shown in Figure 4-1, control treatments are determined
first according to the input data. These treatments include left turn types (protected,
permitted or compound protection), phase swaps and overlaps. In addition, a left turn
equivalence, ELi, is computed. Finally, the phase sequence pattern is recorded.
The phase sequence pattern needs to get more attention because in each iteration, it
is required for the accumulated queue computation and phase time prediction. The
computation of most time elements such as g, r, gf and gq in the QAP are also based on the
phase sequence pattern. The initial phase pattern is from the input of WHICH. Due to the
dual-ring control logic, the phase sequence pattern may change during the iterative process.
Therefore, possible phase sequence patterns are required to be considered in the program.
Figure 4-1. Major structure of the ACT3-48 program.
There are eight possible cases of phase sequence patterns in all. For the purpose of
illustration, only the phase sequence patterns in the north-south direction are shown in figures.
Case 1 is a standard case for permitted turns which is shown in Figure 4-2. Case 2 is the
phase sequence for leading green which is shown in Figure 4-3. In contrast to Case 2, Case
3 is the phase sequence for lagging green which is presented in Figure 4-4. Case 4 shown in
Figure 4-5 is the phase sequence for leading and lagging green. Case 5 is a left turn phase
with leading green which is shown in Figure 4-6. Case 6 is leading dual left turns, and Case
7 is lagging dual left turns. Cases 6 and 7 are shown in Figures 4-7 and 4-8, respectively. In
Cases 6 and 7, the phases for dual left turns will terminate simultaneously. Finally, Case 8
shown in Figure 4-9 is leading and lagging with dual left turns. Case 4 and Case 8 are
interchangeable. For example, when the volume of northbound left turn volumes are heavy
and through traffic is light, Case 4 may become Case 8.
Figure 4-2. Case 1: Phase sequence for simple permitted turns.
Figure 4-3. Case 2: Phase sequence for leading green.
Figure 4-4. Case 3: Phase sequence for lagging green.
Figure 4-5. Case 4: Phase sequence for leading and lagging green.
Figure 4-6. Case 5: Phase sequence for LT phase with leading green.
Figure 4-7. Case 6: Phase sequence for leading dual left turns.
Figure 4-8. Case 7: Phase sequence for lagging dual left turns.
Figure 4-9. Case 8: Phase sequence for leading and lagging with dual left turns.
In "actuated parameter specification", the actuated parameters are specified based on
each NEMA phase which was defined in Chapter 2. The actuated parameters consist of
minimum initial, maximum initial, minimum phase time, maximum green time, allowable gap
recall, detector configuration and so on. Based on the control specification and the actuated
parameter specification, Worksheet 1: Traffic-actuated Control Input Data can be produced
by the ACT3-48 program.
Lane Group Specification
In "lane group specification", the ACT3-48 program will determine the phase
movements for each NEMA phase and the lane group movement within each NEMA phase.
For example, ifa NEMA phase includes all left turns, through traffic and right turns, the phase
movement of this NEMA phase will be specified as "LTR". If a lane group within the NEMA
phase is just for through and right turns, it should be presented as "TR". The purpose for this
specification is to associate each of the lane group with its NEMA phase.
The lane group specification is convenient and necessary for later computation. For
example, the phase time computation for permitted left turn movement from an exclusive lane
("L") will be different from that for through and right turn movements ("TR"). In addition,
the ACT3-48 program will also determine the traffic volume (veh/hr), arrival rate (veh/sec),
saturation flow (veh/hr) and departure rate (veh/sec) for each lane group based on the input
data from WHICH. Worksheet 2: Lane Group Data is then generated.
Accumulated Queue Computation
In a new iteration, the most important step is to create a new queue accumulation
polygon (QAP). With the phase sequence pattern, phase times and other information from
the last iteration, the new QAP can be produced easily for simple through or protected
phases. It becomes more difficult in computation for permitted left turns from either an
exclusive or a shared LT lane and compound left turn protection because more information
is required before accumulated queues can be computed.
In the analytical model for permitted left turns from an exclusive lane, the opposing
queue service time, g, is needed for QAP. For the permitted left turns from a shared LT lane,
both gq and free green, gf are required. In the compound LT protection, an exclusive LT lane
is assumed, so gq must be obtained. Fortunately, the method for estimating g and gf has been
presented in HCM Chapter 9, which is used in this study to compute g and g. In the ACT3-
48 program, the computation of gq is based on 1994 version of HCM Chapter 9. Since the
computation of& is based on the length of green time in the latest HCM version which may
cause unreliable convergence of cycle length, the method presented in 1985 HCM Chapter
9 is used instead. Based on the number of opposing lanes, there are two scenarios described