IMPROVED STRATEGIES FOR TRAFFIC RESPONSIVE
CONTROL IN ARTERIAL SIGNAL SYSTEMS
MOHAMMED ABDUL HADI
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE
UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1990 uVMRSITY OF FLORIDA LIBRARIES
Many people have provided inspiration and encouragement
during the completion of this dissertation. I am grateful
for the suggestions and the assistance given by the members
of my supervisory committee.
In particular, I would like to extend deep thanks and
appreciation to the chairman of my committee, Professor
Kenneth G. Courage, for his inspiring ideas and for his
invaluable guidance and support. His calm and reasoned
approach to problem solving is a model which I need to
I would also like to express my appreciation to Dr.
Gary Long for his guidance and continued support during this
project and during my graduate study. My interaction with
him has been a most gratifying learning experience.
My sincere gratitude is extended to Dr. Charles E.
Wallace for his guidance and assistance. The time he
contributed toward my endeavors is greatly appreciated.
I would like to thank Dr. Joseph A. Wattleworth for his
guidance and for being my teacher for four years. He has
been a source of motivation for this work.
I extend my thanks to Dr. Dennis D. Wackerly for
agreeing to serve on my committee and for his assistance in
this work. His willingness to serve in Dr. Yang's absence
is greatly appreciated.
Dr. Mark Chao-Keun Yang served as the external member
of my committee until late 1989. His helpful assistance and
suggestions were greatly appreciated.
Special thanks are extended to Mr. Charles D. Jacks for
his help in the development of experimental versions of the
off-line signal timing programs and for his suggestions
regarding the modification to the permitted movement model
A note of thanks is due to Mr. Lawrence T. Hagen and to
Mr. William M. Sampson for their help in obtaining
additional outside data required for this research and for
I owe special thanks to Irma L. Smith and Gail
Luparello for their skillful and diligent typing and for
help in the preliminary editing of my dissertation.
My appreciation is also extended to Dr. Melvin Fried
for his assistance in the final editing of this work.
I am indebted to my mother and my family for their
patience and for supporting me in many ways during my
Finally, a very special thanks to my wife Nada. It has
not been easy starting a new life together under the
pressure of graduate school. I thank her for her
understanding, support and love, without which it would have
been much more difficult.
TABLE OF CONTENTS
ACKNOWLEDGMENTS . .
LIST OF TABLES . .
LIST OF FIGURES. . .
LIST OF ABBREVIATIONS. .
ABSTRACT . .
Need for the Research
Objective and Scope .
LITERATURE REVIEW. .
Basic Concepts of Signal Timing ..
Review of Computer-Based Traffic
Control Strategies ..
Timing Plan Selection in First
Generation Control ..
Estimation of Nondetectorized Flows .
Balancing Traffic Counts. .
DEVELOPMENT OF A THRESHOLD SELECTION MODEL
BASED ON ESTIMATED VARIATION. .
Introduction. . .
Data Requirements . .
Reference Volume Calculation. .
Simulating Different Traffic Con-
ditions in the System .
Estimated Variation Model ..
Threshold Determination .
DEVELOPMENT OF A THRESHOLD SELECTION MODEL
BASED ON ASSUMED VARIATION. .
Introduction. . .
Assumed Variation Model .
Threshold Determination .
Application of the Threshold Selection
Model Based on the Estimated and
the Assumed Variations .
INVESTIGATIONS OF PROBLEMS IN OFF-LINE
SIGNAL TIMING PROGRAMS .
Introduction . .
Problems Associated with TRANSYT-7F .
Problems Associated with the Arterial
Analysis Package . .
Problems Associated with the PASSER-II
Program. . .
CONCLUSIONS AND RECOMMENDATIONS. .
Conclusions . .. ..
Recommendations . .
DERIVATION OF THE LEAST SQUARES
ADJUSTMENT MODEL .... .
ESTIMATION OF THE PARAMETERS IN MULTIPLE
LINEAR REGRESSION MODELS .
AN ALTERNATE METHOD FOR OBTAINING THE
WEIGHT MATRIX IN LEAST SQUARES
ADJUSTMENT ............. .
BIBLIOGRAPHY . . .
BIOGRAPHICAL SKETCH. ..................
LIST OF TABLES
3.1 The Estimation Equations for the Non-
detectorized Approach Volumes on
the Four-Intersection Hypothetical
Artery. . .. 79
3.2 The Effect of Changing the Cycle Length on
the PI of the Hypothetical Artery
Determined Using the Estimated
Variation Model . .. 89
3.3 The Cycle Transfer Thresholds Determined
Using the Estimated Variation Model
for the Hypothetical Artery 91
3.4 The Effect of Changing the Offset Plans,
Designed Using PASSER-II, on the
Performance of the Hypothetical
Artery for the 125-Second Cycle 95
3.5 The Effect of Changing the Offset, Designed
Using TRANSYT-7F, on the PI of the
Hypothetical Artery Determined Using
the Estimated Variation Model 104
3.6 Offset Transfer Thresholds Determined for
the Hypothetical Artery Based on the
Estimated Variation; the Offsets Were
Designed Using TRANSYT-7F ... 105
3.7 The Effect of Changing the Split Design
on the PI of the Hypothetical Artery
Determined Using the Estimated
Variation Model . 110
3.8 Split Transfer Thresholds, Determined for
the Hypothesized Artery Based on the
Estimated Variation .. .. 111
4.1 The Estimation Equations for the Volumes
on the Nondetectorized Approaches of the
Lexington Artery. . ... 123
4.2 The Effect of Changing the Cycle Length
on the PI of the Lexington Artery
Determined Using the Estimated
Variation Model . .. 128
4.3 The Cycle Transfer Thresholds Determined
Using the Estimated Variation Model
for the Lexington Artery. . 129
4.4 The Effect of Changing the Offset Design
on the Performance of the Lexington
Artery Determined Using the Estimated
Variation Model .. .. 130
4.5 Offset Transfer Thresholds Determined Using
the Estimated Variation Model for the
Lexington Artery . 131
4.6 The Effect of Changing the Cycle Length
on the PI of the Lexington Artery
Determined Using the Assumed
Variation Model . .. 133
4.7 The Cycle Transfer Thresholds Determined
Using the Assumed Variation Model for
the Lexington Artery. . 134
4.8 The Effect of Changing the Offset Design
on the Performance of the Lexington
Artery Determined Using the Assumed
Variation Model . ... 135
4.9 Offset Transfer Thresholds Determined
Using the Assumed Variation Model for
the Lexington Artery .. .. 136
5.1 A Comparison Between the Results Obtained
from a Quick Cycle Evaluation and
Those Obtained from Normal Optimi-
zation Runs Using TRANSYT-7F,
Release 6 . .. 141
5.2 A Comparison of the Results Obtained Using
the Two Experimental Versions of
TRANSYT-7F with Those Obtained Using
the Existing Version of TRANSYT-7F and
the Trial and Error Procedure 148
5.3 A Comparison Between the Results Obtained
from a Quick Cycle Evaluation and
Those Obtained from Normal Optimi-
zation Runs Using the T7F245 Version
of TRANSYT-7F. .. .. 149
5.4 A Comparison Between the Measures of
Effectiveness for Two Values of the
Upstream Flow Rate at a Given Down-
stream Flow Obtained Using TRANSYT-7F 154
LIST OF FIGURES
2.1 A time space diagram illustrating the
signal progression control concept
for arterial streets. . 12
2.2 The basic configuration of a UTCS System 15
2.3 The basic configuration of a closed loop
system. . .. 17
3.1 Simulating different traffic conditions
in an arterial system ...... 53
3.2 An east-west artery for which the turning
movement volumes have to be adjusted. 61
3.3 The adjustment of the turning movement
volumes on a two-intersection arterial
system in Gainesville, FL .. 68
3.4 The hypothetical artery layout, phase
sequences, and system sensor locations. 76
3.5 The estimation of the nondetectorized
volumes in.the four-intersection hypo-
thetical artery using the estimated
variation model . 82
3.6 The Platoon Progression Diagram for the
hypothetical artery with heavy inbound
volume under a heavy inbound progression
design and 125-second cycle ...... 96
3.7 The Platoon Progression Diagram for the
hypothetical artery with heavy inbound
volume under a balanced progression
design and 125-second cycle ...... 97
3.8 The Platoon Progression Diagram for the
hypothetical artery with a heavy inbound
volume under a heavy outbound progression
design and 125-second cycle .. 98
3.9 The Flow Profile Diagrams of the inbound
approach to the second intersection
under two PASSER-II designs .. ..101
3.10 The Platoon Progression Diagrams for a
two-intersection artery with balanced
volume and under-saturated conditions
under TRANSYT-7F and PASSER-II
designs . .... .. 102
4.1 Estimating the link volumes for an arterial
system using the assumed variation
model . . 117
4.2 The location of the system sensors in the
nine-intersection Lexington artery. 120
4.3 The link volume on the Lexington artery
for period 1300 before and after the
adjustment. . ... 122
5.1 An illustration of the effect of the
problem in TRANSYT-7F adjustment of the
upstream flow on the flow profile
diagram of a link . .. 152
C.1 The adjustment of the turning movement
volumes for a two-intersection arterial
system in Gainesville, FL, using the
alternate method of calculating the
weight matrix . .. 181
LIST OF ABBREVIATIONS
= Arterial Analysis Package
= Arterial Volume Level
= Computer Based Traffic Control System
(Translated from French)
= TRANSYT-7F CHKINP Subroutine
= Cross Street Arterial Volume Differential
= Federal Highway Administration
= FORECAST Program
= Flow Profile Diagram
= Graphic Display File
= TRANSYT-7F HILLCL Subroutine
= TRANSYT-7F INPTRN Subroutine
= Intelligent Signal System
= Inbound Outbound Volume Differential
= Low Limit of Arterial Volume Level
= Microcomputers in Transportation University
= TRANSYT-7F Measures of Effectiveness
= Optimization Policy for Adaptive Control
= Progression Analysis and Signal System
Evaluation Routine, version Two
= 1980 Version of PASSER-II program
= 1984 Version of PASSER-II program
= 1987 Version of PASSER-II program
= TRANSYT Performance Index
= Platoon Progression Diagram
= PROgression Graphic and Optimization Program
= Statistical Analysis System
= SAS Interactive Matrix Language
= Sydney Coordinated Adaptive Traffic
= Signal Control of Isolated Intersections
= Split Cycle and Offset Optimization Technique
= Traffic SIGnal Optimization Model
= Signal Operation Analysis Package
= Signal SysTem Optimization Package
= TRANSYT-7F SUBPT Subroutine
= Time of Day Selection of Timing Plans
= TRaffic Network StudY Tool
= TRaffic Network StudY Tool, Version 7
= TRaffic Network StudY Tool, Version 7, Federal
= Transyt 3800 Closed Loop System
= Traffic Responsive Selection of Timing Plans
= Traffic Responsive and Uniform Surveillance
= Time-Space Diagram
= T7F145 Experimental Version of TRANSYT-7F
= T7F245 Experimental Version of TRANSYT-7F
= Upper Limit of Arterial Volume Level
= Urban Traffic Control System
= Urban Traffic Control System, First Generation
= UTCS First and Half Generation Control
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
IMPROVED STRATEGIES FOR TRAFFIC RESPONSIVE
CONTROL IN ARTERIAL SIGNAL SYSTEMS
Mohammed Abdul Hadi
Chairman: Kenneth G. Courage
Major Department: Civil Engineering
Several types of real-time traffic responsive control
strategies have been developed to select signal timing plans
on-line. The goal has been to improve the traffic
performance through implementation of plans which are more
suited to prevailing traffic conditions. One type of such
strategies uses preset transfer thresholds to select signal
timing plans from a restored library. These thresholds are
currently specified by judgment.
This dissertation proposes a methodology for deter-
mining the transfer thresholds for a traffic responsive
control strategy. The basic technique used is to evaluate
each signal timing design under a range of traffic con-
ditions using TRANSYT-7F. A design is selected for
implementation under a given traffic condition if it
produces the lowest TRANSYT-7F performance index compared to
the other designs. The methodology requires estimation of
the turning movement volumes in the system based on detector
measurements. Two models are developed for the purpose of
Problems are identified by the off-line signal timing
programs used in this study. These programs are AAP,
TRANSYT-7F, and PASSER-II. Since these problems affect
threshold determination, an investigation of the problems is
The application of the methodology proposed in this
study to the determination of transfer thresholds should
improve the system operation by replacing the element of
judgment by a more objective technique. In addition,
solving the problems identified by the off-line signal
timing programs would improve the performance of these
An urban traffic control system is typically designed
around a central computer which communicates by one of
several means with individual intersections which are coor-
dinated within the system. Detector and display information
are received from the field and commands of one kind or
another are returned to the field. The central computer may
vary in size from a simple personal computer to a full-scale
Microcomputer based traffic control systems have become
very popular in the United States. They are less expensive
to install and operate than the more complex centrally
controlled systems of the past decade. The use of personal
computers with dial-up telephone communications provides a
cost-effective method of supervising a large group of traf-
fic signals. The traffic control industry uses the term,
"closed loop system" as a generic reference to this concept.
In the broad terminology of computerized traffic control,
they are classified as "First Generation Systems" because
they use a library of timing plans which were developed
There are four basic operating modes for these systems:
1. The Free Running mode, in which all intersections,
operate independently, typically used only under late-night,
2. The Time of Day or TOD mode, in which all inter-
sections are coordinated based on timing plans which are
switched at specific times of the day to accommodate known
variations in traffic patterns.
3. The Traffic Responsive mode, usually denoted by
TRSP, which is similar to the TOD mode except that timing
plans are switched in response to measured traffic condi-
4. The Manual mode, in which timing plans are
switched by the system operator.
There is a certain amount of theory and probably an
equal amount of practical judgment which apply to each of
these modes. In the case of the TRSP mode, excessive prac-
tical judgment is required because of inadequate theoretical
support. The development of a model to strengthen the
theoretical basis for TRSP operation is the subject of this
Need for the Research
The ultimate objective of the traffic control engineer
is to utilize urban street networks efficiently through the
use of effective control strategies. One of the most im-
portant steps in achieving this goal is the development of
computer-based traffic control systems. In those cities
where computer based controls have been installed, traffic
flow and operational efficiency have improved, and both fuel
consumption and air pollution have been reduced (1,2).
Among the different forms of computer control, first
generation control systems are the most commonly implemented
because of their lower installation, maintenance and operat-
ing costs, together with their proven effectiveness (3,4).
First generation control involves signal timing plans
developed off-line by one of the optimization models and
stored in computer memory as a timing plan library. The
plan controlling the traffic system can then be selected on
the basis of TOD, manual, or TRSP (3,5).
Because of day-to-day fluctuations in traffic patterns,
traffic responsive control strategies are expected to pro-
vide a better match of plan-to-traffic conditions than sim-
ple TOD selection provides. However, TRSP strategies are
considerably more expensive to implement than TOD strate-
gies. TRSP requires the installation of detectors that are
capable of providing an early identification of traffic
trends within the system (6). In addition, it requires the
transmission of detector information to the control com-
puter. This increases the communication cost. Thus, the
primary requirement of any traffic responsive strategy is
that it must provide better performance than off-line meth-
At the present time, there are several limitations to
traffic responsive strategies which reduce their effective-
ness. Although the timing plan design models, such as
TRANSYT-7F1 (TRAffic Network StudY Tool, version 7, Feder-
al) (8) and PASSER-II (Progression Analysis and Signal
System Evaluation Routine, version Two) (9), are adequate
and can create an acceptable timing plan library, there are
still problems associated with the implementation of these
timing plans in a traffic-responsive mode.
Generally, the TRSP timing plan selections in First
Generation Control (1GC) are of two types. In the first
type, the timing plans are selected based on the value of a
comparison function. The function is calculated based on
detector measurements and compared with restored values to
determine which plan should be implemented. The timing plan
selection in the Urban Traffic Control System first genera-
tion control (UTCS-1GC) is an example of this type of selec-
tion (5). In the second type, preset transfer thresholds
are employed to decide which timing plan should be selected
for implementation. This type of timing pattern selection
is used in some types of closed loop systems (3). Several
areas of potential improvement can be suggested for both
types of timing plan selection.
lIn this dissertation the word "TRANSYT" refers to the
TRaffic Network StudY Tool (TRANSYT) often followed by an
extension (e.g., "-T7F") to indicate a specific version.
"Transyt" refers to the Transyt Corporation which manufactures
a closed loop traffic control system.
Currently, the timing plan change thresholds are speci-
fied by judgment in those systems that employ thresholds in
timing pattern selection. No research has been done in the
area of threshold determination.
Any signal timing plan selection strategy (on-line or
off-line) tries to achieve a certain objective when select-
ing the plans. This objective varies from one strategy to
another. For example, it could be maximizing the progres-
sion efficiency or minimizing delays and stops. The engi-
neering judgment is not enough to decide the timing plans
that are capable to achieve this goal. Thus, the thresholds
should be selected through some objective technique. The
use of judgment to select thresholds may give rise to the
selection of plans which are not the best for the conditions
measured through the traffic detection system.
There exists, therefore, a clear need for the develop-
ment of models to improve the timing selection of the TRSP
control in an arterial signal system.
Objective and Scope
The goal of this study is to improve the timing plan
selection process in computer based traffic control systems.
This study presents a methodology for determining the
transfer thresholds for the TRSP mode of operation of a
computer based traffic control system. This methodology
requires the estimation of the turning movement volumes in
the system based on detector measurements. For this
purpose, off-line signal timing programs should be used to
design signal timing plans for the TRSP operation and to
evaluate these plans. Problems have been experienced with
these off-line programs. It is thought that these problems
might affect the results obtained from this study.
This research deals primarily with coordinated traffic
signal systems on arterial highways. The models developed
are limited to recurring operations and normal weekday
variations in traffic flow. Thus, other timing plans based
on judgment may still be required for handling unusual
traffic conditions. In addition, the models developed in
this study require the availability of reliable field traf-
The specific objectives of the study are:
1. Review the literature with respect to subjects
which are pertinent to this study.
2. Develop models to estimate the turning movement
volumes at each intersection in the system based on detector
3. Develop a method to determine the thresholds for
switching between timing plans in a specific closed loop
system. The quality and quantity of detector information
available from a typical closed loop system are not adequate
to support a complex model of the operation. It is, there-
fore, not realistic to seek results which can be demonstrat-
ed to be globally optimum from a mathematical point of view.
A more realistic objective would be to improve the design
results by replacing the element of judgment by a more
objective technique based on system models.
4. Investigate probable problems and inconsistencies
in those off-line signal timing models which are used in
preparing the timing plan libraries.
The models developed in this study should be based on
well developed theories. In addition, the off-line signal
timing models used for design and evaluation of timing plans
are among those most accepted by the traffic engineering
There are some operational differences between dif-
ferent closed loop systems. The models described herein are
generic in nature to the extent possible. The application
of these models must, however, be tailored to a specific
type of system. The system chosen for this study was the
system which has been installed in Gainesville, FL. This
system is a Transyt 3800 closed loop system. This is the
predominant type of closed loop system used in Florida. The
University of Florida Transportation Research Center has a
terminal linked to the Gainesville system operating in its
Traffic Control System Laboratory.
This dissertation is structured according to the objec-
tives stated earlier. The next chapter consists of a review
of the literature that is pertinent to this study. First
the different types of computer based traffic control
strategies are discussed. Then, a review of timing plan
selection in 1GC is presented. Next, a literature review of
the estimation of nondetectorized traffic volumes and the
balancing of input/output flows in a system is presented.
All of these subjects are pertinent to the models developed
in this study.
Chapter Three presents a method for obtaining the
transfer thresholds using an estimated variation model to
determine the turning movement volumes in the system from
Chapter Four presents an assumed variation model as a
simplified alternative to the estimated variation model.
The use of this model in the transfer threshold determina-
tion is also discussed.
Chapter Five investigates some of the problems experi-
enced with the off-line signal timing models used to design
and evaluate the signal timing plans in this study. Some of
those problems were addressed in experimental versions of
Finally in Chapter Six are the conclusions and recom-
mendations obtained from this study. The conclusions
summarize the findings. The recommendations include four
areas: improvements in the TRSP strategy investigated,
further improvements in threshold determination methodology,
treatments of problems identified in the off-line programs,
and further research required for the TRSP selection of
Basic Concepts of Signal Timing
A basic understanding of the concepts of signal timing
is a prerequisite to the discussion presented later in this
The concepts of signal timing are well documented in
the literature. Some of the basic definitions are presented
below for convenient reference (3).
Cycle length. The number of seconds required for a
signal to display its entire sequence of indications and
return to its starting point.
Interval. A discrete portion of the signal during
which the signal indications (pedestrian or vehicle) remain
Offset. The time relationship expressed in seconds or
percent of cycle length, determined by the difference be-
tween a system time reference point and a specific interval
in the sequence.
Phase. The portion of a signal cycle allocated to any
single combination of one or more traffic movements
simultaneously receiving the right to proceed, subject to
other rightful movements, during one or more intervals.
Sequence. A predetermined order in which the phases of
a cycle occurs. Some controller units have skip-phase
capability. Full actuated traffic control provides an
example of skip-phasing. In this type of control, it is
possible to skip phases when no traffic is present and to
terminate certain movements as soon as the traffic on that
movement has been moved into the intersection.
Split. The percentage of a cycle length allocated to
each of the various phases in a single cycle. In pretimed
controls, the splits are fixed, while in actuated controls,
the splits are adjusted continuously in accordance with
The traffic flow control concept for arterial streets
can be represented graphically by a technique known as a
time space diagram as shown in Figure 2.1. A time space
diagram is a two-dimensional representation of (a) the
spacing of the various intersections along the artery, and
(b) the signal indications at each of these intersections as
a function of time.
In the diagram, a "band" of green time is propagated
through the system such that vehicles traveling within its
limits progress throughout the system without being stopped.
A through-band is defined as the time between a pair of
parallel speed lines which delineates a progressive movement
in the diagram. The bandwidth is defined as the width of
the through-band in seconds indicating the period of time
LI Ua LI
II I I II
Figure 2.1. A time space diagram illustrating the signal
progression control concept for arterial streets.
available for traffic to flow within the band. Wider bands
produce better operations as perceived by the drivers.
Review of Computer Based Traffic Control Strategies
Strategies for the on-line computer-based control of
traffic signals have become increasingly important in recent
years. Several types of computer--based traffic control
systems have been developed and implemented throughout the
world. Experiences with these systems have demonstrated
their capability to produce considerable improvements in
traffic operations (10).
The discussion presented in this section is organized
such that the 1GC strategies which have a lower degree of
traffic responsiveness among the real-time traffic control
strategies are discussed first. Then the attempts to
develop strategies with higher degrees of traffic respons-
iveness are discussed.
As mentioned in Chapter One, several computer based
traffic control systems can be classified as 1GC.
UTCS-1GC2, and all types of closed loop systems can be
classified as 1GC.
The 1GC systems use restored traffic signal-timing
plans developed off-line and based on previously collected
2Different Urban Traffic Control System (UTCS) strat-
egies have been developed by the FHWA. Each strategy is
referred to as a generation. The higher the UTCS generation
number, the more it is responsive to traffic conditions.
All UTCS generations will be discussed later in this sec-
traffic data. Timing plans can then be selected on the
basis of TOD, operator selection or TRSP selection. In the
TRSP mode of operation, the timing plans are selected based
upon traffic conditions which are measured through a traffic
In the United States, the predominant on-line control
strategy has been that of the UTCS-1GC developed by the
Federal Highway Administration (FHWA) (1,5).
The UTCS-1GC performance was evaluated in Washington,
DC (11) and New Orleans, LA (12). In its various modes of
operation the UTCS-1GC performed better than a well-timed
UTCS is a centralized computer control system. Cen-
tralized systems are characterized by having all of the
decision-making and surveillance capabilities located at one
geographic point and on one level. The central computer
processes all data and controls all signal phases. The
basic configuration of a UTCS system is illustrated in
Figure 2.2. Problems such as limited capacity, high com-
munication cost, and low flexibility were identified with
such types of controls (13,14).
Closed loop systems have become very popular in recent
years. They avoid many of the problems associated with the
centrally controlled systems by using the decentralized
concept of control. In this concept (10,13), the control
logic and the surveillance capability are decentralized from
Closed Network Signal System Arterial Street
Figure 2.2. The basic configuration of a UTCS system.
NOTE: Communication links connect each local controller
in the closed network signal system with the
central computer. In this figure, only some of
these connections are shown for simplicity.
a geographic viewpoint and placed at various levels in
hierarchial organizations of surveillance and control func-
tions. The basic configuration of a closed loop system is
presented in Figure 2.3.
Although the original concept of closed loop systems
was developed in the mid-seventies, the technology available
at that time could not support it. However, it has become
more attractive with the rapid development in microcomputer
technology in the eighties.
A typical closed loop system consists of a central
computer, on-street microcomputer masters, two-way
communications, local controllers and subsystem detectors
(3,15). The role of the central computer in closed loop
systems is different from that in UTCS. In closed loop
systems, the tasks performed by the central computer are
reduced significantly. The central computer role is limited
to performing such functions as system monitoring, uploading
and downloading of data, and data base storage.
The on-street master has the ability to select one of
its stored signal timing plans. It then commands the local
controller to implement the pattern chosen. The local con-
troller units usually have time-base backup capability.
Continual on-line interconnection between the central
computer and the on-street master is not needed. Thus,
telephone dial-up or direct telephone lines can be used
between the two. However, a higher capacity mode of
Closed Network Signal System Arterial Street
The basic configuration of a closed loop
NOTE: Communication links connect each local controller
in the closed network signal system with the
central computer. In this figure, only some of
these connections are shown for simplicity.
communication is required between the master and local
Closed loop systems are applicable to a wide range of
geographic configurations such as arterials, grids, and
area-wide control. Some of the advantages of such systems
over the centralized systems are (10,13):
1. A reduction of the overall costs of the control
system by decreasing the communication cost. This is
because direct communication between the central computer
and local controllers requires the UTCS to depend on a
complex, more expensive dedicated communication system. In
closed loop systems cheaper modes of communication can be
used between the central computer and on-street masters.
2. An improvement of total system reliability by
making it insensitive to failures of a single decentralized
computer. The system is not dependent on one central com-
puter or central communications gear.
3. A greater capacity to handle real-time elements
(detectors, local controllers) that must be supervised or
4. An increase in the flexibility of the system
structure. The system design permits future expansion
without major modification to existing hardware.
Several types of closed loop systems have been devel-
oped in the 1980s. These systems differ from one another in
specific control and surveillance features (3). In spite of
their differences, all of them can be classified as 1GC
systems. In all types, the signal timing plan selection is
made from a restored library of signal timing plans.
Off-line optimization programs are used to generate
timing plans for the first generation control strategies.
There are two basic approaches for off-line optimization of
arterial timing: (a) minimizing overall delay and stops,
and (b) maximizing the bandwidth efficiency which is the
percentage of the cycle available for progression. TRANSYT-
7F and PASSER-II, the two programs described in this
section, are among the models most widely used for signal
timing optimization of arterial streets.
The TRANSYT model consists of two main parts (8).
1. A traffic flow model which is a deterministic
macroscopic time scan simulation. It simulates the traffic
flow in a given signal system to compute the performance
index (PI) for a given set of signal timings. The PI is a
weighted sum of stops and delays.
2. A hill-climbing optimization procedure which makes
changes to the signal timings and determines whether or not
the PI is improved. By adopting only those changes that
reduce the PI, the optimizer tries to find a set of timings
which makes the PI as small as possible, subject to the
limit placed on the process.
Although there is no guarantee that the global optimum
will always be found, TRANSYT-7F should always produce a
good signal timing plan.
PASSER-II (9) is a macroscopic optimization model based
on the maximal bandwidth efficiency principle. It provides
the best phasing sequence and offsets for maximal bandwidth
efficiency along the artery by minimizing the sum of inter-
ferences to the through bandwidths. The optimal cycle
length is determined by means of an exhaustive search of all
user-allowed values. Splits are calculated for minimum
delay at each intersection on the basis of a modified Web-
ster delay formula (16). The model also allows for varia-
tions in the overall progression speed and weighting of the
One of the problems associated with 1GC systems is the
high cost of preparing and updating timing plan libraries.
This results in the implementation of out-of-date plans
which may not be well-matched to the current flow patterns
(17). An UTCS control strategy referred to as UTCS first
and half generation control (UTCS-1.5GC) has been developed
to solve this problem. This strategy automates the timing
plan development task to the maximum extent possible. The
system regularly (e.g., every six months) tests the timing
plans that are being used against new plans calculated from
the automatically collected traffic volumes. When it
appears that traffic has changed to a point where a new plan
is warranted, the plan is developed and implemented using
the computer-aided techniques (18,19).
The new plan can be prepared using any timing plan
generator. FORCAST (20,21) is one of the programs that has
been used for this purpose. FORCAST executes quickly and
thus is well suited for on-line use. It performs an iter-
ative search for optimum timing plans over a range of cycle
lengths. In this process, each of the permitted cycle
lengths is examined and a best timing plan is developed
which corresponds to this cycle. The optimization logic
involves sequential threading of prescribed movements
through the network using a priority listing of demands to
be accommodated. During this process, FORCAST adjusts the
individual splits and offsets of the intersections so as to
accommodate best the defined movements which pass through
the network. FORCAST computes the cost associated with
stops and delay and selects the timing plan by choosing the
minimum cost solution.
It is possible to replace FORCAST by any timing plan
generator. For example, TRANSYT could be used if the com-
puter system has enough memory and the processor is of high
enough speed. Three programs were investigated for this
purpose (18). These programs were TRANSYT-7F, the traffic
SIGnal OPtimization model (SIGOP) and the Signal SysTem
Optimization Package (SSTOP). It appeared that TRANSYT-7F
was the most suitable program based on the quality of the
timing plans it produced and its insensitivity to errors in
the input data.
Several attempts have been made in different countries
to develop systems which have higher degrees of traffic
responsiveness than the 1GC and the UTCS-1.5GC strategies.
In these systems, the signal timing plans are generated on-
line based on detector measurements.
It was expected that these systems would produce better
results than 1GC, which selects the signal timing plan from
a library generated off-line, based on historical data from
another month, perhaps another year. However, many of the
attempts to develop such systems failed to produce good
results. In the United States, second and third generation
control strategies were developed and tested under the UTCS
research project conducted by the FHWA (1,5).
The second generation control strategy is a real-time
on-line control wherein timing plans are computed and imple-
mented periodically. This type of control is based on a
background cycle but provides for real-time computation of
timing plans. It utilizes a prediction model to predict
near-term changes in traffic conditions. These predictions
are then used in an optimization model to develop the timing
plan. The optimization model used is that of the SIGOP
The third generation control strategy was developed to
implement and evaluate a fully responsive on-line traffic
control system. The cycle length, offset and split timing
plan for each controller were permitted to vary from cycle
to cycle. The increased complexity of the second and third
generation control required additional detectors and more
computer time and memory compared to the 1GC. The evalua-
tions of the two strategies revealed that both were inferior
to the 1GC strategy and that the third generation control
seriously degraded traffic flow under almost all the condi-
tions for which it was evaluated (1,5). Thus, neither
strategy proved workable under the development budgets
provided and appeared to offer insufficient promise to war-
rant further FHWA investment at the time (19).
Several systems (22,23) were also designed and tested
in Great Britain, Canada, and Spain during the late sixties
and early seventies to move from the 1GC type of control
towards more flexible approaches which generate signal
timings in real-time. These attempts proved to give similar
or worse results than a well-optimized three-dial system
Lack of success in those early attempts in the United
States and in other countries has been related to a number
of factors which include (7,19,22)
1. Even the best methods of plan changing cause sig-
nificant transition delay, so frequent plan changing should
not be considered.
2. A prediction of traffic flow for several minutes
into the future is necessary when implementing those strate-
gies. The random variation in traffic makes this prediction
very difficult and some historical data are needed to help
identify trends. Large discrepancies were observed (occa-
sionally in excess of 50%) when comparing the performance of
the UTCS second- and third-generation predictors with actual
volumes over successive five-minute intervals.
3. When an unexpected event occurs, the response is
delayed by the historical element of prediction and the need
for a new plan.
4. Poor plans might be implemented due to faulty
detectors or unexpected events which cannot be corrected
until the next plan update.
5. In such systems, a large number of detectors has
to be installed and maintained. Detectors have proved to be
one of the less reliable components of many systems and the
installation and maintenance costs of the detection systems
In spite of the failure of these early attempts, the
work to develop new systems which are more responsive to
current traffic conditions has continued. Some of these new
systems use versions of the available off-line signal
optimization programs to calculate signal timing plans on-
line. Others adjust the signal timing in real-time,
responsive to changes in traffic conditions. CALIFE (24)
and Traffic Responsive and Uniform Surveillance Timing
System (TRUSTS) (25) are examples of the first type. Split,
Cycle and Offset Optimization Technique (SCOOT) (26), Sydney
Coordinated Adaptive Traffic (SCAT) (27) and Optimization
Policy for Adaptive Control (OPAC) (23) are examples of the
CALIFE is a system developed in France. This system
(24) utilizes a modified version of TRANSYT-7 to calculate
on-line the signal timings based on traffic flows derived
from a prediction model. Two modifications were made to
TRANSYT-7: (a) A preliminary cycle search was first made
in which no offsets and splits optimization was made. At
this stage, the green times are simply set to give equal
degrees of saturation on the critical links. (b) A
supplementary term was added to the performance index of the
TRANSYT-7 optimization procedure. This term, the transition
criterion, was meant to take the proximity of the new plan
into account in relation to the present one. In this man-
ner, the transition delay between successive plans was
Simulation results showed that significant savings can
be obtained with CALIFE compared to the classical 1GC.
TRUSTS is a microcomputer based on-line traffic control
system developed recently in Taiwan (25). The system offers
the user the choice of on-line timing plan generation, on-
line timing plan selection or time-of-day timing plans. The
on-line timing plan generation uses a modified version of
TRANSYT-7F, a maximum progression bandwidth program
(BANDTOP) or a combination of both programs.
Two traffic responsive systems with a high level of
traffic adaptability are currently employed for daily use in
a number of cities. These two systems, SCOOT and SCAT, were
developed in Great Britain and Australia, respectively. The
two systems implement frequent but small changes in cycle
time, phase splits, and offsets to cope with the rapid fluc-
tuations of traffic demand. Both methods abandon the pre-
diction of traffic flow as a mean of controlling traffic.
SCOOT (26,27) is similar to the TRANSYT program in the
principle of optimization. A fundamental component of
TRANSYT is the traffic flow profile. SCOOT uses information
from vehicle detectors to obtain the profiles in real time.
Together with preset saturation flows and link travel times,
these profiles are used to predict the queues at the down-
stream intersection. SCOOT operates groups of adjacent
intersections on a common cycle time. The signal optimizer
adjusts the signal timings in small steps to reduce the
total delay and stops in the system (26). Also, there are
special procedures in SCOOT to deal with congestion. The
SCOOT system has been tested and evaluated in a number of
field trials. The trials show that, on average, SCOOT
reduces the delay to vehicles by 12% when compared to fixed
time control using up-to-date plans calculated employing
The most important parameter used by the SCAT algorithm
(27,28) is one analogous to the degree of saturation. It is
defined as the ratio of the effectively utilized green time
to the total available green time. In this system, the
cycle length is updated each cycle in steps of up to six
seconds according to the degree of saturation of the system.
To select green split plans, once per cycle, a split plan
vote based on the degree of saturation is calculated. Two
votes for the same plan in any three consecutive cycles
result in the selection of the plan. The offsets are also
selected based on an offset plan vote which is based on
directional splits of traffic flow. SCAT was found to
result in similar performance to fixed-time control in
travel time, but was 9% better in stops in the total survey
period (27). The field surveys conducted indicated that
there are periods during which fixed-time control actually
performed better than either SCAT or SCOOT (27).
OPAC is a real-time demand-responsive system developed
in the United States. The system was designed with a high
degree of adaptiveness to traffic conditions (23). The
real-time optimization procedure in OPAC is based on a
"pseudo-dynamic programming technique." The optimization
process is divided into sequential stages of time intervals
(in the range of 50 100 seconds). During each stage there
is at least one signal change (switch-over) and at most
three switch-overs. Then, an objective function (total
delay) is evaluated sequentially for all feasible switching
sequences and the optimal sequence is selected. Simulation
testing of the OPAC strategy showed that it is capable of
providing better performance than other forms of signal
control (29). OPAC was also field tested in two locations.
The results showed that significant improvements can be
obtained when compared with existing traffic-actuated meth-
ods. Average delays were reduced by 5% to 15%. Most of the
benefits occurred in high volume/capacity conditions (29).
One of the latest fields of research in the subject of
real-time control is the attempt to develop on-line control
strategies that use expert systems to decide about the
signal timing pattern under the circumstances. The
Intelligent Signal System (INTEL) (30) and the Signal
Control of Isolated Intersections (SCII) (31) are two
An expert system was also used in the TRUSTS system
discussed earlier, to determine the appropriate type of
operational mode to use under current traffic conditions
(32). As described previously, TRUSTS provides three modes
of operation: TOD, on-line plan selection, and on-line plan
The use of machine vision to detect traffic events in
control is another promising field of research. Several
problems are associated with the use of the existing type of
detectors (i.e., loops) in traffic responsive control. Such
detector types have limited capabilities, present
reliability problems, and require massive and expensive
installation for true traffic responsive control. Recent
advances in image processing and understanding, electronic
cameras, special purpose computer architecture and micro-
processor technology have made the machine vision altern-
ative for vehicle detection attractive, economical and
Timing Plan Selection in First-Generation Control
As stated earlier, in 1GC systems, the timing plans can
be selected on the basis of TOD, TRSP or manual.
Jrew and Parsonson (34) studied a technique for deter-
mining the best time to change timing plans in the TOD
operation of a computerized traffic control system. The
study examined the use of several off-line programs to
determine the time to change from the off-peak timing plan
to the peak-period timing plan in an arterial system. The
use of PASSER-II3 for plan designs was considered
unsuccessful because it was found that both periods required
the same cycle lengths. Thus, TRANSYT-7F was used to design
3The number between brackets following PASSER-II refers
to a specific version of the program. In this dissertation,
when the version is not specified following the PASSER-II
term, it means that the reference is made to PASSER-II
which is the 1984 version of the program.
timing plans for the off-peak and the peak periods.
TRANSYT-7F simulation runs were then performed to determine
the performance of the two plans for each 15-minute interval
during the afternoon. The results were used to plot the PI
of the two plans versus the time of day. The intersection
of the two curves was selected to be the time to change
plans. To reduce the computer time, the possibility of
using the Signal Operation Analysis Package (SOAP) to deter-
mine the time to change plans was investigated. It was
theorized that the TRANSYT-7F procedure might be replaced by
a relatively simple SOAP analysis at only the critical
intersection. However, it was found that during all times
during the afternoon the off-peak cycle length performed
better. Therefore, the SOAP analysis failed to produce an
optimal time to change the plan (34).
In implementing the TRSP mode of the 1GC, timing plans
are selected based on traffic conditions which are measured
through a traffic detection system.
Although many systems can be classified as 1GC, the
algorithms used in timing plan selection vary from one
system type to another. Generally, the base flow parameters
used in the selection are the volume, the occupancy or a
combination of the two. The volume and the occupancy are
measured by system sensors' and are fed into the control
computer for the plan selection purpose. Occupancy is
defined as the percent time that the detector is indicating
a vehicle presence measured over a total time period.
Volume and occupancy are used in timing plan selection due
to their ease of measurement, their accuracy and their
sensitivity to traffic demand (5).
In many instances, volume can be used without occu-
pancy. However, when the intersection approaches satur-
ation, volume will level off to a constant value that is
proportional to the available green time divided by the
average vehicle headways, while occupancy will continue to
increase (4). If this condition persists, long queues
develop and may reach from one intersection to another.
When this occurs, traffic is unable to move even when it
receives a green light and traffic jam conditions result.
Thus, the advantage of using occupancy is that it will
reflect congestion on the link more accurately.
Bell and Gault (35) used volume as the base flow param-
eter to determine the flow level at which it is most effi-
cient to change signal timing plans. TRANSYT-7 was used to
calculate performance indices for the peak and off-peak
plans for a range of average flows. A plot of PI versus
'System sensors are defined as traffic detection de-
vices (detectors) that permit the system master to obtain
information as to the traffic flow characteristics in the
area of the sensor.
flow was prepared for each plan. The flow level at which
the two curves crossed each other was regarded as the best
level to transfer from one plan to the other.
Taylor (36) tested systems that identify the beginning
of successive peak and off-peak conditions by comparing the
detector output with predefined parameters derived from
historical data. A simulation study was conducted to com-
pare the use of three flow parameters for this purpose. The
three parameters used were volume, occupancy and volume-to-
occupancy ratio. The volume was used in the same way as
that used by Bell and Gault (35) as explained above.
The use of occupancy to decide when to change plans was
more complex than using volume. Field surveys were neces-
sary to define the critical occupancy level prior to the
installation of the system. Occupancy was plotted as a
function of volume and the occupancy levels relating to the
critical flow levels were derived. These values were used
as the occupancy based thresholds for changing plans.
The third parameter used was the volume-to-occupancy
ratio. The volume and occupancy were linearly related under
unsaturated conditions, thus the ratio between the two was
constant. However, the onset of peak conditions disrupted
free flow and the ratio changed. From examining the plot of
ratio against flow, a level of ratio was defined at which
the plan change should occur. This level was considered to
be the one at which the ratio became a function of flow.
The study concluded that, under simulation conditions, there
was no difference between the three strategies tested.
However, volume-to-occupancy ratio was recommended for use
because it is more likely to remain stable through short-
term flow disruptions and would be less likely to cause
unnecessary plan changes.
Most of the work concerning the TRSP plan selection of
the 1GC in the United States has been concentrated around
that of the UTCS-1GC.
The traffic flow parameter, used for the timing plan
selection in the UTCS-1GC strategy, is a combination of
volume plus weighted occupancy (37). Corresponding to each
timing plan, there is a restored signature which is the
design value of the traffic flow parameter for the plan. In
the TRSP operation, for each time interval, a flow parameter
index is derived from field detector data as follows
Iit = VOLit + KO*OCCi, (2.1)
Ii = the measured flow parameter index for
detector i and interval t,
VOLit = the smoothed volume for detector i and
OCC, = the smoothed occupancy for detector i and
interval t, and
KO = the occupancy weighting factor.
The deviation of each signal timing plan signature from
the flow parameter index for a time interval t is calculated
using the following comparison function
Tit = Wi I it Si (2.2)
Tit = the value of pattern recognition function
associated with timing plan j at time
W, = the weighting factor for link i,
Si = the signature of link i associated with
timing plan j, and
L = the number of detectorized links in the
The plan with the minimum recognition function is con-
sidered for implementation. Minimum time between changes
and minimum threshold criteria are established by the opera-
tor to prevent excessive switching between timing plans.
The occupancy weight (KO) used in the calculation of
the base flow parameter in equation (2.1) is selected to
scale the occupancy term to a magnitude which is comparable
to the volume term. The traffic volume ranges theoretically
from zero to 2000 vehicles per hour per lane. However, the
occupancy, in percentage, ranges only from zero to 100.
Thus, it is necessary to adjust the magnitude of the
occupancy so that the occupancy is not suppressed by very
large traffic volumes. Twenty is the value that is
frequently used because it causes the magnitude of the
occupancy to approximate the magnitude of the volume when
the system is approaching saturation (5).
A theoretical study (4) indicated that there is some
skepticism about the effectiveness of using the flow parame-
ter index (It) in the deviation computation. It was sug-
gested that using the index will hinder the effectiveness of
the current selection algorithm under congested traffic
conditions. The study suggested that the occupancy informa-
tion should be fully utilized, to describe congested condi-
tions, instead of combining it with the volume to form a
single flow parameter. For this purpose, a modification of
the comparison function was suggested.
The study also questioned whether the constant weight
applied to all occupancy data is appropriate with respect to
selecting the correct timing plan (4). It was suggested
that the weight should be determined for each link individu-
ally. A constant weight cannot be used since there is no
direct linear relationship between volume and occupancy.
Occupancy weights based on the volume density relationship
Another study (38) investigated the effect of the
occupancy weighting factor upon the performance of UTCS-1GC
traffic responsive operation. A simulation study was used
for this purpose. The study found that, for the range of
conditions studied, the value of the occupancy weighting
factor had little effect on the performance of the UTCS-1GC
traffic responsive operation. However, the network invest-
igated operated under uncongested flow conditions. The
volume and occupancy relationship is nearly linear under
these conditions. Therefore, the inclusion of occupancy in
the pattern recognition function provides no more informa-
tion to the timing plan logic than volume alone. Further
work is required to investigate the effect of the occupancy
weighting factor when the network is operating under con-
gested flow conditions.
As stated earlier, all closed loop control systems can
be classified as 1GC systems. However, timing plan selec-
tion algorithms in these systems vary from one system to
another. Volumes and occupancy, as measured by system
sensors, are used differently to decide which timing plan
should be implemented for a given traffic condition (3).
This makes research in the field of improving the timing
plan selection process in 1GC systems more difficult. The
work conducted on a specific system type might not be
applicable to another.
In Florida, the predominant type of closed loop system
has been the Transyt 3800 closed loop system. When compar-
ing the timing plan selection algorithm used by this system
with that used by the UTCS-1GC, two major differences are
apparent. Instead of selecting a whole timing plan, the
closed loop system selects the cycle, the offsets, and the
splits separately in the TRSP mode of operation. Also,
instead of using a pattern matching technique for the
selection, the closed loop system control logic employs
transfer thresholds to determine the set of signal timing
parameters that is best suited to the measured traffic
The pattern selection routine of the system includes
traffic flow analysis in three different areas: volume
level of arterial traffic for cycle length selection, direc-
tionality of arterial traffic for offset plan selection, and
arterial traffic to side street traffic differential for
split plan selection.
The transfer thresholds based on volume calculations in
these areas are entered as percent. Therefore, a base or a
reference volume must be obtained first for the volume in
each movement direction entered in the calculation. The
volume level in a given direction is expressed as a per-
centage of the reference volume in that direction.
The arterial volume level used in cycle length selec-
tion is the inbound or the outbound volume level, whichever
is higher. The master selects one of four cycle lengths or
free operation. The transition points in volume levels for
change to the next higher or lower cycle length are all
The master can select as many as five different offset
plans. Offset plans are chosen based on the differential
between inbound and outbound volume levels. The system
provides the standard inbound, standard outbound and average
offset plans but also offers heavy inbound and heavy out-
bound offsets if required.
The selection of system split plans is based on the
differential between the side street volume level and the
arterial volume level. Again, the arterial volume level is
the maximum of the inbound and the outbound volume level.
The system can provide three split plans.
The threshold volume level required to go to a new
parameter design plan and the level required to leave that
design to go back to the original design should be set
somewhat apart to prevent cycling between plans.
Special patterns selected based on occupancy and queue
can be set to override the patterns selected based on the
normal traffic responsive operation described above. These
special patterns are used to take into consideration the
situation when the traffic within a system approaches
saturated conditions. Two patterns can be selected based on
occupancy and another two can be selected based on queue
detector inputs. The patterns based on queue detectors
override the patterns based on occupancy measurements.
As stated previously, under late night low volume
conditions, computer based traffic control systems can
operate in the free running mode. In this mode, all inter-
sections operate independently.
Luh and Courage (39) presented a method of facilitating
the choice between coordination and free operation on
arterial roadways controlled by semi-actuated signals when
traffic is light during off-peak hours. The decision was
made based upon a disutility function which is a combination
of the number of stops on the artery and the average cross
street waiting time.
Estimation of Nondetectorized Flows
TRSP control strategies need on-line information con-
cerning traffic over the network. One obvious requirement
for an effective TRSP control strategy is the establishment
of a reliable surveillance system. However, we cannot
expect every link in a system to be detectorized because of
the high cost of detector installation and maintenance.
In many situations, we need to estimate traffic con-
ditions at nondetectorized links from information obtained
at detectorized links.
In an evaluation study of the UTCS-1GC system (12), the
volumes on nondetectorized links and links with failed
detectors were needed. These links were matched with "sur-
rogate" detectors located on a link with similar geometric
and traffic demands. A surrogated detector for a link was
located within one block of the link with no detector.
In the UTCS-second generation control strategy, the
timing plans are optimized on-line using the optimization
model of the SIGOP program. This model requires the volumes
and speeds on all links in the system, not just at those
locations where detectors have been installed. Two
alternatives were used to estimate the volumes on the non-
detectorized links (5). These two alternatives were either
to use historical (time-of-day) volumes and speeds for
nondetectorized links or to assume that some combination of
upstream and downstream measurements can be extrapolated to
estimate the volumes on the nondetectorized links. In the
first case, estimates of the time-of-day volumes (guesses by
the traffic engineer) were saved. In the second case, time-
of-day multiplying factors (also guesses by the traffic
engineer) must be saved, representing the relationship
between the volumes on the adjacent links.
Kell and Fullerton (19) tested the validity of using
automatically collected traffic volumes from selected system
detector sites to generate a full TRANSYT-7F input file for
calculating signal timing plans in the UTCS-1.5GC. This
approach assumes that volume shifts on selected links accur-
ately represent shifts throughout the network. Site-
specific algorithms were devised to synthesize the required
TRANSYT-7F data from the system detector data. The optimum
signal timing plans calculated based on these data sets
compared favorably with the optimum plans produced based on
full TRANSYT-7F data (based on field-collected data sets).
The rules used to estimate the turning movements in the
network in that study, were selected individually for each
link in the network by the system traffic engineer. They
were used to update traffic volumes for each time period
based on detector data. Five rules were used, depending on
the availability of detector data. These rules are listed
below in the order of preference.
Rule 1: Traffic volumes for a given link were calcu-
lated based on detector data for that link.
Rule 2: Traffic volumes for a given link were calcu-
lated by summing projected input volumes from upstream
Rule 3: Traffic volumes were calculated based on
detector data for a nearby link.
Rule 4: Traffic volumes were calculated based on the
average detector results from more than one nearby link.
Rule 5: Traffic volumes were calculated based on an
overall average proportional increase in traffic throughout
A great deal of judgment was involved in the rules
described above to update traffic volumes based on detectors
More general algorithms have been presented in the
literature. Chin and Eager (40) examined techniques for
reducing the dimensionality of traffic flow in a network.
They started with an existing set of detectors in the net-
work and tried to reduce the number of detectors without
adversely affecting the pattern matching scheme of the UTCS-
1GC. Two models were presented in that study for the esti-
mation of link volumes from detectorized approach
measurements. The first model was a simple linear
regression model that presented a relationship between the
volume measurements on two links. The dependent variable in
the model was the unknown volume and the independent
variable was the known volume. The data used in model
development were collected by a computerized traffic control
The second model presented in the study was a time
series transfer function model based on the Box-Jenkins
method. Comparing the two models indicated that either of
the two may be employed to reduce the dimensionality of the
flow vector with good reliability (40).
Okutani and Shimosato presented a multivariant regres-
sion model to estimate the nondetectorized link volume (41).
In this model, the independent variables were the observed
link volumes and the dependent variable was the unobserved
Later, Okutani (41) extended the above model to take
time series of the traffic volume into account. This was
done by adding to the regression equation independent
variables representing observed link volumes at time inter-
vals preceding the time interval for which the volume esti-
mation was needed. It was shown that the performance of the
multiple linear regression model improved when link volume
counts from up to seven preceding five-minute intervals were
included as independent variables in the model.
In the same study (41), the Kalman filtering technique
was employed to derive an estimation model of the nondetec-
torized link volume. The Kalman filtering algorithm is one
of the most advanced methods in modern control theory.
Volume estimations using the multiple linear regression and
the Kalman filtering technique were compared using data from
a small network. The results indicated that the Kalman
filtering model produced better estimates compared to the
Balancing Traffic Counts
Partly because of counting errors and partly because
counts may be carried out on different days, traffic counts
on links of a network are unlikely to satisfy the flow
conservation constraint, flow in equal to flow out, at every
node and every approach in the network. The observed flows,
thus, are considered to be internally inconsistent (42,43).
Sometimes balanced data are needed and the counts must
be adjusted. However, a change in one count will affect
many other counts throughout the network. Finding the right
combination of adjustments to make manually can be extremely
Van Zuylen and Willumsen (42) developed a model to
estimate the most likely origin-destination matrix from
traffic counts. For this purpose, the input flow to each
node in the network had to be equal to the output flow from
A statistically based model was developed in that study
to balance a network of traffic counts. The model used a
maximum likelihood method and assumed Poisson distributed
single link counts.
A set of simultaneous equations for each constrained
node (intersection) was constructed. Nodes representing
traffic zones are unconstrained, since the volume entering
does not have to equal the volume exiting during a given
time period for traffic zones.
The flows going into and out of an intersection can be
corrected by means of the following formula.
= V. (1 + 6., M,)-1 (2.3)
V = the corrected flow for link a,
Va = the observed flow,
6a, = 1 for flow going into node i and -1 for
flows out of node i, and
Mi = the Lagrange multiplier and has to be solved
by substitution of equation (2.3) in
SV 6,, = 0 (2.4)
A computer program (44) was written to apply the al-
gorithm described above. This program was written to help
solve the problem of count inconsistency.
DEVELOPMENT OF A THRESHOLD SELECTION MODEL BASED
ON ESTIMATED VARIATION
The models developed in this study for determining the
timing pattern change thresholds deal specifically with the
traffic responsive strategy of the Transyt 3800 closed loop
system. The normal pattern selection process of this strat-
egy is based on arterial traffic volume level for cycle
length selection, on directionality of flow for offset plan
selection and on arterial traffic to side street traffic
volume differential for split plan selection.
When the three signal timing parameters (the cycle
length, the offsets and the splits) are selected in the TRSP
mode, the conditions used in the selection of these param-
eters are analyzed independently in the master controller.
Thus, transfer thresholds should be determined for each of
the three parameters. As explained earlier, due to the
limited detector information available from a typical closed
loop system, the thresholds obtained are not globally
optimal. However, the application of the models developed
herein should improve the system operation by replacing the
element of judgment by a more objective technique.
To obtain the transfer thresholds for a given timing
parameter, it was necessary to identify the traffic condi-
tions5 at which each design of that parameter performed
best compared to the other parameter designs. For this
purpose, traffic flow conditions in the system were varied
in a controlled manner. Then TRANSYT-7F was used to eval-
uate the performance of each design with the resultant
Information about traffic flow conditions in a system
is obtained from system sensors located on only a few
approaches. Thus, the controlled variations in this study
were only applied to the volume on the detectorized
approaches. This meant that for each traffic condition
investigated, only the volumes on the detectorized
approaches were known. However, to evaluate these condi-
tions using TRANSYT-7F, the value of flow on every link in
the system is required. Thus, for each traffic condition
resulting from varying the volumes on the system sensors,
the turning movement volumes in the system had to be
This chapter presents the methodology used to obtain
the transfer thresholds required for the normal operation of
5In this dissertation a traffic condition is identified
by the three traffic parameters used in the selection of the
cycle, the offsets and the splits. These are the arterial
volume level, the directionality of flow, and the arterial
traffic to side street traffic volume differential, respec-
the TRSP mode of the system. First the chapter addresses
the data requirements. A method is then presented to calcu-
late a reference volume for each link in the system. Next,
the method used to vary the volume on the detectorized
approaches to simulate different traffic conditions in the
system is explained. The estimated variation model is then
developed to estimate the nondetectorized volumes in the
system. Finally, the method used to determine the transfer
thresholds for the signal timing parameters is presented.
The data required for the models developed in this
study include information which should be available to the
traffic engineering agency from data collected in the field.
TRANSYT-7F and PASSER-II are used for the design
and evaluation of signal timing parameters. Thus, the input
data required for running these two programs had to be
obtained. Five major types of data were required for this
purpose: network data, traffic volume data, saturation flow
data, speed data and signal timing data (8,9). The traffic
volume data set used consisted of 15-minute turning movement
counts for every approach at every intersection in the
The turning movement counts were utilized in various
steps of the models developed in this study. They were used
in the calculation of reference volumes for each link in the
system. They were also used for estimating the traffic
condition variation during the day and for obtaining the
correlations between the movements in the system.
Count data were also used to estimate the nondetec-
torized traffic volume in the estimated variation model. As
will be explained later, the estimated variation model
depends on reliable traffic volume data. Also, the model
requires that count data should be obtained for as long a
period as possible to reflect the variations in traffic
conditions during the day.
Computer programs were written in this study using
count data in various steps of the models. The count data
were saved in a data set with a standard format for later
use by these programs.
Reference Volume Calculation
In this study, a reference volume was determined for
each link in the system. At any given traffic condition,
the volume level on the link was represented as a proportion
of that reference volume. The reference volume can be
obtained as follows:
REFV = MEANVi + 2 STDVi (3.1)
REFV, = the reference volume on link i,
MEANVi = the mean of volume counts on link i, and
STDVi = the standard deviation of volume counts
on link i.
Equation (3.1) was used for reference volume computa-
tions because this is fairly common in practice. If the
counts are normally distributed, approximately 95% of them
would be less than the reference volume. Traffic counts
tend to deviate from a normal distribution, skewed toward
low volumes, and consequently more than 95% may lie below
the reference volume.
The estimated variation model used to obtain the non-
detectorized link volume in this study requires the adjust-
ment of the traffic counts to achieve a balance between
input flows and output flows for each internal approach in
the system. The adjustment procedure will be described
later. The adjusted counts were used in reference volume
calculations. In this manner, the same count data set was
used in various steps of the model.
The reference volume of an approach is defined as the
sum of the reference volumes of the turning movements down-
stream of that approach.
If a given link volume was computed to be below a
minimum value, 100 veh/hr, the link reference volume was set
to the minimum. The 100 veh/hr is the volume normally
accommodated on the minimum green time. A computer program
was written to calculate a reference volume for each link in
Simulating Different Traffic Conditions in the System
In the normal operation of the TRSP mode, traffic
conditions in the system are defined by system sensor meas-
urements. The system uses three traffic volume parameters
to define traffic conditions for the signal timing select-
ion. These parameters are
1. The arterial volume level (AVL) is defined as the
inbound or the outbound volume level, whichever is higher.
(The volume level in a given direction is defined as the
percentage of a reference volume programmed for that direc-
2. The inbound-outbound volume differential (IOVD) is
defined as the difference between the inbound and the out-
bound volume level.
3. The cross street arterial volume differential
(CAVD) is defined as the difference between the cross street
volume level and the arterial volume level.
This section describes the method used to simulate a
given traffic condition in the system by changing the volume
on the detectorized approaches in a controlled manner. The
basic technique used was to multiply the reference volumes
on the detectorized approaches by factors which were con-
stant for a given direction. This technique is illustrated
in Figure 3.1. Figure 3.1 (a) shows that a system with the
volume on each detectorized approach was equal to the refer-
ence volume of that approach. In this case the AVL was
Figure 3.1. Simulating different traffic conditions in
an arterial system.
(a) An artery with 100% AVL, zero IOVD and zero CAVD.
(b) An artery with 90% AVL, zero IOVD and zero CAVD.
(c) An artery with 90% AVL, 50% IOVD and zero CAVD.
(d) An artery with 90% AVL, zero IOVD and -40% CAVD.
NOTE: Ri represents the reference volume for detectorized
_I I ii
o 4R, 0- 4R4 ----
f0.9 0.9R 2
(c) I I
100%, the IOVD was zero, and the CAVD was zero. By using
appropriate multipliers, the AVL, the IOVD and the CAVD were
changed to produce a required traffic condition as follows:
1. The AVL was changed by multiplying the reference
volumes of the detectorized approaches on the artery by a
constant factor. To keep the CAVD constant, the reference
volumes of the cross street detectorized approaches were
multiplied by the same factor. This is illustrated in
2. At a given AVL, the IOVD was changed by holding
constant the volume in the direction required to be the
heavy direction, while decreasing the volume on the other
direction. In this process, the cross street detector
volumes were kept constant. This is illustrated in Figure
3. At a given level of AVL, the CAVD was varied by
keeping the volume on the arterial detectors constant while
changing the volumes on the cross street detectors by
multiplying them by a constant factor. This is illustrated
in Figure 3.1(d).
The method used to produce different traffic conditions
in the system was in accordance with the closed loop system
definitions of these conditions.
Estimated Variation Model
The threshold model developed in this study requires
evaluation of the performance of each signal timing design
with different traffic conditions obtained as illustrated in
the previous section. The TRANSYT-7F model was used for
TRANSYT-7F needs the value of flow on every link in the
system. In the closed loop system, traffic conditions are
defined by the volume level on the detectorized approaches
in each movement direction. The turning movement volumes in
the network, therefore, had to be estimated based on the
detectorized approach volumes. This section describes a
model developed for this purpose. The model is referred to
as the estimated variation model. First, the concept of
this model is addressed, then the development of the model
Essentially, the purpose of the estimated variation
model is to express the.volume on each nondetectorized
approach in the system as a linear function of volumes on
detectorized approaches. Thus, when the volumes on the
detectorized approaches were known, the volume on each non-
detectorized approach could be estimated using these linear
functions. The turning movement volumes on each approach
were then calculated by assuming constant turning percent-
ages in the system. Better results would be expected if an
estimation equation was obtained for each turning movement
volume in the system. However, more computations will be
required in this case. In this study, it was decided to
simplify the calculations by assuming constant turning
percentages in the system.
The linear functions were derived based on traffic
count data. Before deriving these functions, however, an
adjustment to the count data was needed. Ideally, for a
given count period, input flows and output flows for each
approach in the system should be equal, in order to obtain a
good estimate for the volume on that approach. Normally,
field data do not satisfy this idealization, partly because
of counting errors and partly because counts may be carried
out on different days.
A least squares adjustment model was derived to adjust
the count data such that a balance between the input flow
and the output flow for each internal approach in the system
was obtained. The least squares principle ensured that any
variation in the observations necessitated by the existence
of inconsistencies with the model must be as small as
possible taking into consideration the variable weights and
subjected to the constrains of the problem (45,46).
In mathematical notation the least squares principle is
Minimize P = VtWV (3.2)
V = the vector of the residuals which are equal
to the adjusted variables minus the
W = the symetrical weight matrix of the vari
Vt = the transpose of the V vector.
The least squares adjustment model is a mathematical
model. Michail and Ackermann (45) considered the model to
be composed of two parts: the functional model and the
stochastic model. The functional model describes the deter-
ministic properties of the physical situation or event under
consideration. A set of mathematical equations, referred to
as condition equations, is written to describe the func-
tional model of the adjustment problem. The stochastic
model describes the nondeterministic properties of the
variables. The derivation of the least squares adjustment
model is presented in Appendix A.
After the adjustment, multiple linear regression analy-
sis was used to derive equations which expressed the volumes
on the nondetectorized approaches as linear functions of
detectorized approach volumes. These equations were derived
based on the adjusted count data.
Multiple linear regression permits the assessment of
the relationship between one variable and another set of
variables. The relationship is expressed as a linear equa-
tion that predicts a dependent variable from a function of
independent variables (47,48).
A linear relationship between a nondetectorized ap-
proach volume (the dependent variable) and detectorized
volumes (the independent variables) can be estimated and
tested by estimating and testing the parameters in the model
NONDETk = Po + I DET + P2 DET2 +
+ p, DET, + + DET,
NONDETk = the kth nondetectorized approach
DETi = the ith detectorized approach volume,
pi = the ith parameter of the model.
Appendix B illustrates how to estimate the parameters in a
multiple linear regression model.
The estimated variation model assumes that good esti-
mates of the nondetectorized approach volumes can be ob-
tained from detectorized approach volumes. This depends on
how well the detector locations have been selected and also
on the degree of correlation between the volumes on system
approaches. In fact, good correlations between movements in
any given direction of travel (inbound, outbound and cross
street) are an essential requirement for this type of traf-
fic responsive system to be effective. The small number of
detectors installed in each direction is meant to represent
the volumes on all approaches in that direction.
The model also needs good field count data. Adjusting
unreliable data may adversely affect results with the model.
The least squares adjustment model assumes that all counts
are equally valid and will attempt to adjust all counts to
incorporate incorrect values. Also, the use of unreliable
data to derive estimation equations in regression analysis
reduces the reliability of these equations.
For the estimation model to be efficient, count data
should be obtained for a time period adequate to take into
account as much traffic flow variation as possible during
Step 1: Count data adjustment
A least squares adjustment model was developed to
obtain a balance between upstream input flows and down-
stream flows for each internal approach in the artery. The
sums of the volumes in the system before and after the
adjustment were assumed to remain constant during the
No turning movement contributes to both inbound and
outbound movements. This means that adjustment of a volume
in one direction does not affect the movement volumes in the
other direction. Thus, the adjustment problem was divided
into two problems, one for each direction. This reduced the
sizes of the matrices involved in the computations.
The following condition equations were written to
represent the functional model of an east-west artery with n
intersections, as shown in Figure 3.2. For the east direc-
tion, the equations were:
ET, + NRi + SLi ETi+ ELI+1 ERi+ = 0
For i = 1 to i = n-1
n n-1 n-1 n
Z ET, + s SL, + Z NR, + I EL,
i=l i=1i i=i i+1
+ X ER, = SUMEST
ETi, EL ,
n = the total number of intersections,
ER, = the through, left turn, and right
turn movement volumes,
respectively, at intersection i in
the east direction;
NR, = the northbound right turn movement
volume at intersection i,
SL, = the southbound left turn movement
volume at intersection i, and
EST = the sum of all movement volumes
included in the functional
model for the east direction
SR SR ST ST
SR 1 SR 2 SR3 S
1 R EL2-. '-LR2 EL3 WR
ER1 WLT ET WT ET WT
l;-t ET2- ^ i2 E T3
NL,!, NRI NL | NR2 NL2 2 NR3
NT, NT2 NT3
Figure 3.2. An east-west artery for which the turning
movement volumes have to be adjusted.
For the west direction, the following equations were
WTi + WLi + WR, SRI1 NLi WTI+ = 0
For i = 1 to i = n-1
n n-1 n-1 n
E WT + E WL1 + E WR, + E SR1
i=1 i=1 i=1 i=2
+ E NL = SUMWST
WTi, WLi, WRi = the through, left turn, and right
turn movement volumes,
respectively, at intersection i
in the west direction;
NL = the northbound left turn movement
volume at intersection i,
SR, = the southbound right turn movement
volume at intersection i, and
SUMWST = the sum of all movement volume
included in the functional
model for the west direction
Flows from mid-block sources and sinks should be
included as variables in the equations above.
The least squares adjustment model derived in Appendix
A was used to find least squares estimates for all link
volumes for each count period.
Before balancing the data, two inputs to the adjustment
model had to be obtained. The first was the coefficient
matrix, which included the coefficients of the functional
model of the adjustment problem. This matrix was prepared
The second input matrix required was the weight matrix.
In the theory of adjustment, the term "weight" was used to
express precision by way of an inverse relationship. Thus,
high weight meant high precision which in turn meant a small
standard deviation. A weight matrix should be obtained for
movements in each direction on the artery. In this study,
the inverse of the variance-covariance matrix obtained,
based on the 15-minute historical count data, was used as
the weight matrix. This matrix was obtained based on the
count data using the Statistical Analysis System (SAS) (49).
This concept will be treated in more detail in Chapter Six,
in which an alternate method for obtaining the weight matrix
will be suggested.
Since the least squares adjustment problem involved a
sequence of matrix operations, the SAS interactive matrix
language (SAS/IML) (50) was used for the adjustment model.
The model adjusted the link volumes for a given time period
and for a particular movement direction. The adjustment was
performed for every count period, for both directions.
Some turning movements in the system were not included
in the least squares adjustment process described above.
This was because those movements were neither input flows
nor output flows for any of the system internal approaches.
However, it was logical to modify these movements in order
to take into consideration the adjustments made to other
movements in the system. The unadjusted movements can be
classified into two types:
1. Cross street movements were not included in the
adjustment because they were not input flows to any internal
approach. These included the cross street through movements
on every intersection and also left and right turns from the
cross streets on the first and last intersections. These
movement volumes were adjusted by multiplying them by the
coefficient C which is calculated as follows
C = SUMAF (3.8)
C = a multiplier for cross street movements
which had not been involved in the least
SUMBEF = the sum, before the adjustment, of
cross street turning movement volumes
that were input flows to internal
SUMAFT = the sum, after the adjustment,
of cross street turning movement
volumes that were input flows to
2. Right and left turns from the main street at the
first and the last intersections were not included in the
adjustment because they did not contribute to the output
flow from any internal approach in the system. The volumes
of these movements are adjusted by multiplying their values
by the coefficient Ci, calculated as follows:
C = TAFTi (3.9)
C, = a multiplier for approach i turning
movement volumes which had not been
involved in the adjustment,
TBEF, = the through volume downstream of approach
i before the adjustment, and
TAFT, = the through volume downstream of approach
i after the adjustment.
After the adjustment, the data for all time periods
were appended to one file that had the same format as that
of the data file before the adjustment. This enabled it to
be used as input to the various computer programs developed
in this study.
Example. As illustrated above, the least squares
adjustment involves a sequence of matrix operations. The
size of the matrices involved increased when more turning
movements were involved in the adjustment. Thus, for the
purpose of illustrating the computational technique of the
model, it was necessary to use an artery with few turning
movements as an example.
Three examples were used in developing the various
concepts of this study. These examples are
1. A single bidirectional link in Gainesville, FL,
used only to illustrate ideas which are computationally
2. A six-link hypothetical artery with specified
volume variations and specified relationships between
individual movements. This was used to provide a high
degree of control over the input data so that the relation-
ship between cause and effect could be easily visualized.
3. A nine-intersection (16-link) artery in Lexington,
KY. This was chosen as a practical example to demonstrate
the determination of the thresholds using the estimated
variation model and to compare the results with those
obtained using the approximation (assumed variation) model.
More trivial and hypothetical examples would not make a very
Of these examples, the first one was the most appropri-
ate to illustrate the complex computation of the least
squares adjustment model. This is a two-intersection arter-
ial system on 16th Avenue in Gainesville, FL. Figure 3.3(a)
shows the turning movement volumes in the arterial system
for a given time period.
In this example, least squares adjustment was used to
balance the upstream and downstream flows in the artery for
this time period. As stated above, a SAS/IML program was
written to perform the adjustment. The computations re-
quired for the adjustment are presented here for illustra-
First the movement volumes in the east direction were
adjusted. The following equations were written to represent
the functional model of the adjustment problem in the east
direction (SUMEST was calculated for this count period to be
ETI + SL1 EL, ER, ET2 = 0 (3.10)
ETI + SLI + EL, + ER, + ET2 = 364 (3.11)
Next, the least squares stochastic adjustment model
derived in Appendix A was used to balance the flow in the
system. From equations (3.10) and (3.11), the A matrix and
the D vector were obtained as follows:
",- 22 56-.
--- 133 80 -
10 51 1
RL 20 74 .;
- 115 82 -
14 54 1
Figure 3.3. The adjustment of
volumes on a two-intersection arterial
(a) The turning movement volumes
before the adjustment.
(b) The turning movement volumes
after the adjustment.
the turning movement
system in Gainesville,
in the arterial system
in the arterial system
A 1 1 -1 -1 -1
1 1 1 1 1
Vector F was calculated as
F =D AL
0 1 1 -1 -1 -1 165
364 1 1 1 1 1 56
In this example, the inverse of the variance-covariance
matrix was used as the weight matrix. For the east direc-
tion, the variance-covariance matrix, Q, was obtained based
on count data using SAS. Q, A, and At were substituted in
the following equation to obtain the Q. matrix.
Q. = AQAt
This resulted in
1 -1 -1 -1 -
1 1 1 1 1
S= -0.0002 0.0002
Next, the Lagrange multiplier, K, was calculated as
K = Q F
0.0026 -0.0002 -44 -0.114
-0.0002 0.0002 0 0.0075
The vector of residuals V was calculated as follows:
V = Q A K
Substituting for Q, At, and K in the above equation and
multiplying resulted in
V = +18
The adjusted count data could then be calculated by
adding the vector of residuals to the vector of unadjusted
165 -18 147
39 4 35
L = 56 + +18 = 74
24 + 1 25
80 + 2 82
The vector of residuals was calculated for the move-
ments in the west direction in a similar manner. The fol-
lowing vector was obtained
V = +6
and the adjusted counts in the west direction were calcu-
lated as follows:
133 -18 115
22 2 20
L= 61 + + 6 = 67
10 + 4 14
45 + 9 54
The movements that were not included in the least
squares adjustment calculation presented above were adjusted
using the coefficients C or Ci as described in the model
formulation. The turning movement volumes in the system
after the adjustment are shown in Figure 3.3(b).
A modification of the least squares adjustment method
presented in this step is suggested in Chapter Six. In that
modification, the weight matrix is calculated differently.
To examine that modification, the solution of the problem
presented in this example was repeated using the modified
procedure. The results are presented in Appendix C.
Step 2: Development of volume
estimation model structure
Multiple linear regression was used to derive estim-
ation equations for volumes on the nondetectorized approach-
es (the dependent variables) from detector measurements (the
independent variables). The regression was based on count
data, adjusted as described previously. Approach volumes
were obtained from count data by summing the turning move-
ments on the approach downstream.
Before performing the regression analysis, the correla-
tion matrix between the volumes on the approaches with
system sensors (the independent variables in the regression)
was obtained using SAS. When some of the independent vari-
ables are highly intercorrelated, the computed estimates of
the regression coefficients are unstable and their inter-
polation becomes tenuous (47). This problem is referred to
To solve this problem, if the examination of the cor-
relation matrix obtained above indicates that two independ-
ent variables are highly correlated, then only one of the
two is kept for use in the regression. This is a good way
to handle the problem since one of the two variables conveys
essentially all of the information contained in the other.
The second stage in solving the problem of multicol-
linearity involves the use of a variable selection process
such as stepwise regression in SAS (51), to select the set
of independent variables that best predicts a given
dependent variable from the entire set of possible indepen-
The third stage involves examining the correlation
coefficient (R2). This is a measure that indicates the
portion of the total variation that is attributed to the fit
rather than left to the residual error. This value is
presented in stepwise procedure output whenever an
additional variable is selected. The independent variables
that explain little of the variance in the dependent vari-
able should be excluded.
The variable selection process explained above implic-
itly overcomes the multicollinearity problem. Small num-
bers, possibly one or two, of independent variables are
preferred in the estimation equation.
One assumption of linear regression is homoscedasticity
or the homogeneity of variance assumption. This assumption
requires that the variance of the dependent variable at a
given value of an independent variable be the same for all
values of the independent variable. However, the count data
can be assumed to be Poisson distributed. Thus, their
variance is a function of their mean. This means that the
variance depends on the independent variable values, which
violates the homogeneity of variance assumption. A square
root transformation of the dependent variable is used with
Poisson distributed variables to solve this problem (47),
and was used in this study. The linear regression was thus
performed on the transformed values. A SAS program which
utilizes the SAS REG procedure (51) was used to perform the
Example. A hypothetical route was used to illustrate
the derivation of the estimation equations. This same
example will be used in the remaining sections of this
chapter to illustrate the application of the estimated
variation model and the method used to determine the
thresholds. A simple hypothetical route was chosen as an
example because of the complexity of the models. By apply-
ing the techniques to a relatively trivial case, the results
may be visualized more readily.
As illustrated in Figure 3.4, the hypothetical artery
is an east-west artery with four intersections. The signal
phase sequence, the distance between intersections, and the
detector locations are also shown in Figure 3.4. The three
detector locations were selected such that there was one
detector in each direction (inbound, outbound and cross
street). As described in the data requirement section, 15-
minute counts, for long enough periods, were needed on every
link in the system to obtain the transfer thresholds.
Therefore, in this example, 15-minute counts were fabricated
for a 12-hour period. The following method was used for
1. Hypothetical 15-minute counts on the detectorized
approaches were fabricated to represent variations in the
AVL, CAVD, and IOVD during the 12-hour period.
2. The counts on the nondetectorized approaches were
fabricated such that they had good correlation with the
counts on the detectorized approach in the same direction.
This correlation was necessary for the TRSP selection of
2 ------- 3
00ft 1200 ft 400 ft
t -~r- it
Figure 3.4. The hypothetical artery layout, phase
sequences, and system sensor locations.
__ t _
cycle, offsets, and splits to be effective. The following
formula was used.
VU, = VDi (1 + CV R. ) (3.12)
VU, = the volume on the nondetectorized approach
in the ith direction,
VD, = the volume on the detectorized approach in
the ith direction,
CV = the variation of volume on the non-
detectorized approach compared to
the volume on the detectorized approach, and
R, = a standard normal random variable generated
using the Box-Muller method.
In the above formula, for each count period, a random
error component was added to the volume of the detectorized
approach to represent the volume on a nondetectorized ap-
proach in the same direction. In this manner, the required
correlation was obtained. The magnitude of this correlation
could be controlled by the value of the coefficient of
variation CV in equation (3.12). In this example, it was
assumed that the correlations between the cross street
movements were less than the correlation between the inbound
movements or the outbound movements. Thus, the CV values
used were 0.15 and 0.175 for the arterial and the cross
street movements, respectively. A program written in SAS
was used to generate the counts as explained above.
A multiple linear regression analysis was performed on
the hypothetical data to derive estimation equations for the
nondetectorized approach volumes. Table 3.1 shows the
result of the regression analyses. As shown in the table,
the R2 values were between 0.74 and 0.84 for the cross
street movements and between 0.84 and 0.89 for the arterial
Step 3: Application of the estimated
As explained earlier, examination of signal timing
parameter designs, under different traffic conditions,
requires the estimation of the nondetectorized link volumes.
This estimation was performed for each traffic condition
determined as described in the previous section.
First the estimation equations, derived in step 2, were
used to estimate the nondetectorized approach volumes from
detectorized approach volumes. Then, assuming that the
turning percentages at the intersections were constants, the
turning movement volumes from each approach could be deter-
mined. The turning percentages for a given approach were
obtained based on the reference volumes of the turning
movements downstream of the approach.
A computer program was developed for this study to
calculate the turning movement volumes in the system based
on the regression parameters of the estimation equations,
The Estimation Equations for the Nondetectorized
Approach Volumes on the Four-Intersection
Inter- Equation Coefficientsa
section Approach O f31 P2 P3 R2
1 East Db D Db Db
West 5.346 0 0.045 0 0.89
South Db Db Db Db
2 East 5.501 0.045 0 0 0.88
West 6.571 0 0.035 0 0.83
North 4.07 0 0 0.06 0.74
3 East 6.020 0.038 0 0 0.88
West 5.841 0 0.0431 0 0.89
South 4.271 0 0 0.057 0.80
4 East 5.849 0.0401 0 0 0.83
West Db Db Db Db
North 2.987 0 0 0.073 0.84
aEquation form: (UNDETk 1/2 = + 81 DET, + P2 DET2 + P2 DET,
b D indicates that this approach is detectorized.
the turning movement percentages for each approach, and the
The Arterial Analysis Package (AAP) (52) was used for
coding the data. The AAP data files were then converted to
TRANSYT-7F or PASSER-II input data files as required.
To reduce the effort required to code the data for each
volume condition, a program was written to modify the AAP
input deck such that the coded volume was changed as re-
quired to eliminate the manual coding each time a new volume
condition was investigated.
Example. The four-intersection hypothetical artery of
Figure 3.4 was used to illustrate the nondetectorized volume
estimation. Figure 3.5(a) shows the system with each detec-
torized approach volume equal to the reference volume of
that approach. Figure 3.5(b) shows the volume on these
approaches for a specific volume condition, determined as
explained earlier in this chapter. The volumes on the
nondetectorized approaches were calculated using the equa-
tions presented in Table 3.1 and are shown in Figure 3.5(c).
This section describes the method used to determine
transfer thresholds for the signal timing parameters. To
determine these thresholds for the cycle lengths, the off-
sets and the splits, TRANSYT-7F input files with different
AVL, CAVD and IOVD, respectively, had to be created. These
Figure 3.5. The estimation of the nondetectorizec
volumes in the four-intersection hypothetical artery using the
estimated variation model.
(a) The artery with the volume on all detectorized
approaches equal to their reference volume (AVL -
100%, CAVD = zero and IOVD = zero).
(b) The artery with the traffic condition to be
investigated (AVL = 90%, CAVD = zero and IOVD =
(c) The turning movement volumes in the system estimated
using the estimated variation model.
490 490 519
1010 893 926 516
T364 H 377
files were produced using the method explained in the pre-
vious sections of this chapter. They were used in the
evaluation of different parameter designs under different
traffic conditions. A design was selected for implementa-
tion for a given traffic condition, if it produced the
lowest TRANSYT-7F performance index compared to the other
designs of that parameter.
In the TRSP operation investigated, the system can be
programmed to implement the TRSP selections of the cycle,
the offsets and the splits. The conditions used in select-
ing these parameters are analyzed independently in the
master controller. Thus, transfer thresholds should be
determined for each of the three parameters. This is one of
the limitations of this type of TRSP selection. Ideally,
the signal timing parameters should be optimized simul-
taneously to obtain the best performance of the system.
The TRSP selection of split plans can be disabled by
the system engineer at some or all of the intersections. In
this case, the system supervisors at the local intersections
are programmed to select the split plan based on a combina-
tion of cycle and offset in effect. If this is the case,
one of 12 different split plans can be selected for each
cycle and offset combination. As will be described later,
disabling the TRSP selection of splits affected the method
used to determine the transfer thresholds.
Examining the TRSP operation described above suggests
that there are two situations where the disabling of the
TRSP selection of splits is preferred. The first is when
the cross street movements at an intersection are not corre-
lated with the cross street detectorized approaches. In
this case, no benefit is expected from implementing a TRSP
selection of split plans at that intersection since the
shift in the cross street detectorized volume does not
represent a shift in the cross street volumes at that inter-
section. The second situation is when the left turns from
the main street are more critical than the cross street
movements at an intersection. In the TRSP selection of the
splits, the splits are chosen based on the CAVD independent
of the IOVD. This seems inadequate when the left turns on
the main street are heavy since these turns are normally
related to the IOVD value. It might be better in this
situation to relate the splits to the cycle and offsets in
effect rather than using the TRSP selection of splits. This
is especially true if the cross street movements are not
heavy or if the CAVD do not vary a lot during the day.
Currently, the same split and offset thresholds are
programmed independent of the cycle length in the master
controller. Since the cycle length is selected based on the
AVL, this means also that the same offset and split thres-
holds are used for all AVL. This might be another limita-
tion of the TRSP operation investigated, since the best set