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Development of a vehicle-following model (vehfol) and a heterogeneous traffic simulation model (hetsim) for controlled intersections

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Development of a vehicle-following model (vehfol) and a heterogeneous traffic simulation model (hetsim) for controlled intersections
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Maini, Pawan
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English
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308 leaves : illustrations ; 28 cm

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Subjects / Keywords:
Traffic flow -- Mathematical models -- India ( lcsh )
Traffic engineering -- India ( lcsh )
Roads -- Interchanges and intersections -- India ( lcsh )
Roads -- Interchanges and intersections ( fast )
Traffic engineering ( fast )
Traffic flow -- Mathematical models ( fast )
India ( fast )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

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Bibliography:
Includes bibliographical references (leaves 301-308).
General Note:
Department of Civil Engineering
Statement of Responsibility:
by Pawan Maini.

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University of Colorado Denver
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Auraria Library
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ocm47826718
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Full Text
DEVELOPMENT OF A VEHICLE-FOLLOWING MODEL (VEHFOL) AND A
HETEROGENEOUS TRAFFIC SIMULATION MODEL (HETSIM) FOR
CONTROLLED INTERSECTIONS
by
Pawan Maini
B.Tech., Indian Institute of Technology, Mumbai (Bombay), India, 1989
M.S., North Carolina State University, 1991
A thesis submitted to the
University of Colorado at Denver
in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
Civil Engineering
2001


2001 by Pawan Maini
All rights reserved.


This thesis for the Doctor of Philosophy
degree by
Pawan Maini
has been approved
by
Sarosh I. Khan
IZ
Bruce N^fanson
Anuradha Ramaswami
James E. Diekmann
, 2ool
Date


MainL Pawan (Ph.D.. Civil Engineering)
Development of a Vehicle-Following Model (VEHFOL) and a Heterogeneous Traffic
Simulation Model (HETSIM) for Controlled Intersections
Thesis directed by Assistant Professor Dr. Sarosh I. Khan
ABSTRACT
A vehicle-following model, VEHFOL, is developed to represent the flow of
heterogeneous or mixed flow traffic. This vehicle-following model is implemented in
a comprehensive simulation model, HETSIM, which represents the flow at controlled
intersections in India.
VEHFOL considers the longer term goal of a following vehicle achieving a steady
state with the lead vehicle. The steady state is characterized by a minimum time gap
and equal velocity of the lead and following vehicles. The reaction time of drivers is
considered explicitly. A new non-collision constraint that ensures a safe gap from a
lead vehicle is formulated. Additionally, a perception threshold heuristic ensures that
following vehicles decelerate at an acceptable rate. VEHFOL is validated by
comparing model estimates of headway, velocity and acceleration at every simulation
time step (0.5 seconds) with observed data. A total of 31 vehicle-following cases,
with different combinations of lead and following vehicle types, and modes of
operation (accelerating, decelerating, flow' during green) are considered. VEHFOL is


shown, to perform better than two other vehicle-following models implemented in
heterogeneous traffic simulation models.
The comprehensive model for simulating heterogeneous traffic through controlled
intersections, HETSIM, includes ten vehncle types (seven motorized and three non-
motorized). Video data are reduced and used to model the stochastic variation of
driver-vehicle characteristics such as acceleration and deceleration rates, and stopped
and moving longitudinal and lateral gaps. The unique aspects of lateral movement of
heterogeneous traffic, which typically denes not travel in lanes, are considered. The
four primary vehicle movement sub-mocflels included in HETSIM are: (a) vehicle
generation and introduction (b) overtaking (c) response to turn intention and (d)
response to intersection control.
HETSIM is validated for a wide range off traffic and roadway conditions observed at
six intersection approaches, in two cities- in India. The primary measures of
effectiveness considered are queue lengtEh and stopped delay. The application of
HETSIM, in studying changes to a traffic network and for developing relationships, is
demonstrated. HETSIM may prove to be useful in analyzing the rapidly occurring
changes in urban transportation networks in India, and with few modifications, in
other countries also.
This abstract accurately represents the content of the candidates thesis. I recommend
its publication.
Sarosh I. Khan
v


DEDICATION
This work is dedicated to my wife. Surinder.


ACKNOWLEDGMENT
I would like to express my gratitude to my theses director. Dr. Sarosh I. Khan, for her
invaluable guidance, support and encouragement through all phases of this study. I
am grateful of the support provided by the Colorado Translab that helped provide
partial funding for this study, and to the Civil Engineering Department for the tuition
scholarships awarded. I am also thankful to Malika Rana, an undergraduate student,
who helped in the data reduction work.
My father, Satpal Maini, helped me substantially collecting data in India, and also
performed a significant amount of the data reduction work. My father-in-law,
Harbans Singh Mehta, and my brothers Vineet and Ashish Maini, also helped collect
data for this study. My mother Sudesh Maini always encouraged me, specially in the
lean times. This thesis resulted in numerous hours spent away from my son, Anmol,
and I thank him for the understanding and his nightly prayers. Finally, this work
would not have been possible without the constant support of my wife Surinder, and I
am very thankful for that. I am looking forward to the countless hours that I can now
spend with my family!
A special thank you to Heng Wei for allowing me to use his program, VEVID. This
greatly reduced the data reduction time. Numerous other people in India helped me
in the data collection effort. I would like to acknowledge the help provided by Dr.
T.S. Reddy (Central Road Research Institute, New Delhi), M.S. Upadhye (Deputy
Commissioner of Police, Delhi), and M.K. Tandon (Assistant Commissioner of
Police. Baroda) in helping me gain access to the vantage points for recording the
traffic flow. Additionally, I would like to thank my uncles Madan Maini and Jitendra


Kaushal, and cousin Vivek MainL for helping collect the maximum deceleration rate
data.


CONTENTS
Figures........................................................................xv
Tables......................................................................xviii
Chapter
1. Introduction...........................................................1
1.1 Background.............................................................1
1.2 Need for Heterogeneous Traffic Simulation Model........................2
1.3 Objectives of Study....................................................4
1.4 Scope of Study.........................................................5
1.5 Organization of Thesis.................................................6
1.6 Significant Contributions of Study.....................................7
2. Heterogeneous Traffic Characteristics and Simulation Components........8
2.1 Differences Between Homogeneous and Heterogeneous Traffic Flow.........8
2.2 Simulation Modeling and Components....................................10
2.2.1 Simulation Process....................................................11
2.2.2 Components of a Heterogeneous Traffic Simulation Model................13
2.2.2.1 Roadway...............................................................14
1.2.2.2 Vehicle-Following, Lateral Movement and Overtaking....................15
2.2.23 Lateral and Longitudinal Gaps.........................................17
2.2.2.4 Intersection Geometry and Turning at Intersections....................18
2.2.2.5 Intersection Control..................................................19
2.2.2.6 Creeping at Intersections.............................................21
2.2.2.1 Arrival Pattern.......................................................22
2.2.2.8 Acceleration Rates....................................................23
2.2.2.9 Driver Perception Threshold...........................................23


3. Literature Review.................................................25
3.1 Use of Modified Homogeneous Traffic Models for Heterogeneous Traffic 26
3.2 Microscopic Simulation Models.....................................27
3.2.1 Initial Vehicle-Following Theories................................28
3.3 Recent Vehicle-Following Theories.................................34
3.3.1 CARSIM............................................................34
3.3.2 INTELSIM..........................................................36
3.3.3 Psycho-Physical Vehicle-Following Theory..........................40
3.3.4 Neural-Network Driver Decision Model..............................41
3.3.5 Cellular Automata Theory..........................................42
3.4 Heterogeneous Traffic Microscopic Simulation Models...............44
3.4.1 Heterogeneous Models for Traffic in India.........................45
3.4.1.1 INSWERTS..........................................................45
3.4.1.2 MORTAB............................................................46
3.4.1.3 Urban Uninterrupted Flow Traffic Simulation Model (Singh).........47
3.4.2 Heterogeneous Model for Traffic in Indonesia (TRASMIC)............53
3.4.2.1 Vehicle Characteristics...........................................54
3.4.2.2 Modeling Approach and Vehicle Movement Heuristics.................54
3.4.2.3 Model Validation..................................................56
3.4.3 Heterogeneous Models for Traffic in Bangladesh....................56
3.4.3.1 MDCSIM............................................................56
3.4.3.2 MIXNETSIM.........................................................59
3.5 Reaction Time.....................................................61
3.5.1 Brake Movement Time...............................................62
3.5.2 Total Reaction Time Laboratory/Simulator Measurements.............63
3.5.3 Total Reaction Time Field Measurements............................64
3.5.4 Reaction Time in Vehicle-Following Models.........................66
3.6 Arrival Pattern...................................................68
x


3.7 Simulation Modeling Languages..........................................71
3.7.1 General Purpose Programming Languages..................................72
3.7.2 Simulation Languages...................................................74
4. Data Collection and Analysis...........................................75
4.1 Data Collection Objectives.............................................76
4.2 Data Collection Methods Used In Other Studies..........................77
4.3 Data Collection Procedures.............................................78
4.3.1 Video Data Collection..................................................79
4.3.1.1 Camera Location........................................................79
4.3.1.2 Video Tape Formats.....................................................81
4.3.2 Manual Data Collection.................................................82
4.3.2.1 Location Details.......................................................82
4.4 Video Data Reduction Procedure.........................................89
4.4.1 Video Capture..........................................................89
4.4.2 Coordinate Conversion..................................................90
4.5 Dynamic Data Analysis..................................................94
4.5.1 Velocity and Acceleration Determination................................94
4.6 Vehicle, Driver and Traffic Characteristics Observed and Calculated..95
4.6.1 Vehicle Classification.................................................98
4.6.2 Vehicle Arrival Pattern...............................................101
4.6.3 Stopped and Overtaking Lateral Gap....................................107
4.6.4 Stopped Longitudinal Gap..............................................109
4.6.5 Free Flow Speed......................................................111
4.6.6 Turning Speed........................................................112
4.6.7 Acceleration Rate....................................................114
4.6.8 Normal Deceleration Rate.............................................117
4.6.9 Maximum Deceleration Rate.............................................119
4.6.10 Moving Longitudinal Gap...............................................121


5. Proposed Vehicle-Following Model (VEHFOL).........................123
5.1 Vehicle-Following Principles......................................123
5.2 Drawbacks of Other Vehicle-Following Models.......................124
5.3 Proposed Vehicle-Following Model VEHFOL.........................126
5.3.1 Perception Threshold..............................................128
5.3.2 Vehicle-Following Model...........................................131
5.3.2.1 Case 1: 0 < Estimated Steady State Velocity < min(Maximum velocity of
lead vehicle. Maximum velocity of following vehicle)..............134
5.3.2.2 Case 2: Estimated Steady State Velocity < 0.......................135
5.3.2.3 Case 3: Estimated Steady State Velocity > min(Maximum velocity of lead
vehicle. Maximum velocity of following vehicle)...................136
5.3.3 Special Case for Negative, Small, and Inappropriate T values......140
5.3.4 Non-Collision Constraint..........................................142
5.3.5 Limitations on Acceleration Rate..................................145
5.3.6 Creeping at Intersection Vehicle-Following Heuristic............146
5.4 Examination of Vehicle-Following Models...........................148
5.4.1 Data Considered...................................................149
5.4.2 Model Comparisons Performed.......................................151
5.4.2.1 Qualitative Assessment............................................152
5.4.2.2 Statistical Analyses..............................................165
5.5 Conclusions.......................................................174
6. HETSIM Model Components and Validation............................176
6.1 Vehicle Generation and Introduction Sub-Model.....................177
6.1.1 Vehicle Size......................................................180
6.1.2 Vehicle Free-flow Speed...........................................181
6.1.3 Vehicle Entry' Speed..............................................181
6.1.4 Vehicle Turning Speed.............................................182
6.1.5 Stopped and Overtaking Lateral Gaps...............................183
Xil


6.1.6 Stopped Longitudinal Gap...........................................184
6.1.7 Acceleration Rate..................................................185
6.1.8 Normal Deceleration Rate...........................................187
6.1.9 Maximum Deceleration Rate..........................................187
6.1.10 Steady State Time Gap..............................................188
6.1.11 Lateral Gap from Side of Road......................................189
6.1.12 Summary of Vehicle, Driver and Traffic Characteristics.............190
6.2 Vehicle Movement Sub-Models........................................191
6.2.1 Common Characteristics for Vehicle Movement Sub-Models.............193
6.2.1.1 Lateral Movement Rate..............................................194
6.2.1.2 Simultaneous Decision Making and Impact of Reaction Time...........195
6.2.1.3 Locating Front Vehicle.............................................196
6.2.2 Overtaking Sub-Model...............................................200
6.2.2.1 Determining Side-Vehicle...........................................202
6.2.2.2 Determining Front-Side Vehicle.....................................206
6.2.2.3 Non-Collision Constraint for Overtaking Maneuver.................210
6.2.2.4 Determining Back-Side Vehicle......................................215
6.2.3 Turn Movement Sub-Model............................................217
6.2.4 Intersection Control Sub-Model.....................................227
6.2.4.1 Yellow Interval Response...........................................227
6.2.4.2 Red Interval Response..............................................231
6.3 Vehicle Movement Decisions The Comprehensive Process............232
6.4 HETSIM Implementation..............................................234
6.5 HETSIM Validation..................................................238
6.5.1 Characteristics of the Case Studies................................238
6.5.2 MOE Comparisons....................................................241
6.5.2.1 Queue Length Comparison............................................241
6.5.2.2 Stopped Delay Comparison...........................................245
xm


6.5.2.3 Right-Turning Traffic Comparison..................................248
6.5.3 Conclusions.......................................................248
7. HETSIM Applications...............................................250
7.1 Changes to a Specific Network.....................................251
7.1.1 Determining Optimal Cycle Length..................................251
7.1.2 Impact of Replacing Two-wheelers with Buses.......................257
7.2 Developing Relationships..........................................263
7.2.1 Impact of Roadway Widening on Capacity............................263
7.2.2 Determining Passenger Car/Two-wheeler Equivalency Factor for
Different Vehicle Types...........................................267
7.3 Conclusions.......................................................270
8. Summary and Conclusions...........................................272
8.1 Development of HETSIM.............................................273
8.2 HETSIM Validation.................................................276
8.3 HETSIM Applications...............................................278
8.4 Conclusions and Additional Research Needs.........................281
Appendix
A. Sample Programming Code...........................................284
References...........................................................301
xiv


FIGURES
Figure
2.1 Heterogeneous Traffic Flow at An Intersection Approach..................9
2.2 Components of a Heterogeneous Traffic Simulation Model.................14
2.3 Multiple Lead Vehicles for a Following Vehicle.........................16
2.4 Variation in Stopped Longitudinal and Lateral Gaps.....................18
2.5 Advancement of Small Size Vehicles to Head of Queue....................19
2.6 Creeping of Small Size Vehicles to Head of Queue.......................21
3.1 Pipes Vehicle-Following Logic Vehicle Positions and Characteristics.29
4.1 Ideal Camera Placement at Controlled Intersections.....................80
4.2 Example View at Signalized Intersection (Ashram NB, New Delhi).........81
4.3 Schematic (Plan View) of Khanderao Intersection, Baroda................85
4.4 Schematic (Plan View) of Kothi Intersection, Baroda....................86
4.5 Schematic (Plan View) of Ashram Intersection, New Delhi................87
4.6 Observed and Estimated Time Headway Distributions Ashram EB
Motorized Vehicles Arrivals on Green..................................106
4.7 Observed and Estimated Time Headway Distributions Ashram EB
Motorized Vehicles Arrivals on Latter Part of Red.....................106
5.1 Determining the Following Vehiclesr Acceleration......................139
5.2 Collision Constraint: Showing Lead and Following Vehicle Over Time....143
5.3 Vehicle-Following Case 3; Bus-Bus; Accelerating.......................154
5.4 Vehicle-Following Case 7; Auto-rickshaw-Light Commercial Vehicle;
Accelerating..........................................................155
5.5 Vehicle-Following Case 10; Bus-Auto-rickshaw; Decelerating............156
5.6 Vehicle-Following Case 11; Bus-Auto-rickshaw; Decelerating............157
xv


j
5.7 Vehicle-Following Case 12: Bus-Auto-rickshaw; Decelerating...........158
5.8 Vehicle-Following Case 17; Two-wheeler-Car; Decelerating.............159
5.9 Vehicle-Following Case 21; Auto-rickshaw-Auto-rickshaw; Flow During
Green ..............................................................160
5.10 Vehicle-Following Case 22; Two-wheeler-Auto-rickshaw; Flow During
Green ..............................................................161
5.11 Vehicle-Following Case 24; Auto-rickshaw-Car; Flow During Green......162
5.12 Vehicle-Following Case 26; Car-Car; Flow During Green................163
5.13 Vehicle-Following Case 27; Car-Car; Flow During Green................164
5.14 Cumulative Distribution of Field and Model Estimates of Acceleration
Rate for Flow During Green..........................................173
6.1 Vehicle Position Terminology.........................................193
6.2 Search Area for Locating Front Vehicle...............................197
6.3 Locating Front Vehicles in Search Area...............................199
6.4 Determining Acceleration Rate Based on Front Vehicle Interaction.....200
6.5 Lateral Distance to Move to Overtake from Right......................203
6.6 Search Area for Locating Side-Right Vehicle..........................204
6.7 Search Area for Locating Front-Right-1 and Front-Right-2 Vehicles....207
6.8 Search Area for Locating Front-Right-3 Vehicle.......................209
6.10 Considering Non-Collision while Overtaking...........................212
6.12 Determining Acceleration Rate to Avoid Collision with Front-Side
Vehicle while Overtaking............................................214
6.13 Search Area for Locating Back-Right Vehicle..........................215
6.14 Virtual Turning Lanes and Placement of Vehicles Stopped at Intersection .218
6.15 Impact of Tum Intention on Acceleration Rate.........................220
6.16 Impact of Tum Intention on Lateral Movement..........................221
6.17 Lateral Move for Turning Vehicle to Reach Turning Lane...............223
xvi


6.18 Search Area for Locating Front Vehicle for Right-turning Reference
Vehicle .............................................................225
6.20 Impact of Yellow Signal Indication on Acceleration Rate..............231
6.21 Vehicle Movement Decisions...........................................233
7.1 HETSIM Model Inputs and Outputs......................................250
7.2 Effect of Flow Rate and Cycle Length on Average Travel Time..........255
xvii


TABLES
Table
3.1 Vehicle-Following Theories Key Characteristics........................32
3.2 Deceleration Rate Determination in CARSEtM............................36
3.3 Accelerator-Brake Movement Time...................................... 62
3.4 Field Measured Accelerator-Brake Movement Time........................63
3.5 Reaction Time for Indian Drivers.................................... 64
3.6 Field Measured Reaction Times........................................ 65
3.7 Brake Perception-Reaction Time Summary from 16 Studies................66
3.8 Reaction Time in Different Vehicle-Following Models...................67
4.1 Intersection Approach Details........................................ 83
4.2 Mid-block Location Details............................................84
4.3 Data Observed and Used in Various Heterogeneous Traffic Simulation
Models ...............................................................97
4.4 Traffic Flow Rate and Composition at Six Imtersection Approaches......99
4.5 Vehicle Dimensions and Fleet Composition.............................100
4.6 Arrival Pattern Characteristics at Six Intersection Approaches......103
4.7 Arrival Pattern Comparison Observed andl Estimated Distributions
(K-S Test)...........................................................105
4.8 Stopped Lateral Gap..................................................107
4.9 Overtaking Lateral Gap...............................................109
4.10 Stopped Longitudinal Gap............................................110
4.11 Free Flow Speed .....................................................112
4.12 Turning Speed........................................................113
4.13 Acceleration Rate....................................................116
xviii


4.14 Normal Deceleration Rate............................................118
4.15 Maximum Deceleration Rate ..........................................120
4.16 Steady State Time Gap...............................................122
5.1 Summary of Vehicle-Following Cases Considered.......................150
5.2 Absolute Difference between Field and Model Estimates of Acceleration.. 166
5.3 Absolute Difference between Field and Model Estimates of Velocity..166
5.4 Absolute Difference between Field and Model Estimates of Headway...167
5.5 Comparison of Field and Model Estimates of Velocity Every Half-
Second Grouped by Vehicle Type.....................................168
5.6 Comparison of Field and Model Estimates of Velocity Every Half-
Second Grouped by Mode of Operation................................169
5.7 Comparison of Field and Model Estimates of Headway Every Half-
Second Grouped by Vehicle Type.....................................169
5.8 Comparison of Field and Model Estimates of Headway Every Half-
Second Grouped by Mode of Operation................................170
5.9 Comparison of Field and Model Estimates of Acceleration Every Half-
Second Grouped by Vehicle Type.....................................170
5.10 Comparison of Field and Model Estimates of Acceleration Every Half-
Second Grouped by Mode of Operation................................171
5.11 K-S Test Results for Field and Model Estimates of Acceleration Rate for
Flow During Green Operation Mode...................................174
6.1 Vehicle Sizes in HETSIM............................................180
6.2 Entry Speeds in HETSIM..............................................182
6.3 Turning Speeds in HETSIM............................................183
6.4 Lateral Gaps in HETSIM..............................................184
6.5 Stopped Longitudinal Gaps in HETSIM.................................185
6.6 Initial Acceleration Rates in HETSIM................................186
6.7 Latter Acceleration Rates in HETSIM................................186
xix
I


6.8 Normal Deceleration Rates in HETSIM...................................187
6.9 Maximum Deceleration Rates in HETSIM..................................188
6.10 Steady State Time Gaps in HETSIM.......................................189
6.11 Lateral Gaps from Side of Road in HETSIM...............................190
6.12 Summary of Vehicle, Driver and Traffic Characteristics.................191
6.13 Limits for Search to Locate Front Vehicle..............................198
6.14 Limits for Search to Locate Side-Right Vehicle.........................205
6.15 Limits for Search to Locate Front-Right-1 and Front-Right-2 Vehicles..208
6.16 Limits for Search to Locate Front-Right-3 Vehicle.....................210
6.18 Limits for Search to Locate Back-Right Vehicle.........................216
6.19 Limits for Search to Locate Front Vehicle for a Right-turning Reference
Vehicle .............................................................226
6.21 Driver Response to Yellow Signal Indication............................229
6.22 Sample Methods used in HETSIM Implementation...........................236
6.23 Intersection Approach Characteristics..................................239
6.24 Simulated and Observed Queue Length Comparisons........................243
6.25 Simulated and Observed Stopped Delay Comparisons.......................246
6.26 Simulated and Observed Right-Turning Traffic Comparisons...............248
7.1 Input Data for Evaluation of Optimal Cycle Length......................253
7.2 Average Travel Time (s) Variation with Cycle Length and Flow Rates....255
7.3 Average Queue Length (m) Variation with Cycle Length and Flow Rates.. 256
7.4 Evaluation of Fleet Composition Changes: Traffic Conditions Considered 258
7.5 Queue Length for Alternative Scenarios of Fleet Composition............259
7.6 Travel Time for Alternative Scenarios of Fleet Composition.............259
7.7 Average Emission Factors for Indian Vehicles on Urban Indian Roads ....261
7.8 Total Emissions for Alternative Fleet Composition Scenarios............262
7.9 Evaluation of Impact of Roadway Width on Capacity: Traffic Conditions
for Two Scenarios....................................................265
xx


7.10 Impact of Roadway Width on Capacity Scenario 1 (New Delhi)........266
7.11 Impact of Roadway Width on Capacity Scenario 2 (Baroda)...........266
7.12 PCU Values for Different Vehicle Types from Other Studies...........268
7.13 Saturation Flow Rates and Equivalency Factors of Individual Vehicle
Types ............................................................269
xxi


1.
Introduction
1.1 Background
The growing use of motorized vehicles has led to a significant increase in the
problems associated with traffic in all parts of the world. In most countries this is due
to an increase in automobile ownership per household, coupled with their use for
longer commuting trips to work and the inadequate growth of the transportation
facilities. Although in countries with low levels of industrialization the number of
motorized vehicles is comparatively small, their rapid growth and use in the past
decade has caused significant environmental problems. Some of these countries have
experienced up to 10-15% annual automobile growth rates. In India, there has been a
significant increase in motorized vehicles since the mid 1980's. The number of
motorized vehicles increased from 10.58 million in 1986 to 33.56 million in 1996
(Ministry of Surface Transport 1998), representing an average annual growth rate of
12.25%. The growth in transportation facilities has significantly lagged the growth of
automobiles and their use, resulting in detrimental impacts on the people and their
environment.
A unique characteristic of traffic in developing countries is that there is a wide
variation in the operating and performance characteristics of the vehicle types used,
and a significant proportion of the trips are by smaller sized vehicles or by non-
motorized modes. Various studies in the 1960's (Wilbur Smith and Associates 1963),
(Calcutta Metropolitan Planning Organization 1966) recommended the gradual
phasing out of these "disturbing modes of transportation. However, later studies
have documented the importance of maintaining these modes of transportation, given
the economic and social impacts associated with their removal. In large urban areas.
1


there has been a gradual decrease in the number of non-motorized vehicles, and
consequently the share of total trips that are serviced by this mode. In a
comprehensive study of ten major roads in New Delhi, India with a population of 9.4
million (1991), it was noted that the bicycle traffic had decreased from 38.0% in 1969
to 13.3% in 1984 (Central Road Research Institute 1985). The fast-moving vehicles
had increased from 60.6% to 83.1% in the same period. Although this trend has
continued since then, non-motorized vehicles still play a significant role in medium
and smaller sized cities. In a recent study in a medium sized city in India (Kanpur
population 1.7 million) (Singh 1999), non-motorized vehicles (primarily bicycles and
cycle-rickshaws) comprised over 60% of the traffic flow. Additionally, small sized
motor vehicles (two-wheelers) still account for over half the vehicles on most urban
roads in India.
1.2 Need for Heterogeneous Traffic Simulation Model
Given the continued importance of varied vehicle types, the challenge now is to
accurately evaluate these mixed or heterogeneous traffic flow systems. Initial efforts
in this area focused on evaluating these systems as a special case of the homogeneous
systems found in industrialized nations. The most common technique converts the
different vehicles into equivalent passenger car units, and then applies analysis
techniques such as those presented in the Highway Capacity Manual (Transportation
Research Board 1985). Many such efforts have been conducted in India (Justo and
Tuladhar 1984; Indian Roads Congress 1994; Chandra, Sikdar et al. 1996). As will
be detailed later, other studies (Yanaguaya 1993) have shown the limitations of using
such techniques given the significant differences in the traffic flow characteristics and
dynamics. This is discussed in detail later.
?


Both empirical and simulation techniques have been previously used to model traffic
flow. The empirical techniques have been developed based on detailed observations
of traffic flow. Certain key characteristics, such as roadway width and grade, have
been studied and their impacts have been included in the empirical relationships
developed. These form the basis of the empirical techniques, and an important
background for the simulation techniques. Simulation techniques have been
developed for macro, meso and microscopic conditions, with the primary difference
being in the level of detail of vehicle interactions. Both macro and mesoscopic
techniques are primarily based on analytical relationships that have been developed
by analyzing a significant amount of data. On the other hand microscopic techniques
are based on vehicle-following models.
The use of macroscopic techniques has posed different challenges to researchers. For
example, researchers have faced difficulty in representing congested conditions and
certain geometric features and transportation facility controls in macro and
mesoscopic models. On the other hand, the calibration and validation of microscopic
simulation models has also proved to be very difficult. Analytical models based on
driver behavior under different traffic conditions may not yield direct solutions.
However, numerical solutions of the models may be represented in microsimulation.
Microscopic simulation may be used to evaluate the impacts of changes in the design,
operation and control of transportation systems and therefore serves as a useful tool.
In recent years the use of microsimulation has increased considerably. In some cases,
microsimulations are coupled with macrosimulation as a bi-level formulation, or a
dispersion model for air quality analysis. Therefore, a microscopic simulation for
heterogeneous traffic has wide applications as a traffic analysis tool. A reliable
estimate of vehicle operations and emissions is obtained from a traffic flow
simulation, and subsequently the impact on air quality can be estimated.
3


1.3 Objectives of Study
In transportation networks, controlled intersections typically have significantly lower
capacity than a comparable uninterrupted transportation facility. These intersections
cause a significant proportion of vehicles to slow down or stop, and subsequently
accelerate, thus resulting in increased delay and vehicle emissions. To adequately
study urban transportation networks, it is important to appropriately model controlled
intersections. The primary objective of this study is to develop a microscopic
simulation model to represent the flow of heterogeneous traffic at controlled
intersections. The objectives of this study are to:
1. Study the characteristics of heterogeneous traffic at controlled intersections.
2. Collect data to formulate, calibrate and validate a microsimulation model.
3. Develop a vehicle-following model that adequately represents the interaction of a
pair of vehicles (leader and follower) and generates better estimates of
acceleration rates, the resulting velocity, and position of following vehicles.
4. Compare the performance of the proposed vehicle-following model to existing
vehicle-following models.
5. Implement the vehicle-following model in a comprehensive traffic simulation to
include models for overtaking, response to turn intention, response to intersection
control and creeping of vehicles at intersections.
6. Calibrate and validate the simulation model using measures of effectiveness
(MOEs) such as delay and queue lengths.
4


1.4 Scope of Study
Due to the significant amount of data required in the development of this simulation
model, and the limited resources available for its development, the scope of the study
is limited. The following describes the scope of the study:
1. Flow of traffic at only controlled (signal or police) intersections is modeled.
2. Data collected at 13 intersection approaches (at 5 intersections) in two cities (New
Delhi and Baroda) are analyzed. Right turns are allowed on 10 intersection
approaches, and always operate under a protected phase. Thus, the gap
acceptance of permitted movements is not considered.
3. Video recordings of traffic flow on the intersection approaches were limited to a
view ranging from 30 m to 350 m. The vehicle interactions considered in this
study are based on data reduced from these recordings. Additional video data
collected at mid-bock locations were also analyzed.
4. Video recordings were conducted from buildings adjacent.to the intersections. In
some cases, due to the limited height of the buildings and the building setbacks,
the lateral and longitudinal gaps between vehicles were not always discernible in
all the video recordings.
5. The proportion of bicycle traffic on the different intersection approaches ranged
from 3.4% to 31.4%. Additional non-motorized vehicles comprised 0.4% to 2.6%
of the traffic flow. The bicycles and other non-motorized vehicles typically travel
on the extreme left side of the road, and interact with the motorized vehicles in a
limited manner.
5


1.5 Organization of Thesis
This thesis is presented in eight chapters. In Chapter 2. the differences between
heterogeneous and homogeneous traffic are detailed. Additionally, the components
of a heterogeneous traffic simulation model that are either different from similar
components in homogeneous models or are altogether new are detailed.
In Chapter 3, a comprehensive literature review is presented. Information on various
attempts at using homogeneous models to represent heterogeneous traffic is
presented. This is followed by a summary of microscopic studies, with particular
emphasis on vehicle-following models and previous microscopic models for
heterogeneous traffic. Reaction time and arrival pattern, two important components
of simulation models, are discussed and finally, a review on simulation modeling
languages is presented.
Chapter 4 contains details on the data collection and analysis methodology, and
includes a summary of data reduced in this study. These data include acceleration
and deceleration rates, lateral and longitudinal gaps, vehicle-following time gap, and
turning and free flow speeds.
The vehicle-following model including the enhanced non-collision constraint
developed as part of this study is presented in Chapter 5. A comparison of the
proposed vehicle-following model with two other models that represent
heterogeneous traffic is also presented.
In Chapter 6, other primary components (vehicle introduction, overtaking, response to
turn intention, and response to intersection) of the simulation model are detailed.
Vehicle characteristics used in the model are detailed. All the heuristics considered,
and results on the validation of the model are presented in this chapter.
6


In Chapter 7, applications of the simulation model are demonstrated. These include
using the model to estimate the impact of changes to the design and control at
intersections, and using output from the model to develop theoretical relationships.
The conclusions of the study, including areas for further research are detailed in
Chapter 8.
1.6 Significant Contributions of Study
The significant contributions of this dissertation work are:
1. A vehicle-following model and a comprehensive microscopic traffic simulation
model is developed for controlled intersections in India. Microscopic simulation
models have been developed for uninterrupted roadway facilities such as trunk
roads or highways and mid-block locations. However, this is the first model
developed specifically for intersections.
2. Aggregate measures such as average vehicle delay and queue length have been
used as performance measures for other heterogeneous models. In addition to
these measures, this study also examines vehicle trajectories and reports
performance statistics based on this.
3. Acceleration rate estimates every second are compared to observed data. Other
studies have compared only velocity and headway estimates to observed data.
4. This is one of two studies on heterogeneous traffic, and the first for Indian
conditions, to report acceleration and deceleration rates at intersections, and
lateral and longitudinal gaps for stopped condition.
7


2. Heterogeneous Traffic Characteristics and
Simulation Components
There are many differences between heterogeneous traffic and homogeneous traffic
that is typically found in industrialized nations. These differences include the
physical differences in vehicle sizes and operating characteristics, and differences in
driving behavior. Additionally, the roadway environment is typically very different
for heterogeneous traffic. In this chapter, the primary differences between
heterogeneous and homogenous traffic are detailed. Following this, the general
simulation modeling process is detailed and primary components of a heterogeneous
traffic simulation model are identified. The ways in which these components differ
from homogeneous traffic models are also discussed.
2.1 Differences Between Homogeneous and
Heterogeneous Traffic Flow
The differences that characterize heterogeneous traffic systems or otherwise known as
mixed traffic systems are mainly due to wide variation in the operating and
performance characteristics of the vehicles. The traffic in mixed flow' is comprised of
fast moving and slow moving vehicles or motorized and non-motorized vehicles. The
motorized vehicles include two-wheelers (motorcycles, scooters and mopeds), auto-
rickshaws (motorized three-wheeler vehicle, primarily used as a taxi), cars, buses, and
trucks, and the non-motorized vehicles include bicycles, human-powered or cycle-
rickshaws, human-powered carts and animal-powered carts. The vehicles also vary in
size, maneuverability, control, and static and dynamic characteristics. These vehicles
travel in the same right of way. In urban areas, substantial pedestrian movement,
encroachment along the road, street parking, and narrow roads, often also accompany
mixed traffic flow.
8


The movement of heterogeneous traffic is depicted in Figure 2.1. Lane markings are
typically present for homogeneous traffic, and drivers use the markings to maintain
lane discipline. However, these markings are usually not provided for heterogeneous
traffic conditions, and even where provided are not adhered to. Therefore, mixed
flow traffic does not move in single files. On the contrary, there is a significant
amount of lateral movement, primarily by the smaller sized motorized vehicles (two-
wheelers). Vehicles do not have one leader, but several perhaps front-left, front and
front-right. As vehicles do not follow each other within lanes, the concept of relating
headways and linear densities (such as vehicles per mile) are not meaningful. Also,
as vehicles traverse in both longitudinal and lateral directions, it is inappropriate to
use lane-based vehicle interaction models.
Figure 2.1 Heterogeneous Traffic Flow at An Intersection Approach
9


Vehicle interaction in mixed flow is further complicated by the large? variation in
speed between different vehicle types. In general, these speeds are sngnificantly
lower than the speeds in homogeneous traffic networks. Also, at intersections
specifically, smaller vehicles such as bicycles and motorized two-wh*eelers use the
lateral gaps between larger vehicles in an attempt to reach the head o-f the queue.
There is also a lack of control at many unsignalized intersections and roundabouts,
and priority is typically given to the larger vehicle. Due to these sigmiflcant
differences, it is inappropriate to use models developed for homogeneous traffic to
represent heterogeneous traffic flow.
2.2 Simulation Modeling and Components
A closed-form analytical solution to a mathematical model representing a highly
complex real system may be extraordinarily complex or intractable. The model may
then be studied by means of a simulation, i.e. by numerically exercising the model for
inputs in question to see how they affect the output measures. Trafficc flow analysis is
conducted using either analytical techniques or simulation methods. Each of these
alternatives has its advantages and disadvantages. A simulation may be static or
dynamic, deterministic or stochastic, continuous or discrete. A systean may be
modeled at different levels of detail: micro, meso or macroscopic. Tlhe various
elements that constitute a stochastic microscopic traffic simulation m.odel include
arrival flow pattern, driver behavior (acceleration/deceleration rates, rreaction time),
and intersection control.
Prior to 1980, in the U.S. there were over 25 intersection simulation xmodels, and
another 25 simulation models to evaluate arterial conditions (Transpoortation Research
Board 1981), with approximately half of these being microscopic stimulation models.
Updated versions of some of the microscopic simulation models, sucflh as NETSIM
10


(Federal Highway Administration 1997), and TEXAS (Inman, Lee et al. 1993) are
currently used widely. There are other microscopic simulation models, such as
SWERTS (Brodin and Carlsson 1979) that are used to simulate conditions on two-
lane rural roads in Sweden. Prior to the early 199(Ts, the computing requirements for
most of these microscopic simulation models were significantly greater than those
available to users other than researchers.
In the past ten years, computer simulation has gained significant acceptance for use
by the traffic engineering community. There are three primary reasons for that. The
first is that there is a greater occurrence of congested conditions in most urban
roadway networks. Secondly, the analysis problems have become more complex, e.g.
a greater number of closely spaced intersections, a mix of traffic controls applied at
intersections (two-way stop, all-way-stop, signalization, roundabout), and the need to
consider the impact of freeway entry ramp operations on local street operations. For
some of the conditions mentioned, the analytical procedures may be extremely
complex and can only be applied in simulation models. Finally, the advances in
computer technology have significantly increased the availability of computing
resources. In the past ten years, simulation tools have been used with field
measurements, to enhance the analytical procedures included in documents such as
the Highway Capacity Manual, and this trend is expected to continue. Thus, it is
appropriate to consider further development of such tools to enhance the
understanding of complex traffic situations.
2.2.1 Simulation Process
There are three basic components of any simulation model (Chin 1983; Central Road
Research Institute 1985):
11


1. Inputs: definition of relevant input particulars of interacting components or parts
of the system, and for factors that influence the process being modeled. This
includes the various parameters and variables that may assume different values,
depending on the condition of the system.
2. Decision Logic: rules that form the basis of the simulation model. This includes
both functional relationships describing the behavior of the entities and their
mutual interaction, as well as the constraints imposed on the rules and the values
of variables.
3. Output: definition of the evaluation process of the model (time-driven or event-
driven), and the process of recording the various measures of effectiveness
(MOEs) used to validate and calibrate the model and any additional MOE's of
interest.
The details of each component depend on the process being simulated, its scope
(global vs. local) and subsequently the degree of accuracy required. An important
feature of any simulation process is time management. Any real system is a
continuum with regards to time. Two common methods of time management used in
simulation modeling are:
1. Event Scanning: The time is updated when the next event takes place, and thus
the time interval is a variable. In traffic flow simulation, for a lead vehicle
approaching an intersection, the event may be the change of the signal indication
from green to yellow, which prompts the driver to consider stopping.
2. Periodic Scanning: The time is updated based on a constant interval. The
resolution of the interval length considered is significant, as it has a direct impact
on the computation time required for the simulation. In most previous traffic flow
simulation studies, this has been the preferred method of time management given
the relative ease of implementing this choice.
12


2.2.2 Components of a Heterogeneous Traffic
Simulation Model
As outlined in section 2.1, heterogeneous traffic is significantly different from
homogeneous traffic. Thus, although some of the components of a heterogeneous
traffic model are the same as those of a homogeneous traffic model, there are other
components that are either significantly different or new. The various components,
decision rules, and outputs are depicted in Figure 2.2. The primary inputs for a model
include the roadway and traffic characteristics. Additionally, information on
intersection controls is provided as input. For a microscopic traffic simulation model,
driver and vehicle characteristics are also provided. Several sub-models determine
the movement of vehicles, and the vehicle positions are updated based on the time
management system adopted. Data on the movement of vehicles are then
summarized to obtain MOE's. These MOE?s may be compared either across
different alternative runs, or the model estimated MOE's may be compared with
observed data to evaluate the model performance. The primary differences between
the important components of heterogeneous and homogeneous traffic flow' models are
detailed next.
13


INPUTS
i ROADWAY i r TRAFFIC !
{ Link Length : j Flow rate j
| Link width ! i Composition '
Speed limit j | Vehicle Sizes j 1
T
INTERSECTION Phase lengths (Green/Yellow/Red) or (Go/Stop) 1 1 i ! DRIVER j Reaction Time J Perception j Threshold j | | DRIVER-VEHICLE i j Acceleration/ | j Deceleration rates \ | Longitudinal/Lateral [ j clearances | i Maximum speed 1
1 i j j
j
___________z__________
DECISION LOGIC
Lateral movement
Following
Overtaking
Response to signals
Turn movement logic
Creeping at intersections
i
I
______________i_____________
OUTPUTS
Travel time/Delay
Queue length
Acceleration/Deceleration rates
Velocity
Headway
Figure 2.2 Components of a Heterogeneous Traffic Simulation Model
2.2.2.1 Roadway
As detailed earlier in section 2.1, heterogeneous traffic flow is typically non-lane
based. This is evident in the flow at two intersection approaches depicted earlier in
Figure 2.1. Even though striping may be provided on the pavement, it is normally not
14


adhered to. Thus, it is only the usable lane width that is important, and not the
number of lanes. Also, the speed limit is defined for very few roadways, and even
where it is defined it is neither adhered to nor enforced. The free flow speed of
vehicles on a certain roadway link is based on the width, pavement condition, and the
purpose it serves. For simulation purposes, the free flow speed is determined by field
observations.
2.2.2.2 Vehicle-Following, Lateral Movement and
Overtaking
In most homogeneous traffic systems, a vehicle traveling in a lane may be following
only one vehicle. This occurs when the vehicle in front is traveling slower, and the
following vehicle cannot overtake the vehicle in front. However, in heterogeneous
traffic systems vehicle sizes are significantly different and vehicles are not restricted
to lanes but rather can maintain any position laterally. Thus, a vehicle may have
multiple lead vehicles, and it considers the actions of all those vehicles in determining
an appropriate response. In the photograph in Figure 2.3, Car 1 is the following
vehicle, and considers the action of the vehicles that are directly in front. Car "2 and
Car "3.
15


1
I
I
Figure 2.3 Multiple Lead Vehicles for a Following Vehicle
In homogeneous traffic, a following vehicle overtakes from only one side (from the
right side in a left-hand drive system, and from the left side in a right-hand drive
system) by moving completely from one lane to the other. However, in most non-
lane based heterogeneous traffic systems, although vehicles have a preference for
overtaking from the right (in a left-hand drive system), they also consider overtaking
the lead vehicle from the left side. Additionally, as the traffic flow is non-lane based,
the vehicle does not necessarily have to move an entire lane width, but rather can
move any distance laterally. In heterogeneous traffic systems, a faster vehicle
approaching a slow moving vehicle from behind may use the horn as a means of
requesting the slower vehicle to move to the side so that the faster vehicle can
overtake. Although this latter behavior is quite prevalent, it results in a very complex
model, and thus a simplified approach is considered in this study.
Also, in homogeneous traffic systems, when a vehicle decides to move laterally
(changes lane), it considers the nearest vehicle behind it in the lane it intends to move.
16


Typically, the vehicle will change lanes only if it determines that a sufficient gap
exists such that the vehicle behind does not have to decrease its speed. However, in
heterogeneous traffic systems the burden of avoiding a collision is transferred to the
vehicle that is behind. The vehicle will typically move laterally if it determines the
other vehicle that is behind can avoid a collision, even though the other vehicle may
need to apply its emergency brakes.
2.2.2.3 Lateral and Longitudinal Gaps
Lateral or sidew'ay gaps are typically not considered in homogeneous traffic
simulation models, as it is expected that traffic is traveling in lanes. However, in the
non-lane based heterogeneous traffic system, there is considerable variation in the
lateral gaps maintained by different drivers. The variation is important to consider as
it has an impact on the overtaking maneuver. The longitudinal gaps maintained while
following other vehicles, and in the stopped condition (at intersections) are also
different for different vehicle types. Drivers of smaller sized motorized vehicles and
non-motorized vehicles (bicycles and cycle-rickshaws) have a much better view of
the road, and are located close to the front of the vehicle. This helps them in
estimating the gaps from other vehicles more easily, and thus they maintain
comparatively smaller stopped longitudinal gaps. However, most vehicle types
maintain larger gaps from large sized vehicles such as trucks and buses, possibly to
decrease the risk of collision and significant injury and vehicle damage. The
variations in the stopped longitudinal and lateral gaps are evident in Figure 2.4.
When the vehicles are moving, the longitudinal gap maintained with other vehicles
appears to increase with vehicle size. However, an exception to this general rule of
thumb is the smaller gap maintained by auto-rickshaw drivers, who are typically more
aggressive.
17


Figure 2.4 Variation in Stopped Longitudinal and Lateral Gaps
2.2.2.4 Intersection Geometry and Turning at
Intersections
The differences in intersection geometry in heterogeneous traffic systems compared
to homogenous traffic systems are similar to the roadway differences outlined earlier.
At most intersections in heterogeneous traffic systems, there is no channelization
provided for turning movements with either striping or other physical means. Thus,
frequently vehicles proceeding through the intersection, or turning left or right occupy
the same lateral space. This characteristic also has an impact on the intersection
control adopted at most intersections, where all the movements on a given approach
are given the green signal simultaneously, and the intersection is operated as the
equivalent of a split phase control. This form of control is not very efficient.
18


Occasionally right turning vehicles that may be discharging at a slightly slower rate
delay vehicles that are proceeding straight through the intersection.
At many intersections the intersection is flared at the comers, and thus the left turning
traffic (in a left-hand drive system) is frequently not affected significantly by the
intersection control. Additionally, smaller sized vehicles use this additional space to
advance to the head of the queue. This phenomenon is shown in Figure 2.5, in which
the motorized two-wheelers visible on the right side of the photograph have reached
the head of the queue by using the space provided for the left turning traffic.
2.2.2.S Intersection Control
For homogeneous traffic, intersection control is provided at most intersections. The
typical forms of intersection control are traffic signal, stop signs (two-way or all-
way), yield signs and roundabout (yield on entry). In heterogeneous traffic systems,
intersection control in the form of traffic signal or police control is provided only at
the major intersections. In most countries, the traffic signal phase for a movement
includes three intervals. These are the green, yellow and red intervals. The yellow
19


interval is provided so that an approaching vehicle has the opportunity to react to the
signal change, by either slowing down and stopping before the red interval starts or
by continuing at the same speed/increasing speed to proceed through the intersection.
In some countries, an all-red interval is also used, which allows vehicles entering the
intersection space at the end of the yellow interval to clear the intersection before the
next traffic movement is allowed to move. The all-red interval is not provided in
most countries with heterogeneous traffic, including India. Thus, in some cases
vehicles entering the intersection during the yellow interval result in a delayed start
for vehicles in an opposing movement.
The operation at police controlled intersections is a bit different. The traffic police
personnel are located either in a booth in the center of the intersection, or at the end of
the median on one or more of the intersection approaches. The traffic police attempt
to optimize the flow through the intersection by considering various factors, including
the length of the queue, the delay experienced by vehicles, and the arrival pattern of
vehicles. However, this optimization proves to be difficult at times because the
traffic police are attempting to optimize the flow from four approaches
simultaneously.
Due to the signal phasing adopted in which the green period for each approach is
exclusive (split phasing), during peak periods vehicles are subject to long delays.
Some drivers of motorized vehicles turn off the engine in an effort to conserve fuel.
Although most vehicles start their engines prior to the start of the green interval, some
vehicles do not. Thus, occasionally the discharge of vehicles is delayed due to the
delayed starting of such vehicles.
20


2.2J2.6 Creeping at Intersections
Typically, in a stopped queue on the intersection approach, smaller sized vehicles,
both motorized and non-motorized, creep up to advance to the head of the queue
using the gaps between the larger sized vehicles. This behavior is not observed in
homogeneous traffic networks, as the lateral gaps between the vehicles are typically
smaller than the width of the vehicles, and also because such movement is not
allowed. This phenomenon has an impact on the length of the queue and the
discharge from the intersection. As the smaller sized vehicles from behind are able to
reach near the head of the queue, the queue length is less than what it would be
without this phenomenon. The movement of these smaller sized vehicles also results
in increased gaps in the back of the queue, and occasionally larger vehicles are also
able to creep up towards the head of the queue, albeit by a smaller magnitude. As the
small sized vehicles are at the head of the queue, the discharge from the intersection
is dependent on the performance characteristics of these vehicles. The results of the
creeping phenomenon can be observed in Figure 2.6, where small sized vehicles have
reached or are proceeding towards the head of the queue.
Figure 2.6 Creeping of Small Size Vehicles to Head of Queue
21


2.2.2.1 Arrival Pattern
The arrival pattern of vehicles can have a significant impact on the various measures
of effectiveness (MOE's) considered in simulation models. The arrival pattern is
typically random when the traffic flow rate is low, and when intersection control
located upstream of the approach does not have a significant impact on the arrival
pattern. The random arrival pattern can be represented by the negative exponential
distribution. As the traffic flow rate increases, there is increasing interaction between
vehicles, and under high flow conditions almost all the vehicles interact with each
other and there is a near constant time difference between the vehicles. Various
researchers have observed that the time headways are typically in the medium flow
range, bounded by the low flow and high flow conditions. There have been various
attempts at using various distributions to represent the medium flow conditions, such
as Pearson Type III distribution being a generalized mathematical model (May 1990).
Other attempts at representing such distributions have considered them as a
combination of constrained (or platooned) and unconstrained (or free-flowing)
vehicles.
A common feature in most arrival distributions considered for homogeneous traffic in
single lanes is the consideration of a minimum time headway, which defines the
minimum time between the passage of the same part (e.g. the front bumper) of two
consecutive vehicles at a common point. Typically this is considered as 0.5 seconds,
and is incorporated in the various distributions as a shift parameter. However, in
heterogeneous traffic, as the vehicles are not traveling in lanes, this minimum time
headway is typically not required, and thus no shift parameter is considered while
representing the arrival patterns in such systems.
22


2.2.2.8 Acceleration Rates
In most traffic simulation models, tJhe vehicle-following model is based on
determining the acceleration rate fou the follower, in response to the location, velocity
and acceleration rates of the lead anid the following vehicles. Based on this
acceleration rate, the distance moveed during the simulation interval and velocity at
the end of the simulation interval axre calculated. However, for the traffic simulation
models for which comparisons are presented between field and simulated data, only
the headway and velocity variables are detailed (Benekohal 1986), (Aycin and
Benekohal 1999). In this study, there is a concerted attempt at comparing the field
and estimated acceleration rates, wliich in turn forms the basis for all the other
comparisons. Although this component is not specific to heterogeneous traffic
models, it is detailed here for its importance. Typically, vehicle emission estimates
are made based on velocity and acceleration data generated by a simulation model.
Therefore, the accuracy of acceleration estimates of a vehicle-following model is
expected to have a significant impact on related vehicle emission estimation studies
and subsequent air pollution studiers.
2.2.2.9 Driver Perception Threshold
Driver perception threshold is the threshold at which the following vehicle driver
recognizes the stimuli based on the lead vehicles actions. It is not different for
heterogeneous and homogeneous traffic. However, it is detailed here because it is an
important component of vehicle-following models. Changes in the dynamic status of
the vehicle ahead can be recognized by the following vehicle only if the change in the
apparent size of the lead vehicle iss recognized. The factors impacting this recognition
include the size of the vehicle ahesad, and the acceleration, velocity and position of the
following and lead vehicles. In orne study it was reported that the human perception
of acceleration is very gross and imaccurate, and it is difficult to distinguish between
23


constant velocity and acceleration unless the target vehicle is observed for at least 10
to 15 seconds (Boff 1988). On the other hand, two other studies estimated the
threshold rate of change in the visual angle as between 0.0003 and 0.001
radians/second (Micheals 1963) and 0.0035 radians/second (Mortimer 1988). The
driver perception threshold has been considered in three recent models, in very
different ways. Details on those considerations, and the methodology adopted in
these models are provided in later Chapters.
I
I
24


3. Literature Review
A microscopic simulation model is considered a useful tool to evaluate the impacts of
changes to the design, operation and control of transportation systems. The primary
goal of this dissertation work is to develop a microscopic simulation model to
simulate heterogeneous traffic flow at an intersection approach, and through the
intersection.
The most important component of a microscopic simulation is the vehicle-following
model. This forms the core of the simulation, and is the focus of the review presented
in this chapter. As a precursor to this, a discussion on the inappropriateness of using
modified homogeneous traffic models for heterogeneous traffic conditions is
presented. Next, (microscopic) vehicle-following models developed for
homogeneous traffic conditions are reviewed, as they form the basis of some of the
models developed for heterogeneous traffic. Details of two modified homogeneous
models that have been used to represent heterogeneous traffic are also presented in
this chapter. An important consideration in all vehicle-following models is the
reaction time considered. This is used to determine the application of the response of
the following vehicle, and a review is presented following the review of different
vehicle-following models. The arrival pattern of vehicles also is an important
consideration in vehicle simulation models, and is briefly discussed. Finally,
different general purpose and simulation programming languages are detailed, along
with the advantages of using object oriented programming to implement a
microscopic simulation model.
25


3.1 Use of Modified Homogeneous Traffic Models for
Heterogeneous Traffic
Over the past four decades, traffic models developed for homogeneous traffic
conditions have been used, with varying degrees of modification, to analyze mixed
flow. Two recent studies reported the application of a macroscopic (SATURN)
(May, Phiu-Nual et al. 1993) and a microscopic (TRAF-NETSIM) (Paksarsawan and
May 1995) simulation model for modeling heterogeneous traffic conditions in
Bangkok, Thailand. Over two-thirds of the motorized vehicles in Bangkok are two-
wheeler motorcycles. For the past decade, motorized vehicles in Bangkok have been
increasing at an average annual rate of 14%, which is typical of large cities in
countries with lesser levels of industrialization.
In both studies, various modifications are made to the individual models prior to
modeling traffic networks in Bangkok. However, certain key elements such as the
varied composition of traffic flow, queuing at intersections and the resulting impact
on intersection capacity could not be modeled. Both studies noted that further work
is needed to adequately model the heterogeneous conditions.
Similar problems are also faced when modeling the limited mixed flow that is present
in industrialized countries. The greatest disparity in terms of size and speed can be
found in the mixed flow of bicycles and motorized vehicles. Typically, bicycles are
an insignificant part of the total traffic stream (less than 1 percent). However,
bicycles are a significant part of the traffic stream in some areas, especially university
towns or in the vicinity of college campuses. A representation of the two-way
interaction between bicyclists and motor vehicles is attempted for conditions in a
university town in the U.K. using SATURN, a macroscopic simulation model
(Sharpies 1993). The study details various characteristics that have to be modeled to
accurately reflect the two-way interaction. These include the speed variation, the
26


platoon dispersion, lane sharing and interaction with motor vehicles and gap
acceptance characteristics. However, none of these characteristics are modeled due to
the limitations of the model, and thus the two-way interaction is not represented.
A study evaluating the use of western models in developing countries (Yanaguaya
1993) highlights the reasons such models are generally inappropriate. These reasons
include the differences in heterogeneous traffic behavior, the high proportion of
public transportation and non-motorized vehicles in the urban traffic, and the largely
informal forms of public transport that cannot be neglected.
This preceding discussion further demonstrates the importance of developing models
specifically for heterogeneous traffic conditions, as modified homogeneous traffic
models do not appear to be adequate. As detailed earlier, microscopic tools appear to
have potential for modeling heterogeneous traffic. A discussion of the various
vehicle-following models, for both homogeneous and heterogeneous conditions, is
presented next.
3.2 Microscopic Simulation Models
Microscopic simulation techniques have proved to be particularly useful in cases
where either the scope of analytical solutions are too limited, or the use of analytical
techniques requires an oversimplification of the problem to the extent that the results
can no longer be considered reliable. These techniques also allow the distinct
modeling of stochastic elements that are an inherent part of the various components
of traffic. Additionally, these techniques can be used to evaluate anticipated changes
in traffic systems.
The most important component of simulation models is the vehicle-following
heuristic. Various other characteristics within each model, such as overtaking
27


behavior and departure from a stop condition are based on the vehicle-following
heuristic. The development of vehicle-following theories for homogeneous traffic is
briefly presented, followed by adaptations made to represent heterogeneous traffic
conditions.
3.2.1 Initial Vehicle-Following Theories
In the simplest case, vehicle-following theories are those that define the reaction of a
following vehicle driver, based on an action taken by the lead vehicle driver. The
bases for these theories can be represented as
Response = Sensitivity Stimulus
where, a stimulus is the action taken by the lead driver, sensitivity is the variation in
the reaction of the following driver, and response is the final decision of the following
driver (accelerate, decelerate, or continue at same speed/remain stopped). The initial
vehicle-following theories were developed in the 1950s and 60s. The first vehicle-
following theory, developed by Pipes (Pipes 1953), is based on the premise that a
following vehicle always maintains a safe distance from the lead vehicle, and the
response of the following vehicle is a linear function of the speed of the lead vehicle.
The minimum safe distance maintained by vehicles is depicted in Figure 3.1, and can
be represented by Equation (3.1).
28


Velocity = vfj Velocity = vUn
Vehicle "F" Vehicle "L"
Figure 3.1
xUn XF,tn
where,
tn
c
Pipes Vehicle-Following Logic Vehicle Positions and Characteristics
= (d + Ll) + cvFjn (3.1)
= Time at the beginning of the nth simulation time step
= Reaction time of driver of following vehicle
= Position of front bumper of lead vehicle at time tn
d
Ll
Position of front bumper of following vehicle at time tn
Velocity of following vehicle at time tn
Stopped distance from rear bumper of lead vehicle to front
bumper of following vehicle
Length of lead vehicle
According to this theory, the minimum safe distance increases linearly with speed.
Although the results from Pipes' theory closely follow the observations in the speed
range of 30 to 65 km/h (approximately 20 to 40 mph), they underestimate the
minimum safe distance headway at lower speeds, and overestimate it at higher speeds
(May 1990). Additionally, Pipes theory suggests that the flow rate continues to
increase with increasing speed, as the time headway continues to decrease. However,
field observations have shown that maximum flow rates are obtained in the speed
range of 30 to 40 mph. Thus, this theory is not entirely correct.
29


A group of researchers at General Motors extended the basic model, first by
considering the acceleration response proportional to the difference in the velocities
of the vehicle (linear form) (Chandler, Herman et aL 1958) with the sensitivity term
assumed as a constant.
ac = A. F.tn+c l r- 1 VF.r n _ (3.2)
where,
tn+c = Time at the end of the reaction time, after the nth simulation
time step has started
a F.t n-r-C Acceleration/deceleration response of follower calculated at
time tn and applied at time tn+c
1 = Sensitivity, sec'1
VL.tn = Velocity of lead vehicle at time tn
Based on field experiments, it was determined that the sensitivity value varies widely
(0.17 to 0.74), and an attempt was made to improve the model by considering two
distinct values for different vehicle-following modes (following closely and not
following closely). However, this change was not sufficient, and the distance
headway was then incorporated into the sensitivity parameter. Recognizing the
impact of the speed of the following vehicle on the response that is generated, this
variable wras also incorporated in the sensitivity term. Finally, a generalized model
was developed which considers a range of exponent values for the sensitivity
components (Gazis, Herman et al. 1961). The final generalized equation developed
was:
a
F.t+c
p ! m

A, l.m VFj +c
L n
r -it
XLu ~XFj
n n
L.t
v
F.t
(3.3)
30


where,
Speed of following vehicle at time tn+c
l
Distance headway exponent, ranges from 0 to 2
Speed exponent, ranges from 0 to 4
m
As seen in Equation (3.3), the acceleration of the following vehicle is determined to
be directly proportional to the difference between the velocities of the two interacting
vehicles and the speed of the following vehicle (raised to an exponent m). The
acceleration is also determined to be inversely proportional to the distance between
the two vehicles (raised to an exponent 1). Various other vehicle-following
formulations developed around this time may be represented as special cases of the
generalized model, considering specific values for the two exponents. There are other
significantly different vehicle-following models. One is based on a quadratic
relationship between speed and spacing (Kometani and Sasaki 1961). The key
characteristics of various major vehicle-following theories are summarized in Table
3.1. Some of these models have been tested recently based on data collected from
aerial photographs and global positioning systems (GPS) (Aycin and Benekohal
1999; Khan, Maini et al. 2000).
31


Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
u>
to
Table 3.1
No. Name
1 Pipes'
2 GM-I2
3 GM-21
4 iidic'1
5 Kometani
& Sasaki5
Vehicle-Following Theories Key Characteristics
Formula
Response Response Directly Proportional to
Difference in Reaction time
distance Follower velocity
Acceleration of Difference in
follower after velocities
reaction time k (Average 0.37;
range 0.17-0.74)
Acceleration of Difference in
follower alter velocities
reaction time ^l,m (Follower velocity
alter reaction
limc)m
X Leader velocity
Acceleration of Distance between
follower alter vehicles
reaction time c,
Response Inversely Special
Proportional to Characteristics
Leader length Stopped gap Reaction time:
Average =1,55 seconds; range 1- 2.2 seconds)
(Distance Generalized
between equation: covers
vehicles)1 all GM models.
(Distance Low flow
between conditions
vehicles)2 Change of visual
Leader velocity c2 angle


Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

Table 3.1 (cont.)
No. Name Formula Response
6 NETSIM6
7a CARSIM:
A47
a. Jli 1
C.l,,/ c UJ
2df
V, 4


{r/, (2c + l) + 2v/,,J
Acceleration of
follower after
reaction time
'/..'ml
(0.5(/f4)A/3)
> Ll + K
Acceleration of
follower
7h CARSIM:
A5 non-
collision
constraint7
'/'ml
Xl:'n + (%,A') +
(0.5(/I5)aij)
-A' Maximum of j^iy. ^ +(/I5a/)J cj or
IMH1+
K+W] "uj
^ al'Mn 2 ai.Max
Acceleration of
follower
Response Directly Response Inversely Special
Proportional to Proportional to Characteristics
Difference in
velocities
Follower
deceleration rate
Distance between
vehicles
Distance between
vehicles
Distance between
vehicles
Difference in
velocities: only in
special cases
Reaction time
Follower velocity
Follower velocity
Follower velocity
Brake reaction lime
No lane
changing case
Leader length
Stopped gap
Similar to Pipes
Leader length
Stopped gap
'(Pipes 1953), 2(Chandler, Herman et al. 1958), 3(Gazis, Herman et al. 1961), 1(Edie 1961), 5(Kometani and Sasaki
1961), 6(Halati, Lieu et al. 1997), 7(Benekohal 1986; Benekohal and Treiterer 1988).


3.3 Recent Vehicle-Following Theories
There are five recent car following theories that are notable for either the unique
approach adopted, or for unique characteristics considered. One of these (CARSIM)
has been applied to heterogeneous traffic, and elements of another (INTELSIM) have
been used to formulate the vehicle-following model in the current study. A brief
discussion of these theories is presented next.
3.3.1 CARSIM
CARSIM was developed to refine the vehicle-following logic observed for freeway
traffic under both normal and stop and go conditions (Benekohal 1986; Benekohal
and Treiterer 1988). For congested conditions, a lower maximum deceleration rate
was considered for the following vehicles. The acceleration/deceleration of a lead
vehicle may be determined from one of three formulations (A1 to A3). They are
based on the physical capacity of the vehicle to accelerate at a certain rate. The
acceleration/deceleration of a following vehicle considers the limitations of A1 to A3,
and also one of two formulations (A4 and A5), presented next. The first formulation
(A4) ensures that if it is applied, the following vehicle will maintain a minimum
distance from the lead vehicle for the next simulation interval. This constraint
formulation is:
(3.4)
where.
A4
x
L-tn+l
Time at the beginning of the n+lth simulation time step
Acceleration of following vehicle determined at time tn and
also applied at time tn
Position of front bumper of lead vehicle at time tn+i
34


Simulation time step, 1 s
Buffer space between vehicles; K = 10 feet when density is not
very high. Near jam density: K = 5 to 7 feet
At
K
The acceleration/deceleration rate A5 ensures that the following vehicle maintains
sufficient distance to react to a rapidly decelerating vehicle, and can either stop or
slow down to a safe driving speed. This formulation is:
1
Maximum of
LVK>
or
XFj + (v.^H-5(^>2)_
(,45a/)] cj
k +('45")]2 -uj
VFj +<
_VF.tn + (A5a/)]
2 a
F.Max
2 a
LMax
(3-5)
where,
A5 = Acceleration of following vehicle determined at time tn and
also applied at time tn
aL Max = Maximum deceleration rate of lead vehicle, 16 ft/s2 in
CARSIM
aF Max = Maximum deceleration rate of following vehicle, CARSIM: 16
ft/s2 when density < 60 vehicles per mile (vpm), and 13 ft/s2
when density < 60 vpm
c = Brake reaction time, assumed distribution with time ranging
from 0.4 to 1.5 seconds (average = 0.75 seconds)
The minimum value of the five acceleration rates (A1 to A5) is applied at each time
step. Determination of the deceleration rate requires evaluating four scenarios and
the corresponding deceleration rates are detailed in Table 3.2. This determination is
35


governed by the comfortable deceleration rate (AC), based on the speed of the
following vehicle. A2 is the acceleration/deceleration rate used to achieve the desired
free speed in the next time step. Thus, A2 is a deceleration rate applied only when a
vehicles speed is greater than its desired free speed.
Table 3.2 Deceleration Rate Determination in CARSIM1
Scenario Deceleration Rate
A2< AC and AC < Minimum (A4, A5) AC
A2 < AC and AC > Minimum (A4, A5) A5
AC < A2 and AC < Minimum (A4, A5) A2
AC < A2 and AC > Minimum (A4, A5) A5
*AC = 7.77 ft/s2 for 0-15 mph; 6.74 ft/s2 for 15-30 mph; and 4.84 ft/s2 for >30 mph.
The primary contribution of this vehicle-following model is the formulation of A5,
which is also termed as the non-collision constraint. As will be detailed later, two
researchers have used this formulation to model heterogeneous traffic, as drivers
frequently take rapid action to avoid collision with other vehicles. These researchers
have reported good agreement between modeled and observed values. However,
their findings are based on field data collected in one city in Bangladesh. CARSIM
model was tested for normal flow and stop and go conditions based on data collected
for a freeway section in the U.S. and the measures compared were limited to average
headway and velocity. Acceleration rates were not included in its validation.
3.3.2 INTELSIM
The models discussed so far, including GM and CARSIM, are all based on a
following vehicles response to a lead vehicles action every second. The INTELSIM
car-following model specifically considers a following vehicles longer-term goal of
achieving steady state condition, i.e. achieving the same velocity as the leader while
36


maintaining a minimum preferred time headway (Aycin and Benekohal 1998: Aycin
and Benekohal 1999). Although a similar goal can be inferred from the other vehicle-
following models, INTELSIM appears to be the first that uses this as a basis for the
model formulation. In addition, the acceleration of the following vehicle is
considered to vary linearly, and not as a step function. A summary of the derivation
of the vehicle-following model is provided next.
For the lead vehicle, the acceleration rate is considered to vary as a step function.
Based on the equations of motion the position of the lead vehicle at time tn+T (where
T = time to reach steady state):
x, = x,, + v, T + 0.5a, T2
L-n+T L.n L,tft L.[n
0-6)
and velocity of the lead vehicle at time tn+T
v, , = v. +a,T
-tn-r l-.tn L-tn
(3.7)
The position and velocity of the following vehicle at the steady state time are:
XF.ln+T = XFj +VF.lnT + ()'5aF.[n'r~ +0.167^7-
VF.,., +O'S^.,
where,
(3.8)
(3.9)

= slope of linear acceleration of follower at tn, m/s3
The two steady state conditions are (a) velocities of the leader and follower are equal
at time tn+T and (b) minimum gap headway (dp) is achieved at time tn+T. The gap
headway is based on field measured preferred time headway. This yields the
following two conditions:
+aL.J = vr,n +aF,tT + 0.5sFjmT1
(3.10)
37


(3-11)
where.
Preferred time headway, s
Equation (3.10) yields the slope of the acceleration as:
(3.12)
0.5T2
Equations (3.6) to (3.12) form a quadratic equation in terms of T. The two roots
provide the time to reach steady state. For both roots positive, the lower positive
value, and for at least one positive root, the positive root is applied. For both negative
roots, eight sub-cases are presented. When the discriminant is negative, a constant
acceleration model is considered and this results in a definite solution.
INTELSIM does not include a typical non-collision constraint that checks to ensure
that a safe spacing between vehicles is maintained even when a leader applies an
emergency deceleration. Instead, the non-collision constraint is applied only when a
lead vehicle is in deceleration, or if the following vehicle's time to reach steady state
(T) is greater than the time it would take a leader to come to a complete stop. This is
expressed as follows:
(3.13)
where,
d
f
Gap between vehicles after the reaction time c.
d
L
Distance for leader to stop =-
n
38


dbvff = Buffer gap between the vehicles when stopped- Value not
specified, but typically considered as 5 or 10 feet (1.5 or 3.0 m)
in other models. In ENTELSEM, actual buffer space data from
the field were used (Aycin and Benekohal 1998).
INTELSIM is one of the few models to use perception thresholds, to determine
whether a vehicle is in the following mode or in the free flow mode. The three
perception thresholds are (Aycin and Benekohal 1998): (1) relative deceleration of
0.5*average deceleration rate of the vehicles, (2) approaching speed of 0.06*average
speed, and (3) headway deviation of 0.05*average headway. The average values
considered for the deceleration rate and speed are assumed to be the same for all
vehicles in the simulation. For example, when a simulation is performed for highway
conditions, an average speed of 70 feet/s is considered. The relative deceleration rate
and approaching speed are calculated at the instance when the decision is being
considered. For time headway, the difference in time headway over the last interval
is considered, and the average time headway observed for the field data (e.g. 1.5
seconds) is used. When any of the three thresholds are crossed, the following vehicle
driver recognizes the stimulus and then considers implementing an appropriate
response.
It may be mentioned that the INTELSIM model is work in progress. The model
presented here is based on two publications of the model (Aycin and Benekohal 1998;
Aycin and Benekohal 1999). According to these papers, for both negative roots of
the quadratic equation, the solution may be obtained from the eight sub-cases
presented. However, these cases are not presented clearly in the publication (Aycin
and Benekohal 1998). Additionally, when the difference in velocity between the lead
and following vehicle decreases and therefore the time to steady state (T) is low, the
acceleration, and therefore the velocity and headway oscillate significantly. This
39


occurs as the acceleration slope estimated by Equation (3.12) produces large values,
for small values of T. In ENTELSIM no limitations are specified for the acceleration
values. Thus, the following vehicle is unable to achieve the steady state. The
solutions to the quadratic equation may result in a steady state velocity that is either
negative or greater than the maximum velocity of the following vehicle. Both these
results are not realistic, but ENTELSIM does not address these situations.
Additionally, the simple non-collision constraint does not prevent collisions in all
cases, as it is applied selectively only when the lead vehicle is decelerating.
Discussions with the principal researcher suggest that various modifications are being
considered to the ENTELSIM model to address these issues.
3.3.3 Psycho-Physical Vehicle-Following Theory
Earlier researchers recognized the inexplicable relationship between the laws of
physics used to describe the vehicle motion, and the psychology of drivers making the
decisions. However, it is only recently that applications of such theories are being
seen in the field of traffic simulation. In one such recent study (Fritzsche 1994), a
psycho-physical vehicle-following theory' is described with the help of a Driver-
Vehicle element (DVE). The properties of the driver (perception, intention to change
lanes/overtake, etc.) are combined with those of the vehicle (acceleration and braking
performance) through this element. The researcher recognized that the ideal
representation of the dynamic characteristics of a particular vehicle could be a
function of the characteristics of all the vehicles around it. However, because of the
difficulty in modeling such a situation, only the nearest DVE interaction was
considered.
It is a well known, but often ignored, fact that a following vehicle cannot easily
distinguish small changes in the speed or acceleration of a lead vehicle. Other than
40


INTELSIM, all the vehicle-following theories presented until now do not explicitly
account for this fact. In this study, the threshold difference in speed that can be
recognized by the following driver is explicitly considered, and the follower DVE
reacts only if the difference in the velocities is greater than the threshold. Also, this
study assumes that threshold difference varies with the magnitude of the negative or
positive difference in the velocities between the two vehicles, as would be generally
expected.
3.3.4 Neural-Network Driver Decision Model
Typical vehicle-following theories are based on the representation of response of a
following vehicle as a function of stimuli. These stimuli include visual input that is
received continuously. Various attempts have been made to model the driver
behavior using the neural network technique (Fix and Armstrong 1990; Lyons and
Hunt 1993). A neural network consists of a number of neurons that are organized in
layers based on similar characteristics. Each neuron in a particular layer is connected
to neurons in the layer immediately above/below, and each connection is assigned a
range of weights. The neurons also have internal transfer functions that direct the
reaction of these units to the inputs received. The main power of this technique is
derived from the fact that the neural networks, as massively parallel structures,
provide a non-linear mapping between a set of inputs and outputs.
It was postulated that a neural driver based driving model may decipher a
representation of visual images for making decisions. The study (Lyons and Hunt
1993) noted that neural networks require large data sets for training/model
calibration, and subsequently model validation. Ideally, these data would include
details on the interaction of each vehicle with other vehicles over a considerable
41


distance (possibly 100 km). An alternative is to use data collected from driving
simulators, such as the Advanced Driving Simulator at Leeds University.
A subsequent study (Lyons 1995) clearly defined the various elements of the model,
and reported on calibration and validation of a simpler model. This study also
correctly hypothesized that a driver makes decisions based not only on the activity in
a certain distance ahead of the subject vehicle, but also the activity within a certain
distance behind this vehicle. This area is defined as the zone of influence, and is
further subdivided into a number of windows''. The patterns formed by the absence
or presence of other vehicles in the windows contained in the zone of influence
describes the change in the traffic environment around the subject vehicle. The
microscopic validation of individual driver behavior, which is more rigorous than the
validation of other rule-based simulation models, showed that the model correctly
classified 70% of the individual driving examples. Given these good results, the
researchers suggest that by establishing certain override rules, the model can be
enhanced to not predict dangerous situations. Thus, the use of the neural network
technique in modeling an important part of a microscopic simulation was well
demonstrated.
3.3.5 Cellular Automata Theory
Recognizing the significantly large computing resources required for modeling the
detailed vehicle-following theories, there has been an attempt at simplifying the
process without losing the essential characteristics of traffic flow. This work is based
on the cellular automata (CA) theory, which has been used in physics for a long time
to simulate complex dynamical phenomena (Schreckenberg and Nagel 1995). The
basic idea is to simplify the driver behavior as much as possible, without sacrificing
the essentials of the traffic flow dynamics. It is postulated that traffic has certain
42


universal properties, which will be reproduced by both simplistic and extensive
microscopic models. By considering only simplistic rules, and using parallel
computing techniques, the traffic for very large networks (such as the entire German
Autobahn network (Esser and Schreckenberg 1997)) can be simulated in real time.
The basic premise of the CA model is that it uses spacing as a stimulus and the
velocity is assumed to be constant as soon as the maximum value is obtained. The
roadway is considered to be composed of a long string of cells, some of which are
occupied by vehicles. In one particular application, these cells were considered to be
7.5 m long (one vehicle length in jam conditions) and 3.6 m wide (one lane width).
The driver behavior in this application incorporates simple rules and therefore the
velocity of the next car ahead is not taken into account explicitly. Additionally,
coarse approximations are considered with the intent of reducing computation. For
example, if freeway conditions (maximum speed of 100 km/h (65 mph}) were being
represented, then a velocity value of 4 on a scale of 1 to 5 would represent any speed
(3.5 to 4.49) from 70 to 89.99 km/h (Nagel, Stretz et al. 1998). However, even with
this coarse approximation the researchers have been able to simulate real traffic
reasonably well.
Although this approach has shown promise, its application has definite limitations.
Due to the bitwise approach and simplistic rules adopted, this technique can be used
for models that do not require high fidelity, such as transportation planning models.
Traditional models in this area have used techniques such as modeling delays on links
based on the level of congestion. However, these techniques typically do not
adequately represent nearly saturated or over-saturated conditions, and such
conditions can be effectively represented using the CA approach. This model has
been implemented in the TRANSIMS traffic simulation program. However, it is
uncertain if this method offers superior benefits for modeling detailed traffic behavior
43


as in microscopic simulation programs such as CORSIM (Federal Highway
Administration 1997), and thus the overall merits need to be evaluated further.
3.4 Heterogeneous Traffic Microscopic Simulation
Models
Since the early 1980s, there has been considerable interest in the development of
microscopic heterogeneous traffic models. Initially, two models. Indo-Swedish Road
Traffic Simulation Model (INSWERTS) (Palaniswamy. Gynnerstedt et al. 1988) and
MORTAB (Model for Depicting/?oad Traffic ZJehavior) (Ramanayya 1988) were
developed for representing uninterrupted flow behavior. Of these two models, the
more detailed model. INSWERTS, considered only inter-city roadways. The unique
characteristics associated with overtaking on narrow two-lane roads were represented
in this model. Both these initial models were developed for Indian traffic conditions.
Subsequently, models were developed to represent traffic in an urban environment.
These models, developed at two universities in the U.K. (University of Southampton
and University of Leeds) represent traffic conditions in Bangladesh and Indonesia.
The development of the three models represents a sequential increase in complexity'
considered. The first model, TRASMIC (TRAffic Simulation for Mixed Condition)
(Sutomo 1992), considered only a single approach to a signalized intersection. The
second model, MIXSIM (SEMulation of MIXed Traffic Stream) (Hoque 1994)
considered all approaches of a signalized intersection, and the third model,
MIXNETSIM (Hossain 1996), considered an urban roadway network consisting of
roundabouts, signalized and unsignalized intersections. The latter two models were
developed for traffic conditions in urban networks in Bangladesh. Recently, a
simulation model was developed for urban uninterrupted traffic flow for Indian traffic
conditions (Singh 1999). These models are detailed next.
44


3.4.1 Heterogeneous Models for Traffic in India
3.4.1.1 INSWERTS
The first model developed for mixed flow traffic was for two-lane and multi-lane
highways (Palaniswamy, Gynnerstedt et al. 1988). This stochastic, discrete-event
based simulation model was based on modifications made to the Swedish Road
Traffic Simulation Model (SWERTS) (Brodin and Carlsson 1979), designed for
motorized traffic. The model was modified to simulate Indian roadway and traffic
conditions including narrower, bi-directional roads with widths varying from 3.75 m
(12.3 ft) to 7 m (23.0 ft), different shoulder types, alignments, terrain, desired speed,
and power-to-mass ratio. The modified model is referred to as INSWERTS.
3.4.1.1.1 Vehicle Characteristics
Nine different vehicles were modeled, and these were grouped in four similar
categories: (a) passenger cars, pickups, and jeeps; (b) trucks and buses; (c) farm
tractors and animal driven vehicles (ADVs); (d) motorcycles and scooters. The
bicycles, cycle-rickshaws, and other slow-moving non-motorized vehicles, and their
effect on the traffic stream were "taken as noise on the system and the calibration
was adjusted to account for this noise.
3.4.1.1.2 Modeling Approach and Vehicle Movement
Heuristics
The behavior of mixed flow traffic on single-lane bi-directional roads was modeled
appropriately. Due to space limitations, vehicles typically travel in the middle of the
road, and move to the soft shoulder (depending on the condition of the shoulder) for a
faster vehicle to overtake or for an opposing vehicle to pass. Video and radar
speedometer data were recorded and used to determine the yielding probability
45


distribution of the slower vehicle as a function of roadway and vehicle parameters.
Detailed measurements were made to study the overtaking gap acceptance behavior
and passing speeds adopted. The presence of platoons in one or both directions added
complexity to these determinations.
3.4.1.1.3 Model Validation
The model was validated for 28 flows for four different roadway configurations. The
observed and modeled number of overtaking maneuvers, segment travel speeds, spot
speeds and time-headways were compared. Additionally, headway distributions were
compared by vehicle type. The observed data were replicated well in the INSWERTS
model.
It appears that there has been further work based on this approach. However, the only
information obtained so far has revealed that another study has been performed, and
is currently being reviewed by the sponsoring agency in India (Indian Roads
Congress 1999).
3.4.1.2 MORTAB
Another micro-simulation model, MORTAB (Model for Depicting Road Traffic
Behavior), was developed for uninterrupted Indian traffic conditions in the mid-
1980s (Ramanayya 1988). The paper detailing this effort listed the various factors
included in the model, but provided few details.
3.4.1.2.1 Vehicle Characteristics
Eight vehicle types were modeled: cars, buses, trucks, auto-rickshaws (three-wheeler
motorized vehicle, typically used as taxi), motorcycles/scooters, bicycles, cycle-
rickshaws, and bullock carts (ADV). The component sub-models related to vehicle
46


characteristics included: (i) generation of arrival patterns (ii) different category of
vehicles (iii) speed models (iv) vehicle driver characteristics (v) minimum desired
spacing (vi) acceleration characteristics and (vii) deceleration characteristics. The
required inputs to the model are: (I) traffic composition (II) traffic volume and (III)
ffee-flow speed by vehicle type. In this study the vehicle arrival pattern for low flow
conditions (less than 500 vph) is represented by the exponential distribution, for
medium flow conditions (500 to 650 vph) by the shifted negative exponential
distribution and for higher flow (650 to 900 vph) by the log-normal distribution.
3.4.1.2.2 Modeling Approach and Vehicle Movement
Heuristics
The different heuristics included in the model are (i) vehicle tracking (ii) car-
following models (iii) overtaking criteria (iv) lateral gap adequacy and (v) merging
logic. However, no details are provided about critical elements including the vehicle-
following logic considered. The output produced by the model for each vehicle type
included: (a) speed (b) delay (c) number of overtakings and (d) distributions of spot
speeds and headways at control points.
An interesting approach adopted in the study was the formulation of macroscopic
speed, flow and density relationships based on the results obtained from the
microscopic simulation model. This approach shows promise if the microscopic
simulation is well validated and calibrated.
3.4.1.3 Urban Uninterrupted Flow Traffic Simulation
Model (Singh)
The first detailed microscopic simulation model for modeling heterogeneous traffic
for urban uninterrupted divided facilities in India has been recently developed (Singh
1999). Data for this model were collected at two locations on a major arterial divided
47


roadway in Kanpur, India, The width of the road in each direction is 7 m, and the
directional traffic volume during the peak periods varied from 1,600 to 3,000 vehicles
per hour. Over 60 percent of the traffic consists of non-motorized vehicles, with
bicycles accounting for almost 50 percent of all the vehicles. The motorized vehicles
included two-wheelers (18%), auto-rickshaws (13%), cars (5%) and buses/trucks
(2%).
3.4.1.3.1 Vehicle Characteristics
Eight different vehicle types were modeled. These include (i) Car/Van/Jeep (ii)
Tempo (includes 3-seater and 8-seater auto-rickshaws) (iii) Light Commercial
Vehicle (LCV) (iv) Bus (v) Motorized two-wheeler (vi) Push-cart/ADV (vii) Bicycle
and (viii) Cycle-rickshaw. Detailed free flow speed data were collected by observing
the speeds of the vehicles during low flow conditions. The average speeds for the
motorized vehicles ranged Grom 9.05 m/s (auto-rickshaw) to 13.05 m/s (Maruti car).
The average free speed of the bicycles was 4.5 m/s. Lateral and longitudinal gaps
maintained between vehicles were determined from video data collected at the two
locations. Lateral gaps maintained while overtaking were analyzed separately for the
different vehicle pair types. Subsequently, in the calibration of the model, a factor of
0.7 was applied to the lateral gaps determined initially. Lateral gap maintained from
the side of the road was also determined as a function of the speed at which vehicles
were moving. The arrival pattern of vehicles was represented by considering a
composite Schuhl's distribution for both motorized and non-motorized vehicles.
3.4.1.3.2 Modeling Approach and Vehicle Movement Heuristics
A simple car following algorithm, the first algorithm developed by the GM
researchers, was adopted in this model. The algorithm adopted, which is the same as
in Equation (3.2), is
48


(3.14)
n _
A value of 1/s was assumed for the sensitivity parameter, X. and the reaction time for
following drivers, c, was assumed to be 1 second. Although the algorithm in itself is
simple, the manner in which it is applied is complex. The car following logic is
applied only when the expected headway one simulation time step later is less than a
certain threshold headway. Additionally, three checks are applied to ensure that a
reasonable acceleration rate is applied by the following vehicle. These processes are
detailed next.
In the model the vehicles are processed from the upstream end of the link to the
downstream end. Thus, the lead vehicle characteristics at time tn+i are known. A
slightly different formulation is considered for estimating the following vehicles
velocity and position at time tn+i, and this is presented next.
According to the formulation used for estimating velocity and position, the following
vehicle uses the acceleration rate it will apply one second later (at time tn+i) to
determine the velocity and position at that instant (at time tn+i). Initially, it is
assumed that the following vehicle will apply the maximum possible acceleration
rate. The maximum acceleration rate is calculated from the following force equation:
(3-15)
(3.16)
dv p CaA
dr v m
-{Cr\+Cr2v)~Si
(3.17)
49


where,
dv ~dt Acceleration capability of vehicle, m/s2
m = Vehicle mass, kg
S = Gravitational acceleration, 9.81 m/s2
i = Gradient
P = Power mass ratio
Ca = Air resistance coefficient, kg/mJ
A - Frontal area, m2
Crl,Cr2 = Rolling resistance coefficients
V = Vehicle speed, m/s
The values of the different parameters in the force equations are based on results of
an exhaustive study of different vehicle types in India (Central Road Research
Institute 1994). However, as this equation results in extraordinarily high values of
acceleration rates at low speeds, a threshold value is considered for the maximum
acceleration rate.
A vehicle is considered to be in the car following mode when the space headway one
time step ahead (tn+i) is less than a certain minimum headway, represented as the sum
of the tail length of the lead vehicle and the head length of the following vehicle (both
calculated at time tn+i).
taillengthLl^ = max \Ll, vu^th j (3.18)
2 2 r 1 L.tn+j headlengrhFjn+i ^ (3.19)
where.
50


th = minimum time headway, assumed as 1 second for all vehicle
types
d = deceleration rate, assumed to be 2 m/s2 for all vehicle types
The tail length represents the minimum spacing maintained from the lead vehicle, and
the head length represents the sufficient distance required to avoid a collision, if the
lead vehicle were to decelerate to a stop. In the process of the model calibration, a
multiplicative factor of 2 is applied to the sum of the tail and head lengths, and when
the headway is smaller than this value the follower is considered to be in the car
following mode.
Three different checks are applied to ensure that an appropriate acceleration rate is
applied by the following vehicle. The first check ensures that the acceleration rate is
neither greater than the maximum acceleration rate, nor less than the maximum
deceleration rate. The maximum deceleration rate was assumed to be 2 m/s2 and was
assumed to be the same for all vehicle types. The maximum acceleration is the
minimum of the acceleration determined from Equation (3.17) and the threshold
maximum acceleration rate.
The second check is to ensure that the vehicle speed does not exceed its free flow
speed, nor goes below zero. The acceleration rate (aF t ^) determined after the first
check is applied to estimate the following vehicles speed one second later, using
Equation (3.15). If this speed is greater than the free flow speed or less than zero, a
new acceleration rate is determined.
The third check is made to ensure that the following vehicle does not collide with the
lead vehicle. In the first part of this check, the acceleration rate after the second
check is used to estimate the following vehicles position and speed at time Vi.
51


Based on the lead and following vehicles positions, the expected space headway is
calculated. Also, an emergency space headway is calculated, as the sum of the tail
and head length assuming an emergency deceleration rate of 4 m/s2 (twice the
maximum deceleration rate). When the expected headway is less than the emergency
space headway, an iterative calculation is performed by decreasing the acceleration
rate the follower expects to apply one second later, till the expected and the
emergency space headway are the same. Following this an additional non-collision
constraint, which is similar to that considered in other models, is applied.
In the second part of the third check, two constraints are considered to ensure that the
following vehicle maintains a safe distance from the lead vehicle. These constraints
are:
TLUn i +HLFj^ >0
+ HLFj^ xu^ +(xFjn
where,
+ vfj +
-250^
TLLj t = Tail length of lead vehicle at time tn_i
HLFj i = Head length of following vehicle at time tn+i
(3.20)
(3-21)
Equation (3.21) can be expanded and rewritten as
+ vf,. +0.25[aFA + aFJnt ]) >
(vo, + -5[ar., ]) K, )'
2dFMax 2dLMax
TLl,
(3.22)
Equation (3.22) results in a quadratic equation in terms of the acceleration rate that is
applied after one simulation time step (aF ). The roots obtained from this equation
are used to verify the constraint specified in Equation (3.20). If one root satisfies the
52


constraint, it is the solution, and if both roots satisfy the constraint, the minimum
value is selected.
The overtaking behavior of vehicles was modeled by considering the difference in the
free flow speeds of the two interacting vehicles, and the lateral gap between the
vehicles. The yielding behavior of slower moving traffic, to give way to faster
moving following vehicles, was also modeled as a function of the difference in the
free flow speeds and the lateral gap between the vehicles.
3.4.1.3.3 Model Validation
The model was validated for a flow rate (2,332 vehicles per hour) that was different
from the flow rate used in the calibration stage. Simulated and field data were
compared for various measures of effectiveness, including space mean speed, time
headways, traffic density, and number of overtakings. The simulated average space
mean speeds for a 100 m distance (range of 2.2 to 7.5 m/s for different vehicle types)
were within 0.4 m/s of the observed data. The variation of these simulated speeds
within each vehicle type were also similar to the observed data, as the standard
deviations were within 0.3 m/s. The other simulated measures of effectiveness also
compared well with the observed data. However, the vehicle-following model was
not validated separately.
3.4.2 Heterogeneous Model for Traffic in Indonesia
(TRASMIC)
The simulation models developed in India only considered uninterrupted facilities
(i.e. without intersections). The TRASMIC (TRAffic Simulation for Mixed
Condition) model (Sutomo 1992) has been developed for an intersection approach for
Indonesian traffic conditions. Recognizing the basic distinguishing element for
53


mixed traffic being non-lane based movements, each approach (road width) of the
intersection was considered to be composed of 1 m wide strips. Each vehicle type
occupies a certain number of strips based on their width.
3.4.2.1 Vehicle Characteristics
A total of 10 vehicle types were considered in this study. The vehicle types
considered included (i) Car (ii) Mini-bus (iii) Mini-truck (iv) Bus (v) Truck (vi)
Semi-trailer (vii) Trailer (viii) Motorcycle (ix) Bicycle and (x) Becak. The Becak is a
non-motorized three-wheeler vehicle. At two of the four sites where data were
collected the proportion of NMVs was insignificant, and at the third and fourth sites
it was 2.3% and 4.7%. The primary vehicle types were motorcycles and cars, and
they comprised 70-90% of the traffic at the three locations (Cars: 31 to 75% and
Motorcycles 13 to 48%). The study noted that ideally the data collected should
include acceleration capabilities and lateral and longitudinal gaps between vehicles.
However, due to limited resources, only vehicle dimension data were collected, and
the dynamic characteristics were assumed based on data collected for homogeneous
traffic and observations of heterogeneous traffic.
3.4.2.2 Modeling Approach and Vehicle Movement
Heuristics
The generalized GM car-following model detailed in section 3.2.1, with one
modification, was implemented in TRASMIC. The modification considered was the
headway between the two vehicles was replaced by the gap between the vehicles.
The final representation considered was:
\5m! s
a
nl
Fj
n
FJn+c
*L'n XFjn Ll
VL.t ~VF,t
rt n J
(3.23)
54


As shown in the equation, values of 2 and l were considered for the distance
exponent 1 and velocity exponent m respectively, and A.[ m was considered to be 15
m/s. A simplistic non-collision constraint, in which the impact of reaction time was
not considered, was applied. The following vehicle maintained a minimum gap from
the lead vehicle based on the following formulation
minGap = (minStopDistance) F + (minSpacing) p_L (brakeDistance) L (3.24)
where,
(minStopDistance) f Stopping distance of following vehicle =
K):
VFJ,C +
2 a
F,max
(minSpacing) f-l = Minimum spacing between following and lead
vehicle at the time they stop = xun+s ~xf,!+s > where S = time from
tn until all vehicles stop.
(vA')
(brakeDistance)f= Braking distance of following vehicle =-----:
2aL.mcx
Additionally, a perception threshold gap was considered, beyond which the following
vehicle did not necessarily apply the acceleration determined from the vehicle-
following heuristic. This threshold gap was similar to the minimum gap detailed in
Equation (3.24) with the (minStopDistance)f term being replaced by the normal
stopping distance in which the normal deceleration rate of the following vehicle was
considered in place of the maximum deceleration rate considered earlier. The
perception threshold considered in the Singh (Singh 1999) model is similar to that
considered in TRASMIC.
55


I
i
Although it was mentioned that a reaction time was considered for all vehicles, the
mean value was not reported, and also its application was not detailed. As is apparent
from Equation (3.24), it does not appear that the reaction time was considered in the
non-collision and threshold perception heuristics.
3.4.2.3 Model Validation
The model was validated for four intersection approaches with the flow ranging from
1,520 to 2,405 vph. The primary MOE's used were queue length, travel time and
discharge profile. Although the model was able to replicate the queue length and the
discharge profile reasonably well, the model estimates for travel time were
significantly lower (approximately 10 to 17% lower). The vehicle-following model
was not validated separately.
3.4.3 Heterogeneous Models for Traffic in Bangladesh
3.4.3.1 MIXSIM
To overcome the shortcomings in TRASMIC, MIXSIM SIMulation of MIXed
Traffic Stream (Hoque 1994), was developed to model isolated signalized
intersections for mixed flow conditions. Hie unique elements considered in this
effort included:
more than one lead vehicle impacts the behavior of following vehicles
queue formation is based on making maximum use of available roadway space
queue discharge characteristic is a function of police enforcement and/or red
violation
I
56


3.4.3.1.1 Vehicle Characteristics
Nine vehicle types were considered in this study. These included (i) Motorcycle (ii)
Auto-rickshaw (iii) Car/Jeep/Taxi/Micro-bus/Pick-up/Van (iv) Mini-Bus/Truck (v)
Bus (vi) Truck (vii) Bicycle (viii) Tricycle (Rickshaw) and Rickshaw van and (ix)
Push-cart. These vehicle types are similar to the vehicle types considered in the
Indian traffic simulation models. The static parameters for which data were collected
included the stopped lateral and longitudinal gaps. Additionally data were collected
for free speed (at low flow conditions), free turning speed, free flow acceleration rate,
free flow deceleration rate and maximum deceleration rate. It was observed that there
was little interaction between motorized and NMVs upstream of the intersection, and
separate distributions were considered for representing the arrival pattern of vehicles.
For motorized vehicles, a log-normal distribution was used at four of the five
locations, with the shifted negative exponential distribution being considered for non-
motorized vehicles, and the motorized vehicles at the fifth location.
3.4.3.1.2 Modeling Approach and Vehicle Movement
Heuristics
The approach of using strips to model traffic flow (TRASMIC) is also used in this
study. However, to better model the traffic, 0.5 m wide strips are used. The
narrowest vehicle, a bicycle, occupies one strip; a motorcycle 2 strips; a tricycle,
push-cart, and auto-rickshaw three strips; cars and mini-buses 5 strips; and buses and
trucks occupy 6 strips.
The non-collision vehicle-following algorithm (A5) developed as part of CARSIM
was adopted as the basic vehicle-following model. The constraint of maintaining a
safe distance results in the following vehicle always considering the speed and the
maximum deceleration rate of the preceding vehicle and keeping track of the target
57


position of the stopping vehicles. The non-collision based equality constraint is
detailed in the earlier section 3.3.1 on CARSIM. Because of the mix of vehicles of
widely varying operating characteristics it was determined this approach provided
better results than the stimulus-based approach. The acceleration and deceleration
rates considered were based on the data collected in Bangladesh. In a departure from
the step wise acceleration rate considered in CARSIM. a linear acceleration model
based on a constant rate of acceleration jerk was considered. The acceleration rate, a,
at any speed, v, was determined as
(3.25)
where,
ao = initial acceleration rate, m/s2
vMax = maximum speed, m/s
Although a description of the various heuristics considered for lateral movement
(lane-changing, overtaking) is provided, implementation details are not provided.
The lane changing heuristics considered are similar to those considered in TRASMIC.
Right-turning motorized vehicles were introduced into the model on the right side of
the road. Left turning motorized vehicles considered the turn intention 75 m before
reaching the last queued vehicle in the left turn lane. Similarly, right-turning HMV's
considered the turn intention 50 m prior to reaching the last queued vehicle in the
right turn lane.
3.4.3.1.3 Model Validation
The model was calibrated using data collected from four intersections with a wide
range of traffic situations 400 vehicles per hour to 3,400 vehicles per hour on 9 to 13
m wide approaches. Queue lengths were measured at the end of the red interval and
58


travel times were measured between specific control points. The MOE's used were:
saturation flow rates, queue lengths and travel time. Most of the comparisons made
between observed and simulated runs were significant at the 5% or 1% level of
significance. However, the core vehicle-following model (modified version of
CARSIM), one of the sub-models of the comprehensive simulation model, was not
validated separately.
3.43.2 MIXNETSIM
The MIXNETSIM (Hossain 1996) model was developed for simulating mixed traffic
flow conditions within a roadway network, using the MDCSIM model as a starting
point. The different intersection configurations modeled included unsignalized
intersections, signalized intersections and roundabouts.
3.4.3.2.1 Vehicle Characteristics
As the development of this model was preceded by the development of MIXSIM,
various characteristics such as the vehicle sizes, lateral gaps maintained by different
vehicles, stopped gaps, and free flow speed distribution were assumed to be the same.
However, additional data w'ere collected on gap acceptance, approaching speed at
intersections, free flow deceleration distance and free flow circulating speed around
roundabouts. Vehicle arrivals were represented by separate shifted negative
exponential distributions for motorized (shift 0.5 seconds) and non-motorized (shift
1.5 seconds) vehicles. However, it was noted that as the negative exponential model
performed poorly for high flow conditions, multiple generators were used for
representing such conditions.
59


3.4.3.2.2 Modeling Approach and Vehicle Movement
Heuristics
The same non-collision based vehicle-following model (CARSIM-A5) and the linear
acceleration model used in MEXSIM, were adopted for this study also. One major
difference with the MIXSIM model is the manner in which vehicle positions are
referenced. Recognizing the limitations associated with the strip-based approach, a
new coordinate based representation of vehicle position is adopted in this simulation.
As traffic following non-lane based movements can occupy any lateral position
across the road width, coordinate referencing is the most accurate method for
referencing such vehicles.
A common phenomenon considered in the modeling of turn movements at both
signalized and unsignalized intersections was that the vehicles decelerated to either
the turn speed or a stop condition, depending on the availability/non-availability of
the acceptable gap. This approach was also considered in the modeling of roundabout
approaches, as they are considered to operate on the yield on entry rule.
Although gap acceptance data were collected, due to the lack of disciplined driving
behavior no specific gap acceptance characteristics could be determined. Rather it
was found that often enough drivers would take extremely small gaps, and this would
result in delays to vehicles that had the right-of-way. Observations of this behavior
further reinforced the applicability of the non-collision based vehicle-following
algorithm adopted.
3.4.3.2.3 Model Validation
The results of the simulation runs were validated by comparing it with observed
values in the field for two corridors. Travel time was a common measure used for all
60


the individual intersection types modeled (unsignalized, signalized and roundabout).
Additionally, queue lengths and saturation flow rates at signalized intersections, and
entry flow versus major road/circulating flow relationships were compared for
roundabouts and unsignalized intersections. The validation efforts were encouraging
in that barring a few exceptions, all of the comparisons were significant at the 5%
level of significance. However, the core vehicle-following model, one of the sub-
models of the comprehensive simulation model, was not validated separately.
3.5 Reaction Time
Reaction time is an important component of all vehicle-following models, as it
determines the timing of the application of the response of the following vehicle. It
has a significant impact on the performance of different vehicle-following models.
Reaction time is typically defined as the lag in time between detection of an input and
the start of a response (May, Phiu-Nual et al. 1993). This term is used
interchangeably with perception-reaction time, and has four components (Rao and
Srihari 1976; Bates 1995):
Perception: Detection of a change/hazard
Intellection: Identification of the change
Emotion: Decision to react to the change
Volition: Initiating the change (e.g. moving the foot from the accelerator to the
brake pedal)
The reaction time magnitude is proportional to the complexity of the input and the
resulting decision. It has been reported that the reaction time to simple stimuli such as
light, sound and touch vary from 0.14 to 0.18 seconds (Rao and Srihari 1976).
However, the reaction time for other complex decisions is significantly greater. Thus,
61


in every study it is important to consider the input to which the driver response is
measured.
3.5.1 Brake Movement Time
Reaction time for drivers has been measured for various situations. In most studies
the total reaction time is measured. However, in some studies the movement time or
volition time, which is the time interval! between leaving the accelerator pedal and
pressing the brake pedal has been meas'.ured separately. The results of three recent
studies in which movement time estimaates have been developed are reported below in
Table 3.3 (Koppa 1997). The mean valine varies from only 0.20 to 0.26 seconds, but
the distributions are different.
Table 3.3 Accelerator-Brake Movement Time (Koppa 1997)
Reaction Time (s)
Standard 95th
Source Samples Average Deviation Percentile
Brackett 24 0.22 0.20 0.68
Hoffman 18 0.26 0.20 0.84
Berman 24 0.20 0.05 0.32
Another exhaustive field study was comducted in the US in 1983 (Olson, Cleveland et
al. 1984). In this study the accelerator-brake movement time or volition time, which
was termed as the reaction time, was m.easured. Electronic sensors were used to
record the instantaneous times at whichi the foot was lifted off the accelerator, and at
which the brake pedal was depressed. TThere were two series of tests performed for
surprise and alerted conditions, in whic':h the input was an object on the roadway. A
third series of tests was performed withi the input of a brake light that was installed on
62


the hood of the car. The movement time determined for these different conditions are
summarized in Table 3.4.
Table 3.4 Field Measured Accelerator-Brake Movement Time1
Input Type Reaction Time (s) Younger/OIder drivers
5th Percentile 50th Percentile 95th Percentile
Object Alerted 0.12/0.11 0.19/0.22 0.41/0.52
Surprised 0.25/0.19 0.38/0.32 0.73/0.50
Brake Light Alerted 0.11/0.05 0.18/0.18 0.28/0.47
'Adapted from (Olson, Cleveland et al. 1984). First value is for younger drivers, and
second value for older drivers.
As can be seen from the movement time values reported in Table 3.4, the mean
values from this study are in agreement with the values reported for the three studies
in Table 3.3. Thus, the mean movement time may be considered to be approximately
0.2 seconds.
3.5.2 Total Reaction Time Laboratory/Simulator Measurements
In some studies, reaction time measurements have been made under laboratory
conditions, and typically the driver being tested is informed in advance about the
purpose and process. An example of such a study was performed using the Action
Based Computerized Driver Evaluation System by researchers at the Central Road
Research Institute in India (Saxena, Suri et al. 1997). Two comprehensive studies
have been performed to measure the reaction time of Indian drivers (Central Road
Research Institute 1983; Central Road Research Institute 1992a) for a wide range of
conditions and the values determined are summarized in Table 3.5. The mean, mode
and median values in both the studies are nearly equal, and the distribution can be
approximated by a normal distribution.
63


Table 3.5 Reaction Time for Indian Drivers
Reaction Time (s)
Samples Average Standard Deviation Minimum Maximum
961 0.53 0.09 0.36 0.67
622 0.49 0.07 0.27 0.72
1 (Central Road Research Institute 1983)
2(Central Road Research Institute 1992a)
3.5.3 Total Reaction Time Field Measurements
A few studies have been conducted to measure the reaction times in the field. In one
extensive study (Johansson and Rumar 1971), 321 drivers were asked to depress the
brake pedal when they heard the sound of a hom. This horn was sounded
approximately five miles after the drivers had received this instruction, and the time
the brake light glowed was recorded using an electronic timer. As the drivers had
been informed before hand, the reaction time was considered to be representative of
an alerted condition. Repeated sets of measurements for a different input were made
for alerted and surprise conditions for a smaller set of drivers (ten), and it was
determined that a correction factor of 1.35 could be used to convert alerted reaction
times to surprise reaction times. The reaction times obtained in that study are
summarized in Table 3.6. As reaction times can never be less than zero, they typically
have a positive skew and can be represented as a log normal distribution, and this is
the case for the reaction times determined in this study.
64


Table 3.6
Field Measured Reaction Times
Reaction Time (s)
Input Type 5m Percentile 50m Percentile 9 5m Percentile Average
Horn1 Alerted 0.41 0.61 1.29 0.75
Surprised 0.55 0.82 1.74 1.01
Object2 Alerted 0.53/0.56 0.70/0.72 1.13/1.28 3
Surprised 0.87/0.85 1.10/1.05 1.60/1.50 3
Brake Light Alerted 0.40/0.50 0.60/0.65 0.85/1.04 3
1 Adapted from (Johansson and Rumar 1971).
2Adapted from (Olson. Cleveland et al. 1984). First value is for younger drivers, and
second value for older drivers.
JValues not reported.
In another exhaustive field study mentioned earlier (Olson, Cleveland et al. 1984), the
perception time was considered as the time after which the foot was removed from
the accelerator after the response had been received. The total perception-reaction
time was the time gap between receiving the visual input to pressing the brake pedal,
and the measurements for the different tests conducted are also summarized in Table
3.6.
In a recent study (Fambro 1994) the reaction time for both young and old adults were
measured in response to an obstacle suddenly appearing on the road (from a slot in a
closed course, and a barrel on the open road test). There were a few cases in which
the drivers did not respond to the input at all (7 out of 38), and thus, only limited
conclusions can be made from this research. The mean reaction times determined for
three different scenarios varied from 0.82 to 1.14 seconds.
65


A recent literature review (Koppa 1997) on the subject of brake reaction times has
considered the values in sixteen different studies. In this study, summary values for
the alerted and surprise conditions were determined and presented, and these are
detailed in Table 3.7.
Table 3.7 Brake Perception-Reaction Time Summary from 16 Studies (Koppa
1997)
Reaction Time (s)
Input Avg. Std. dev. 5th Percentile 50th Percentile 95th Percentile
Expected 0.54 0.10 0.53 0.72 0.82
Surprise 1.31 0.61 1.18 2.45 3.31
Thus, the laboratory/simulator studies suggest a mean reaction time of about 0.5
seconds, and the field studies from 0.75 to 1.25 seconds for the alerted condition. The
studies also suggest that the reaction time for a surprise condition is approximately 35
to 50% greater than for the alerted condition.
3.5.4 Reaction Time in Vehicle-Following Models
There have also been limited attempts at determining the reaction time of drivers by
analyzing data collected for vehicle-following studies. In one such study (Helly
1959), the reaction time was estimated by analyzing the speed of the lead vehicle and
the estimate of the speed of the following vehicle based on its acceleration and the
speed of the lead vehicle. The reaction times for six drivers were determined to vary
from 0.5 to 1.0 second, with the average value of 0.63 seconds.
In most of the vehicle-following models, the reaction time is considered to remain the
same for all types of traffic conditions (congested and uncongested). Additionally,
some vehicle-following models, as the one implemented in CORSIM (Halati, Lieu et
66


al. 1997), use a constant reaction time for all drivers. The reaction times considered in
different vehicle-following models are illustrated in Table 3.8. The reaction times
considered in the MIXSIM and MIXNETSIM model are the same as those considered
for the alerted condition in the CARSEM vehicle-following model.
Table 3.8 Reaction Time in Different Vehicle-Following Models
Models Reaction Time Avg. Min. Max.
CARSIM1, MIXSIM1, MIXNETSIM1 0.75 0.4 1.5
Urban uninterrupted heterogeneous traffic simulation model (Singh)2 1.0 -
CORSIM3 0.3 - -
MITSIM4 0.5/1.05 - -
INTELSIM6 0.88 1.51 1.18
1 Used values for alerted (congested) condition from Johansson and Rumar study
(Johansson and Rumar 1971).
2 (Singh 1999)
J (Halati, Lieu et al. 1997)
4 (Yang 1997)
5 Lower value when lead vehicle is decelerating or stopped, and larger value when
lead vehicle is accelerating or cruising.
6 (Aycin and Benekohal 1998)
For most of the models except INTELSIM, when the lead vehicle is decelerating and
the following driver is in alerted condition, the reaction time varies from 0.3 to 0.75
seconds. In an earlier section, the average reaction time of Indian drivers was shown
to be approximately 0.5 seconds, and this appears to be in agreement with the value
implemented in most models.
67


3.6 Arrival Pattern
The arrival pattern of vehicles is an important consideration in any analysis of traffic
flow. The arrival pattern is typically random when the traffic flow rate is low. and
when intersection control located upstream of the approach does not have a
significant impact on the arrival pattern. This is typically observed when the
intersection control is located a significant distance upstream and platoons formed
have an opportunity to disperse. Typically the time difference between the passage of
the front of two consecutive vehicles at a particular observation point is termed as
time headway.
The random arrival pattern can be represented by the negative exponential
distribution, as shown in the following equation.
t
P(h>t) = eT (3.26)
where,
t = time headway, s
P(h>t) = Probability that headway is greater than time t
t = mean headway time, s, = , where V- hourly flow rate
For homogeneous traffic (lane-based) in a single lane, typically there is a theoretical
minimum time headway of 0.5 seconds. Although the probability' of such low time
headways is very low for low flow conditions, this characteristic may be included and
a shifted negative exponential distribution may be considered. This is represented by
a modified Equation (3.26) as
('-g)
P(h>t) = e(r-a) (3.27)
where,
68


a = minimum time headway (shift parameter), typically 0.5 s
Although, this approach is appropriate for lane based systems, it is not appropriate for
non-lane based (heterogeneous traffic) systems. In heterogeneous traffic, particularly
when the roads are more than 7 m (equivalent of two lanes) wide, due to the presence
of many smaller sized vehicles, the arrival of any one vehicle does not necessarily
impact the arrival of other vehicles. Thus, there is no theoretical minimum time
headway, and the use of the negative exponential distribution is appropriate.
As the traffic flow rate increases, there is increasing interaction between vehicles, and
under high flow conditions almost all the vehicles are interacting with each other and
there is a near constant time difference between the vehicles. For this flow condition,
the time headways can typically be represented by a normal distribution. This
distribution is appropriate as drivers attempt to maintain a constant headway, but
there are some variations caused due to differences in driver behavior and response.
The normal distribution can be specified by the mean and the standard deviation. For
single lane cases, as there is a minimum theoretical time headway (typically 0.5
seconds), the standard deviation value is revised to account for this minimum time
headway.
Various researchers have observed that the time headways are typically in the
medium flow range, bounded by the low flow and high flow conditions. There have
been various attempts at using various distributions to represent the medium flow-
conditions, such as Pearson Type III distribution being a generalized mathematical
model (May 1990). This generalized model represents a family of models, including
the Gamma distribution, the Erlang distribution, and the Negative Exponential and
Shifted Negative Exponential distributions described earlier. This generalized
mathematical model is represented by the following equation.
69


(3.28)
/(r)=rw[/i('~a):l
*-_1 -A(r-cr)
e '
where,
m
K
a
s
A
t
r(K)
Probability density function
Parameter affecting shape of distribution, initially estimated as
T-a
s
shift of distribution, s
standard deviation of time headway distribution, s
K
T-a
time headway being considered
Gamma function
As in the case of the negative exponential distribution, the probability of a headway
greater than some specified value t can be represented by
P(h>t) = m\f{t)dt (3.29)
Additionally, the probability of a headway between two specific time headways, t and
t+At can be calculated as
ao ac
P{t t t+ZJ
Based on traffic observations, in 1955 Schuhl proposed that traffic is made of free-
flowing and constrained (following other vehicles) vehicles (Schuhl 1955), and that
the arrival pattern may be represented by a composite model. A shifted negative
70


exponential distribution was used to describe the arrival pattern of constrained
vehicles and a negative exponential distribution for free-flowing vehicles.
('-g) t
P(h>r) = Ce {T'-a) +(1 -C)e 5 (3.31)
where,
C = proportion of total traffic made up of constrained vehicles
h average headway of constrained vehicles, s
r2 = average headway of free flowing vehicles, s
A modification proposed to this approach was the consideration of a shifted negative
exponential distribution for the free-flowing vehicles also (Kell 1962).
As mentioned earlier, for wide streets with heterogeneous traffic, there is no
theoretical minimum headway, and typically no shift needs to be considered.
Additionally, as detailed earlier, previous studies performed for traffic in India and
Bangladesh have considered various distributions for different flow patterns. These
include the negative exponential distribution, the shifted-negative exponential
distribution, the log-normal distribution and a composite modified Schuhl's
distribution.
3.7 Simulation Modeling Languages
Most of the microscopic simulation models in use today were developed in the
1970s, and were written in the general purpose programming languages popular at
that time, such as FORTRAN. Since then, there have been numerous developments
in computer science pertaining to modeling techniques and programming languages
that are beginning to have a significant impact on microscopic simulation modeling.
71


Newer programming languages with potential for applications in transportation
simulation are detailed in this section.
3.7.1 General Purpose Programming Languages
The general purpose programming languages include Basic, Pascal, C and
FORTRAN. Most of the earlier traffic simulation models were written in these
languages. For example, NETSIM and CORSIM (Federal Highway Administration
1997), which are the most frequently used microsimulation models in the U.S. were
written in FORTRAN. Languages such as FORTRAN and C are well suited for
programs in which a significant number of computations have to be performed.
MIXSIM (Hoque 1994) and MIXNETSIM (Hossain 1996) are programmed in
FORTRAN and Singh (Singh 1999) is programmed in C.
Objected-oriented programming (OOP) can be used to implement simulation models
more easily than using traditional procedure-based structured programming
techniques. One of the earliest OOP languages is SIMULA. The SWERTS (Brodin
and Carlsson 1979) and INSWERTS (Palaniswamy, Gynnerstedt et al. 1988) models
were programmed in SIMULA. Two popular OOP languages are C++ and Java, with
the latter having gained a lot of popularity since it was announced in May 1995.
In OOP, interactions between objects take place only when needed, thus simplifying
the computations that take place. All the information relating to an object, including
both the data (static features) and the code (methods, functions, behavior, and
interactions) is included in its own definition. The object types are specified as
classes, and they relate to each other through the sharing of structures or behaviors
defined in one or more other classes through a hierarchical structure. Connections
(pointers) between the various objects define the order of interactions.
72


Two recent simulation models have used the OOP technique. The first model.
HUTSIM (Kosonen and Pursula 1995). uses a very simple vehicle-following routine
to model the flow of traffic through a signalized intersection network. The basic
object type is a lane segment (pipe), and intersections are derived from a combination
of pipes. Other defined objects include vehicles, signal heads, traffic signs, detectors,
and pedestrians. The speed of a vehicle can undertake three possible states at the end
of each time step: it can increase by 5 km/h; remain the same; or decrease by 5 km/h.
Additionally, vehicles will increase speed if they are at less than the cruising speed;
will slow' down if a safe distance is not being maintained; and will not slow' if the
speed is less than that of the leader. If a vehicle cannot accomplish a desired lane
change because of a leader in the desired lane, it will slow down a little and then
attempt to locate an adequate gap.
The vehicle dynamic parameters used to model the driver behavior were based on a
large amount of data collected for an earlier study (Niittymaki 1993). The study
achieved the goal of using OOP to construct a reasonably accurate and reliable
microscopic simulation model. The open character of the system also allowed
efficient teamwork in the development of the model.
In the second study, OOP (C++) was used to implement SIMLAB (Yang 1997) for
homogeneous traffic conditions prevalent in the U.S. The MITSIM model within
SIMLAB uses one of the initial linear vehicle-following theories. Various software
elements, including the general road network, the information network, vehicle trip
table and others are used in the formulation of the program. This study also
concluded that OOP offered a lot of flexibility and wfas thus an appropriate method to
use for simulating traffic conditions.
73


3.7.2 Simulation Languages
There are various simulation languages, such as ACSL, GPSS/H, SLAM II and
SimScript that offer several advantages in programming simulation models. Most of
these simulation languages provide many built-in features to program a simulation
model. These languages also typically provide dynamic storage allocation during
execution, and also better error detection. However, the flexibility of such languages
is limited, and in some cases their execution time is high.
One of the primary reasons that such languages have not been used for modeling
traffic is their relative inflexibility. Although these simulation languages have been
used to model other complex systems, the tools included have allowed such
modeling. These languages can be used to model simple transportation networks, or
simpler representations of complex transportation networks. However, when more
specific behavior or characteristics have to be modeled, the general purpose
languages detailed earlier are typically used.
74


4. Data Collection and Analysis
The primary goal of this dissertation work is to dewelop a simulation model to
represent the flow of heterogeneous traffic at controlled urban intersections. To
ensure that the model is a reasonably accurate representation of the real world
conditions, a significant amount of data are requiresd. Data for roadway, traffic and
vehicle characteristics as well as several measures of effectiveness (MOEs) were
collected.
In the past fifteen years there have been a few stud_ies to analyze the flow of
heterogeneous traffic. In four recent studies (Sutormo 1992; Hoque 1994; Hossain
1996; Singh 1999) specific heterogeneous traffic d,ata, both static and dynamic, have
been collected. However, as the traffic compositiom and the roadway environment in
each of the countries is different (India, Bangladeslh, and Indonesia), a comprehensive
data collection effort was conducted for this study. In addition, none of the previous
efforts included collecting detailed vehicle trajecto:-ry data. Since one of the goals of
this study is to compare vehicle trajectory estimate-s for different vehicle types, a
more comprehensive data collection effort was required. In this chapter the data
collection methods used in other studies are presented. Procedures adopted for data
collection and analysis in this study are outlined. DData collected on various static and
dynamic vehicle, driver and traffic characteristics are also presented.
The data for this study were primarily collected in September and October, 1998 in
two Indian cities. New Delhi and Baroda. Other fiesld data were also collected in
March and June 1999. New Delhi has a population of 9.4 million, and Baroda has a
population of about 1.2 million (1991 data). New Delhi is representative of the large
Indian metropolitan cities, but is unique as it has thee highest motorized vehicle
75


ownership and correspondingly the highest levels of vehicle emissions. The primary
motorized vehicle types are two-wheelers and cars, as these constitute 60-70% of the
motorized vehicles. Cars form a significant proportion (about 35%) of the motorized
traffic in New Delhi, and a significantly smaller proportion in Baroda (about 5%).
Baroda represents the mid-sized metropolitan cities in India. The population of cities
of this size is also growing rapidly, as is the ownership of motorized vehicles, and the
combination leads to significant traffic congestion in the peak periods. It is expected
that the simulation model developed in this study will help in the analysis of traffic
congestion in similar medium and large sized Indian cities.
4.1 Data Collection Objectives
There are several objectives for collecting data, and these are listed in order of
importance:
1. Develop an understanding of various characteristics (driver behavior and vehicle
characteristics) to construct a model.
2. Identify the elements that represent the behavior of heterogeneous traffic drivers.
3. Identify the various static and dynamic vehicle characteristics required to
represent heterogeneous traffic in a simulation model.
4. Identify and select the MOE's to be used to evaluate the performance of vehicle-
following models.
5. Collect detailed vehicle trajectory data for different vehicle types.
The primary aspects of driver behavior include vehicle-following and overtaking.
Secondary aspects include queue formation (creeping at intersections), discharge
from the intersection, response to intersection control, and turn movement heuristics.
1
76


The static and dynamic characteristics include vehicle size, acceleration and
deceleration rates, lateral and longitudinal gaps, and free flow and turning speed.
4.2 Data Collection Methods Used In Other Studies
Various data collection methods have been used in different vehicle-following and
traffic simulation development studies. The initial car-following experiments
conducted by researchers at General Motors (Herman, Montroll et al. 1958) were
based on data collected on a one-mile test-track. A pair of lead-following vehicles
were instrumented and connected together with a pulley system. Twenty to thirty
minute tests were conducted with speeds ranging from 10 to 80 mph (16.1 to 128.8
km/h), including several braking actions by the lead vehicle. The Ohio data (Treiterer
1975) used in the development of the CARSEM and INTELSIM models were
collected using aerial photogrammetric techniques on a four-lane, 3.5 mile (5.6 km)
section of the 1-70 freeway in Columbus, Ohio. Most photographs were taken from an
altitude of about 3,000 feet (914.4 m) at one-second intervals. The data reduced were
reported to be accurate within 0.5 feet (0.15 m) for location and 1 mph (1.6
km/h) for velocity. The photographs provided headway, longitudinal positions and
velocity for 115 individual vehicles for about 4 minutes (between 7:45 and 7:50 A.M.
on July 25, 1967). Four platoons of five to fifteen vehicles were tracked under stop-
and-go conditions. These data sets were used in the calibration and validation of the
CARSIM and INTELSIM car-following models.
Data in the four recent studies on heterogeneous traffic (TRASMIC, MIXSIM,
MIXNETSIM, and Singh) were collected with video cameras placed on buildings or
structures adjacent to or on top of the road where the data were being collected. In
these studies, markings were made on the pavement at periodic intervals (typically
every 5 m). Vehicle positions were estimated at periodic intervals, ranging from 0.1
77


to 1 second. Characteristics such as the lateral and longitudinal gap maintained
between vehicles were estimated from the video data. For some parameters for which
it was difficult to obtain estimates from the video data, additional data were collected
in the field.
In a recent study (Khan, Maini et al. 2000) in which several vehicle-following models
were examined, two vehicles were instrumented with GPS units, with one vehicle
following the other vehicle. These data were collected on three days (February 27,
1999; March 12, 1999 and March 24, 1999) for several hours on a 3-mile section of
the NB 1-25 freeway in Denver, Colorado between Evans and Logan. A limited data
set (six cases), from this large data collection effort, was used for the study. In these
six cases, car-following was observed for a period ranging from 20 to 76 seconds
(total of 275 seconds).
4.3 Data Collection Procedures
The field data for this study were collected using two techniques:
1. Video Recording: To determine various static and dynamic vehicle and traffic
characteristics and several measures of effectiveness variables.
2. Manual Recording: To record the geometric layout of the intersection, locations
of traffic signs and signals, and to qualitatively observe the traffic flow.
The video recording is a common method that has been used by several other
researchers (Singh 1999; Wei 1999). Several aspects of this data collection
methodology are detailed next.
78


4.3.1 Video Data Collection
There are several advantages of using this method, the primary one being that
macroscopic and microscopic traffic and vehicle characteristics may be reduced from
the video by repeatedly viewing the recording. As the vehicles are not instrumented,
the drivers are not aware of the data collection, and no behavioral bias is introduced.
This method also provides an accurate record of traffic for further study, including
any special occurrences or anomalies that impact the flow of traffic such as an
accident, passage of an emergency vehicle, or non-starting of a vehicle.
As the primary goal of this dissertation work includes comprehensive evaluation of
vehicle-following models, it was considered imperative to have vehicle location data
to compare the performance of these models. The various aspects to ensure proper
data collection are detailed next.
4.3.1.1 Camera Location
As the vehicle locations are of primary concern, the ideal view is to obtain video
images from a point directly above the roadway, such that the camera lens is parallel
to the roadway. However, other parameters to be estimated from the video that are
also important include discharge from the stop line, vehicle-following interaction, and
queue length. Thus, the view length typically extended from the middle of the
intersection till the maximum queue length observed. However, in certain cases when
the queue length exceeded 150 m, the entire queue was not included in the view.
The ideal location to place a camera is the rooftop of tall buildings next to the
roadway. An example of the ideal locations for a single intersection is depicted in the
schematic in Figure 4.1.
79


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