A STUDY TO EXAMINE BICYCLIST BEHAVIOR AND TO DEVELOP
A MICROSIMULATION FOR
MIXED TRAFFIC AT SIGNALIZED INTERSECTIONS
by
Winai Raksuntom
B. Eng., Khon Kaen University, Khon Kaen, Thailand, 1992
MSCE, Illinois Institute of Technology, 1998
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
2002
2002 by Winai Raksuntom
All rights reserved.
This thesis for the Doctor of Philosophy
degree by
Winai Raksuntom
has been approved
by
Bruce N. Janson
Thomas Clark
e Dougherty
Date
Raksuntom, Winai (Ph.D., Civil Engineering)
A Study to Examine Bicyclist Behavior and to Develop a Microsimulation for
Mixed Traffic at Signalized Intersections
Thesis directed by Associate Professor Sarosh I. Khan
ABSTRACT
A stochastic, microscopic simulation model, BMVSIM (BicycleMotor Vehicle
Mixed Traffic SIMulation), is developed to represent the behavior of bicyclists in
bicyclemotor vehicle mixed traffic at signalized intersections in the United States.
As part of this study, various aspects of bicyclebicyclist unit behavior are examined
based on data collected in four cities in the United States. Video images of mixed
traffic scenes are analyzed to examine bicycle trajectories. Based on this data, various
characteristics and behavior of bicyclists studied include speed, acceleration and
deceleration of bicycles departing and approaching an intersection, passing,
following, arrival distribution, gap acceptance, stopped distances of motor vehicles
and bicycles, and saturation flow rate and startup lost time of bicycles at signalized
intersections. Each model developed to represent the various aspects of these
characteristics is developed and validated separately, based on field data.
To represent the behavior of bicyclists, a generalized linear modeling (GLM)
framework is used. A discrete choice logit model represents the passing decision of
bicycles and the probability of accepting a gap. The generalized estimating equations
IV
represent the initial acceleration and deceleration of bicyclists, bicycle following, and
the turning speed of bicycles. The generalized linear modeling framework assumes
that the observations are independent. However, as bicycle trajectory data collected
every second for bicycles are used to develop the model, the measurements are
repeated on the same subject across time thus forming clusters of correlated
observations. The correlation among observations is addressed in the generalized
estimating equations using the quasilikelihood estimation method.
Based on the behavioral models developed, a simulation model is implemented in
Visual C++ programming language. BMVSIM is validated using travel time data
collected from the field for motor vehicles and bicycles. This validation demonstrates
that the BMVSIM performs well in representing the bicyclemotor vehicle mixed
traffic at signalized intersections and may be utilized to evaluate the design and
operations of signalized intersections. Several applications of the simulation are also
demonstrated. Additionally, the characteristics and behavior of bicyclists presented in
this dissertation may also be used to develop new procedures and improve existing
methods included in the Highway Capacity Manual (HCM) to evaluate the capacity
and level of service of onstreet bicycle facilities.
This abstract accurately represents the content of the candidates thesis. I recommend
its publication.
Sarosh I. Khan
v
DEDICATION
I dedicate this work to my mother for her support.
ACKNOWLEDGMENT
I would like to express my gratitude to my advisor, Dr. Sarosh I. Khan, for her
guidance, support, and encouragement during these past four years. I would also like
to thank graduate research assistant Sompop Sedhaphak and undergraduate research
assistants Malika Rana and Shadi Hakimi for data collection and reduction.
Appreciation is also expressed to undergraduate research assistant Matthew Tang for
helping me develops the BMVSIM simulation model. Without all of their
dedications and assistances, I could not have completed this dissertation.
CONTENTS
Figures......................................................................xiii
Tables.......................................................................xvi
Chapter
1. Introduction............................................................1
1.1 Background..............................................................1
1.2 Need of a Simulation Model for Mixed Traffic............................2
1.3 Review of Literature on Traffic Simulation Models.......................4
1.4 Components of a Traffic Simulation Model................................6
1.5 Components of a Proposed BicycleMotor Vehicle Mixed Traffic
Simulation Model........................................................8
1.6 Purpose of the Study...................................................10
1.7 Main Contributions of Study ...........................................11
1.8 Organization of the Dissertation.......................................12
2. Data Collection and Data Reduction.....................................14
2.1 Study Sites ...........................................................14
2.1.1 Intersection at Russell Boulevard and Sycamore Lane in Davis, California ..14
2.1.2 Intersection at B Street and Third Street in Davis, California.........15
2.1.3 Intersection at Folsom Street and Arapahoe Avenue in Boulder, Colorado ...16
2.1.4 Cherry Creek Bicycle Path in Denver, Colorado..........................17
2.1.5 Marion Parkway between Cedar Avenue and Alameda Avenue in Denver,
Colorado...............................................................18
2.1.6 Intersection at Lincoln Avenue and 12th Street in Denver, Colorado.....19
2.1.7 Intersection at Harmony Road and Minor Road in Fort Collins, Colorado ....20
2.2 Data Collection Techniques.............................................21
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2.2.1 Bicycle Speeds..........................................................22
2.2.2 Deceleration and Initial Acceleration Rates ............................23
2.2.3 Bicycle Passing and Following...........................................23
2.2.4 Bicycle Arrival Distribution ...........................................24
2.2.5 RightTurning Gap of Motor Vehicles with a Conflicting Through
Moving Bicycle..........................................................25
2.2.6 Stopped Distance between Bicycle and Motor Vehicle......................25
2.2.7 Bicycle StartUp Lost Time and Saturation Headway.......................27
2.3 Data Reduction Technique and Its Accuracy...............................28
2.3.1 Study Site and Video Data Collection ...................................28
2.3.2 Methodology.............................................................30
2.3.3 Analysis and Results....................................................37
2.3.4 Speed and Acceleration Estimation from Video Screen Coordinates ........39
2.3.5 Conclusions.............................................................43
2.4 Data Reduction..........................................................43
2.4.1 Normal Speed of Bicycles ...............................................44
2.4.2 Speed of Bicycles at Signalized Intersections ..........................44
2.4.3 Rightturning Speeds of Bicycles .......................................44
2.4.4 Normal Acceleration and Deceleration Rates of Bicycles at Normal Speed .45
2.4.5 Initial Acceleration Rate of Bicycles ..................................45
2.4.6 Bicycle Deceleration Rate at Intersection...............................46
2.4.7 Bicycle Passing Behavior ...............................................46
2.4.8 Bicycle Following Behavior..............................................46
2.4.9 Bicycle Arrival Distribution ...........................................47
2.4.10 Gap Acceptance of Motor Vehicles with a Conflicting Through Moving
Bicycle ................................................................47
2.4.11 Stopped Distance of Bicycle and Motor Vehicle..........................48
2.4.12 Saturation Flow Rate of Bicycles ......................................49
IX
3. Bicycle Characteristics and Models to Represent Bicyclist Behavior.......51
3.1 Bicycle Speed........................................................... 51
3.1.1 Literature Review........................................................51
3.1.2 Objectives ..............................................................53
3.1.3 Data Analysis and Results ...............................................53
3.2 Acceleration and Deceleration of Bicycles at Signalized Intersections....64
3.2.1 Literature Review........................................................64
3.2.2 Objective................................................................65
3.2.3 Data Analysis and Model Development......................................66
3.3 Bicycle Passing Model....................................................92
3.3.1 Literature Review........................................................93
3.3.2 Objectives ..............................................................95
3.3.3 Data Analysis and Results ...............................................96
3.4 Bicycle Following Model ................................................Ill
3.4.1 Literature Review.......................................................Ill
3.4.2 Objectives .............................................................114
3.4.3 Data Analysis and Results ..............................................114
3.5 Arrival Distribution of Bicycles........................................123
3.5.1 Literature Review.......................................................124
3.5.2 Objectives .............................................................125
3.5.3 Data Analysis and Results ..............................................125
3.6 RightTurning Gap of Motor Vehicles with a Conflicting Bicycle..........130
3.6.1 Literature Review.......................................................130
3.6.2 Objectives .............................................................131
3.6.3 Data Analysis and Results ..............................................131
3.7 Stopped Distances of Bicycle and Motor Vehicle .........................136
3.7.1 Literature Review.......................................................136
3.7.2 Objectives .............................................................137
x
3.7.3 Data Analysis and Results .............................................137
3.8 Saturation Flow Rate, StartUp Lost Time, and Capacity of Signalized
Intersections for Bicycles.............................................144
3.8.1 Literature Review......................................................145
3.8.2 Objectives ............................................................146
3.8.3 Data Analysis and Results .............................................146
4. BMVSIM Simulation Model and Model Validation...........................149
4.1 Model Description .....................................................149
4.2 BMVSIM SubModel ......................................................155
4.2.1 Vehicle Generation ....................................................155
4.2.2 Lane Changing Model for Motor Vehicles.................................160
4.2.3 MotorVehicle Following Model..........................................162
4.2.4 Passing and Following Models of Bicycles...............................165
4.2.5 Bicycle Turning Speed..................................................166
4.2.6 Response to Signalized Control.........................................167
4.3 Network Coding.........................................................174
4.4 Model Validation.......................................................180
4.4.1 Characteristics of the Site ...........................................180
4.4.2 Measure of Effectiveness (MOE) Comparisons ............................182
4.5 Application............................................................184
4.5.1 Application for BMVSIM.................................................184
4.5.2 Application for Highway Capacity and Design............................194
5. Conclusion and Recommendations.........................................199
5.1 Bicycle Characteristics and Behavior of Bicyclists.....................200
5.1.1 Bicycle Speed..........................................................200
5.1.2 Acceleration and Deceleration of Bicycles at Signalized Intersections.201
5.1.3 Passing Behavior of Bicyclists.........................................202
5.1.4 Behavior of a Following Bicyclist......................................204
xi
5.1.5 Arrival Distribution of Bicycles.......................................205
5.1.6 RightTurning Gap of Motor Vehicles with a Conflicting Through
Moving Bicycle........................................................205
5.1.7 Stopped Distance ......................................................207
5.1.8 Saturation Flow Rate and Saturation Headway ...........................208
5.2 BMVSIM Validation ................................................... 208
5.3 Additional Research Needs..............................................209
References...................................................................212
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FIGURES
Figure
1.1 Components of a Proposed BicycleMotor Vehicle Mixed Traffic
Simulation Model.........................................................9
2.1 Intersection at Russell Boulevard and Sycamore Street....................15
2.2 Intersection at B Street and Third Street................................16
2.3 Intersection at Folsom Street and Arapahoe Avenue........................17
2.4 Cherry Creek Bicycle Path.......s..;.....................................18
2.5 Marion Parkway between Cedar Avenue and Alameda Avenue...................18
2.6 Intersection at Lincoln Avenue and 12th Street...........................19
2.7 Intersection at Harmony Road and Minor Road..............................20
2.8 Typical Data Collection and Locations of Camcorders......................23
2.9 Typical Data Collection and Locations of Camcorders for Bicycle
Passing and Following...................................................24
2.10 Typical Data Collection and Location of Camera for RightTurning Gap
of Motor Vehicles with a Conflicting Through Bicycle...................26
2.11 Typical Stopped Distances of Bicycles and Motor Vehicles.................26
2.12 Bicycles in Queue at a Signalized Intersection...........................27
2.13 Bicycle Path Located by Cherry Creek in Denver, Colorado.................29
2.14 Reference and Known Points on Roadway....................................30
2.15 Points that Lie in a Perspective Position................................31
2.16 Distance Traveled Based on Roadway Coordinates...........................36
2.17 Location Error as a Function of Distance from Camera.....................39
2.18 Absolute Error of Speed Estimates for Different Video Frame Processing
Intervals, when 100fit Roadway Section is Used in the Video Image......40
xm
2.19 Absolute Error of Acceleration Estimates for Different Video Frame
Processing Intervals, when 100ft Roadway Section is Used in the Video
Image ..................................................................41
2.20 Standard Error of Speed Estimates for Different Video Frame Processing
Intervals ..............................................................42
2.21 Standard Error of Acceleration Estimates for Different Video Frame
Processing Intervals....................................................42
2.22 Bicyclist makes a RightTurn at an Intersection...........................45
2.23 Typical RightTurning Gaps................................................48
2.24 Stopped Distances Measured at Intersections...............................49
3.1 Speed Distributions.......................................................55
3.2 Bicycle Speeds and Distance to the Stop Line for All Locations............67
3.3 Deceleration Model for Bicycles at a Signalized Intersection..............71
3.4 Relationship between Distance to the Stop Line, Bicycle Speed, and
Bicycle Deceleration Rate...............................................78
3.5 Bicycle Speeds and Distances from the Stop Line of Bicycles at Signalized
Intersections...........................................................80
3.6 Acceleration Model for a 100ft Wide Intersection.........................82
3.7 Bicycle Speed, Acceleration Rate, and Distance or Time as a Function
of Distance and Time for a 100ft Wide Intersection.....................85
3.8 Acceleration Model for a 50ft Wide Intersection..........................87
3.9 Bicycle Speed, Acceleration Rate, and Distance and Time as a Function
of Distance and Time to Stop Line for a 50ft Wide Intersection.........91
3.10 A DistanceTime Plot Showing a Passing and a Passed Bicycle Traj ectory.. .93
3.11 Speed of Passing and Passed Bicycles during Passing Events...............104
3.12 Lateral Spacing between Bicycle and Motor Vehicle at an OnStreet
Bicycle Facility.......................................................108
3.13 Acceleration Rates of Following Bicycles at Different Distance Headways 117
3.14 Comparison of Observed and Proposed Distributions for Data Set #1........129
3.15 Plots between Time Gaps and Cumulative Number of Gaps....................133
3.16 Probability of Accepting a Following or Lateral Gap......................136
xiv
3.17 Headways of Bicycles in Queue for an 8fit Wide Bicycle Lane.......148
4.1 Network Representation in BMVSIM...................................150
4.2 BMVSIM Flowchart Representing Bicycle SubModels...................151
4.3 BMVSIM Flowchart Representing MotorVehicle SubModels.............152
4.4 Bicycle Following SubModel........................................165
4.5 Bicycle Passing SubModel..........................................166
4.6 The Dilemma Zone...................................................168
4.7 Bicycle Behavior at the OnSet of Yellow Phase.....................172
4.8 BMVSIM Main Window.................................................175
4.9 Network Window.....................................................176
4.10 Picture Represents a Network after the First Six Steps.............177
4.11 Illustrate the BMV SIM Signal Timing Editor........................178
4.12 Volume Editor......................................................179
4.13 Captured View from an Animation in BMVSIM..........................180
4.14 Signal Timing Plan and Locations of Cameras at Intersection between
Folsom Street and Arapahoe Avenue.................................181
4.15 Geometry of the Tested Intersection................................185
4.16 Bicycle Flow Rate and Average Delay for Bicycles...................187
4.17 Bicycle Flow Rate and Average Delay for Motor Vehicles in
a RightTurn Lane Group...........................................188
4.18 Effect of Bicycle Flow Rate on the Average Delay of Motor Vehicles
in a LeftTurn Lane Group.........................................189
4.19 Effect of the Percentage of RightTurning Motor Vehicles on Average
Delay of Motor Vehicles in a RightTurn Lane Group.................191
4.20 Effect of the Width of a Bicycle Lane on the Average Delay of
Motor Vehicles in a RightTurn Lane Group.........................193
4.21 Effect of the Width of a Bicycle Lane on the Average Delay for Bicycles... 193
4.22 Approach Speed and Required Yellow plus AllRed Clearance Intervals
for Bicycles......................................................197
5.1 Conflict Zone Locations............................................206
xv
TABLES
Table
2.1 Data Collection and Locations.........................................21
2.2 Various Aspects of Bicyclist Behavior and Location on the Roadway
Network..............................................................22
2.3 Transformation Coordinates for the Cherry Creek Bicycle Path for
Different Roadway Length in View.....................................38
2.4 Absolute Errors of Location Estimates for Different Roadway Length
in View..............................................................38
3.1 Statistical Summary of Bicycle Speeds.................................55
3.2 A Comparison of Mean Speeds (paired ttest) of Through Bicycles.......57
3.3 A Comparison of Mean Speed Ratios of Through Bicycles during
the Yellow and Green Phases..........................................58
3.4 A Comparison of Mean Speed Ratios of Through Bicycles for Different
Intersection Widths..................................................58
3.5 A Comparison of the Mean of Distance Ratios during the Yellow and
the Green Phases.....................................................60
3.6 A Comparison of the Mean of Distance Ratios for 100ft and 50ft Wide
Intersections........................................................60
3.7 Comparison of the Speed Ratios for RightTurning Bicycles during
the Red and Green/Yellow Phases......................................63
3.8 Test of Normal Speed for Bicycles in the Deceleration Mode............68
3.9 Analysis of Variance of Speed Ratio With Respect to Distance to
the Stop Line........................................................70
3.10 GoodnessofFit Measures for the Deceleration Model...................75
3.11 Speed Ratio of Bicycles Accelerating at a Signalized Intersection.....81
3.12 GoodnessofFit Measures for the Acceleration Model for a 100fit wide
Intersection.........................................................83
xvi
3.13 GoodnessofFit Measures for the Acceleration Model for a 50ft wide
Intersection...............................................................87
3.14 Analysis Results of Passing Decision Using Logistic Regression for
an OffStreet Bicycle Facility.............................................98
3.15 Comparison of Passing and Following Decisions of Bicycles for
an OffStreet Bicycle Facility.............................................99
3.16 Test to Check for Significant Influence in Passing Decision with and
without a Presence of a Motor Vehicle................................... 100
3.17 Analysis Results of Passing Decision Using Generalized Linear Model
for an OnStreet Bicycle Facility.........................................100
3.18 Comparison of Passing and Following Decisions of Bicycles for
an OnStreet Bicycle Facility.............................................101
3.19 Statistics on Critical Distance Headway before Passing....................102
3.20 Statistics on Maximum Lateral Spacing during Passing......................104
3.21 Statistics of Lateral Speeds before and after Passing Point...............106
3.22 Statistics of Lateral Position of Bicycles................................109
3.23 Statistics of Lateral Position of Motor Vehicle from the RightEdge
of Bicycle Lane...........................................................110
3.24 Statistics of Lateral Position of Bicycle from the RightEdge
of Bicycle Lane...........................................................Ill
3.25 Comparison of Normal Acceleration and Deceleration Rates of Bicycles
on OffStreet and OnStreet Bicycle Facilities............................115
3.26 Normal Acceleration and Normal Deceleration Rates of Bicycles.............116
3.27 Acceleration and Deceleration Rates of Following Bicycles at Different
Distance Headways.........................................................118
3.28 Analysis Results Using Generalized Estimating Equation (GEE)..............121
3.29 A Paired tTest between Model Predicted and Observed Speed and
Distance Headway of Bicycles in Following.................................123
3.30 Statistical Summary of Bicycle Arrival Data...............................126
3.31 ChiSquare Test Results for Proposed Distribution.........................129
3.32 Statistical Summary of Following Gaps.....................................132
3.33 Statistical Summary of Lateral Gaps.......................................132
XVII
3.34 Analysis Results of Lateral Gaps Using Generalized Linear Model......134
3.35 Analysis Results of F olio wing Gaps U sing Generalized Linear Model.135
3.36 Lateral StoppedDistance between Motor Vehicles and a Bicycle Lane,
With and Without a Bicycle Present..................................139
3.37 Lateral StoppedDistance between Motor Vehicles and a Bicycle Lane...140
3.38 Lateral StoppedDistances of Bicycles from the Curb or the Right and
the Left Adjacent Lanes.............................................141
3.39 Lateral StoppedDistance of Bicycles from the Adj acent Lane.........142
3.40 Longitudinal StoppedDistances between Bicycles at Intersections.....143
3.41 Lateral StoppedDistance between Bicycles at Intersections...........144
4.1 Vehicle Sizes in BMVSIM..............................................157
4.2 Stopped Distances between Vehicles in BMVSIM.........................158
4.3 Maximum Deceleration and Normal Acceleration Rates of Vehicles in
BMVSIM..............................................................159
4.4 Acceptable Gap Sizes for Motor Vehicle...............................160
4.5 Traffic Volume by Approach...........................................182
4.6 Observed and Simulated Turning Movement Comparisons..................183
4.7 Observed and Simulated Travel Time Comparisons.......................184
4.8 The Number of SubLanes and Saturation Flow Rate of Bicycle Lanes....195
4.9 Approach Speed and Required Yellow plus AllRed Intervals for
Motor Vehicles......................................................198
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1.
Introduction
1.1 Background
According to the Nationwide Personal Transportation Survey (NPTS) (US
Department of Transportation 1997) conducted by the US Department of
Transportation, the number of bicycle trips in the United States has doubled over the
last two decades. Over the same period, the percentage of bicycle trips increased by
50 percent. Additionally, the same study also reported that almost 50 percent of these
trips were school, work, shopping, and personal business trips. Given the increased
use and to encourage use of bicycles, new federal guidelines require states to include
bicycle projects and programs in the development of multimodal transportation plans
(US Department of Transportation 1994). Most states now include bicycle
coordinators in state departments of transportation.
Appropriate techniques, that consider bicycle and bicyclist characteristics, to estimate
the capacity of signalized intersections for motor vehicles and bicycles are needed to
develop guidelines to plan, design, and operate bicycle facilities. It has been shown
that bicycle facilities encourage the use of bicycles as an alternative mode of
transportation. Currently, in the US, state and local agencies are seeking better
guidelines as they attempt to include bicycle facilities in their analysis of
transportation systems. However, a recent comprehensive review of the literature on
bicycle facility design and operation (Taylor and Davis 1999) suggests that very
limited studies have been done on the basic characteristics of bicycles.
The 2000 Highway Capacity Manual (HCM 2000) (Transportation Research Board
1
2000) includes a methodology to determine the capacity and level of service of
exclusive and shared bicycle paths based on studies conducted in the Netherlands on
shared bicycle paths with mopeds (Botma and Papendrecht 1991; Botma and
Papendrecht 1993; Botma 1995). The HCM also includes methodologies to analyze
the impact of bicycles on rightturning motor vehicles at intersections based on a
study conducted in the US (Allen, Hummer et al. 1998). Given the lack of studies in
the US on bicycle and bicycle characteristics, the chapter dedicated to the HCM is
quite limited, unlike other sections of the manual that includes methodologies to
evaluate the capacity and level of service of basic freeway sections, freeway weaving
sections, signalized and unsignalized intersections, urban arterials and rural highways.
1.2 Need of a Simulation Model for Mixed Traffic
In recent years, microscopic simulation models are increasingly being used as a tool
for supplementing traditional highway capacity analysis. Intervalbased, stochastic
simulation models such as CORSIM (Federal Highway Administration 1996),
FLEXSYTII (Taale 1997), HUTSIM (Kosonen 1996), and VISSIM (PTV 2000)
mainly represent motorvehicle traffic flow in transportation networks. Although they
have been developed in different countries, they mainly serve the same purpose. They
represent transportation networks as a set of links and nodes. Individual vehicle
movement through the networks, interactions between vehicles, interruptions such as
lane blockages or incidents, and driver responses to signal control are explicitly
modeled. These models are used to evaluate the design and operations of
transportation networks. Unlike the HCM, interactions between individual vehicles at
intersections can be modeled in a stochastic modeling framework. Hence, a
simulation model serves as a powerful tool to study and evaluate the intersection
capacity. Further, the application of a simulation enables users to evaluate and predict
the effects of alternatives, different situations, and future changes. Because it is often
2
difficult to find a location where a desired situation occurs, a simulation model
provides an alternative. Simulations serve as more cost effective, flexible evaluation
tools for engineers, planners, and decisionmakers, compared to field experiments. To
be a useful tool, simulations must represent the behavior of the drivervehicle unit in
traffic and the transportation network; provide estimates of traffic measures that are
comparable to field data, and is easy to use.
To study and determine the impact of bicycles on intersection capacity for bicycle
motor vehicle traffic, a computer simulation may be utilized to model the mixed
traffic flow. So far, there are four computerized models that allow users to model
bicycles in mixed traffic. They were developed specifically for motorvehicle traffic
including several types of motor vehicles including passenger cars, buses, and trucks.
Since the static and dynamic characteristics of these vehicle types have been widely
studied, they are well represented in the simulation. However, very few studies have
been conducted on bicyclist behavior and the static and kinematic characteristics of
bicycles. Even though simulation models such as HUTSIM, FLEXSYTII and
VIS SIM may be used to create a vehicle type bicycle, bicyclist behavior or
characteristics cannot be modeled due to lack of field studies. Another simulation
model, BICSIM (Faghri and Egyhaziova 1999), although developed specifically for
mixedtraffic including bicycles, it was not calibrated or validated based on field
studies. For example, a vehicle following model for motor vehicles was used to
represent bicycle following. However, its performance to represent bicyclist behavior
has not been tested based on field data. Passing maneuvers of bicyclists, and
acceleration, and deceleration characteristics of bicyclists are not represented based
on field studies.
The main focus of this dissertation is to study the bicycle characteristics and bicyclist
behavior in mixed traffic and to develop a new, stochastic simulation model to
3
represent bicycle flow at intersections based on empirical studies. To develop a
simulation model, understanding of bicyclist behavior and the static and kinematic
characteristics of bicycles based on extensive field studies, is required. However,
there are very few studies that provide these characteristics of bicycles. This need has
been highlighted in a recent dissertation research (Taylor and Davis 1999). Most of
the very limited studies on bicycles in the US are based on very small sample sizes,
including only volunteer bicyclists, or on test tracks.
The vehicle size and the static and kinematic characteristics of bicycles and motor
vehicles are significantly different. In addition, the driver behavior is also different.
For example, bicyclists do not form one queue per bicycle lane at an intersection.
They attempt to form one or more queues based on the space available in the bicycle
lane. Bicycles also make passing maneuvers within the bicycle lane, but motor
vehicles do not. The interaction between bicyclists in traffic stream is significantly;
different than motorists. Thus, the current motorvehicle traffic simulation models, in
their current form, may not be used to represent bicyclemotor vehicle mixed traffic.
In the following section, a comprehensive literature review of microscopic simulation
models related to only bicyclemotor vehicle mixed traffic is presented. It is followed
by a discussion on the components of a traffic simulation model. All the components
of a comprehensive simulation model that have been developed as part of this study
are also detailed in this chapter.
1.3 Review of Literature on Traffic Simulation Models
In recent years, microscopic simulations have been developed mainly for motor
vehicle traffic and have become an important tool used for decision making, design,
and operations analysis. So far, four simulation models (Kosonen 1996; Taale 1997;
4
Faghri and Egyhaziova 1999; PTV 2000), allow users to model bicycles in the
bicyclemotor vehicle mixed traffic: three in Europe and one in the US.
FLEXSYTII (Taale 1997) was developed mainly for motor vehicles in the
Netherlands. In this simulation, bicycles can also be modeled, but bicycles are not
allowed to use the same roadway as motor vehicles. The speeds of bicycles are not
affected by motor vehicles and therefore are determined by the speed specified for the
bicycle paths. Bicycles move in a very simple way, they stand still or travel at full
speed. Therefore, acceleration or deceleration of bicycles is not modeled.
A simulation model developed in Germany, VISSIM (PTV 2000) uses a car
following model to represent the behavior of bicyclists. In addition, the bicycle
characteristics data required by a traffic simulation model is expected to be provided
by a user. However, given the unavailability of studies in this area, bicycles can not
be realistically modeled. HUTSIM (Kosonen 1996), a computer simulation model
developed in Finland, allows bicycles to use the same roadway as motor vehicles, but
does not represent any bicycle characteristics. In other words, bicycles may be
modeled as a particular vehicle type. However, users have to provide the
characteristics of this vehicle. Moreover, interactions between bicycles and motor
vehicles occur only at crosswalks in HUTSIM.
In summary, these European simulation models attempt to represent the effect of
bicycles in the bicyclemotor vehicle mixed traffic. However, they were developed
specifically for motor vehicles that include passenger cars, buses, and trucks. These
simulation models represent both motorist behavior and vehicle characteristics that
have been widely studied; and therefore are well represented in the simulation.
Nevertheless, very few studies have been conducted to develop an understanding of
the behavior of bicyclists. Even though users may create a vehicle type bicycle in
5
these European simulation models, bicyclist behavior is not modeled based on field
studies.
Recently, Faghri and Egyhaziova (Faghri and Egyhaziova 1999) developed a
simulation model for mixed motor vehicle and bicycle traffic in the United States
called BICSIM (BICycle SIMulator). Each bicycle and motor vehicle on the network
is treated as an identifiable entity. These vehicles interact with other vehicles and are
affected by the traffic control, parking vehicles, pedestrians, roadway geometry, and
bus stops. This computer model, however, does not represent bicycle characteristics
or bicyclist behavior such as bicycle following, gap acceptance, lane changes, initial
acceleration, deceleration, lost time, and signal responses based on any field study.
1.4 Components of a Traffic Simulation Model
The components of a microscopic simulation model may be categorized into three
modules: (1) Input module (2), User Behavior Module, and (3) Output Module.
1) Inputs Module:
The inputs to a traffic simulation model include the components of a transportation
system that may be modified to represent a specific network and its users. These
inputs include:
Roadway geometry
Number of through lanes
Number of leftturn lanes
Number of rightturn lanes
Grade
6
Lane width
Length of lane
Speed Limit
Traffic characteristics
Volume of bicycles
Volume of motor vehicles
Traffic composition proportion of passenger cars, trucks, and buses
Arrival pattern of vehicles
Startup lost time of vehicles
Traffic control
Phase sequence
Duration of green, yellow, and red interval for each phase
Startup lost time
Saturation flow rate
2) User Behavior Module:
This module represents the behavior of all types of users, including motorists and
bicyclists under various traffic, network and control conditions. These include vehicle
following behavior, startup lost time of vehicles at signalized intersection,
acceleration and deceleration rates of vehicles, stopped distances between vehicles,
signal responses, and lane changing behavior.
3) Outputs Module:
For a transportation network under study, several performance measures may be
7
evaluated using a simulation model. The output module is designed to provide reports
of various measures of effectiveness (MOEs) such as travel time, delay, queue
length, speed, and volume over spatially disaggregated transportation links, and
discrete time intervals, for a transportation system. These reports may be used to
calibrate and validate a simulation model for use in planning, design and operations
of a transportation network.
1.5 Components of a Proposed BicycleMotor Vehicle
Mixed Traffic Simulation Model
The three components relevant to a mixed traffic simulation model are illustrated in
Figure 1.1. The main inputs of a simulation model specify the roadway geometry,
traffic, traffic control, and user characteristics of a specific transportation network. As
part of user characteristics, several aspects of bicyclist characteristics, including the
startup lost time and saturation headway of both bicycles and motor vehicles are also
provided as inputs. Several submodels representing the behavior of users determine
the movement of both bicycles and motor vehicles every time interval in the
simulation. Vehicle position, speed, and acceleration in the network are updated every
time interval based on these models. Their movement data are summarized to obtain
several measure of effectiveness (MOE) such as travel time, delay, speed,
acceleration, deceleration, and distance headway. These MOEs may be used to
calibrate and validate a traffic simulation model for use in planning, design and
operations of a specific transportation network.
As discussed in Section 1.2, bicyclemotor vehicle mixed traffic is significantly
different from motor vehicle traffic. Since the behavior of motorists has been widely
studied, they are well represented in the simulation. However, very limited studies
have been done on the basic characteristics of bicycles, bicyclist behavior and
8
interactions between bicycle and motor vehicle. To develop a comprehensive
simulation model for a bicyclemotor vehicle mixed traffic, several aspects of
bicyclist behavior need to be studied. These include normal speed of bicycles or free
flow speed, acceleration and deceleration rates of bicycles, passing and following
behavior of bicycles, arrival pattern of bicycles, turning speed of bicycles, stopped
distance between bicycle and motor vehicle, startup lost time and saturation headway
of bicycles, and gap acceptance of motorists with a conflicting through moving
bicycle.
Figure 1.1 Components of a Proposed BicycleMotor Vehicle Mixed Traffic
Simulation Model
9
1.6 Purpose of the Study
The main purpose of this dissertation is to develop a new, intervalbased, stochastic
simulation model to represent the behavior of bicyclists at intersections, based on
extensive field studies. As part of this study, several static and kinematic
characteristics of bicycles and the behavior of bicyclists are examined. The simulation
model may be used to analyze intersection capacity, level of service, develop optimal
signal control strategies, and to evaluate the benefits of implementing new traffic
control technologies to improve intersection operation or innovative designs for
bicycle facilities.
The main objectives of this research are to study the following:
The static and kinematic characteristics of bicycles and behavior of bicyclists
in bicyclemotor vehicle mixed traffic at signalized intersections:
Bicycle speeds
The acceleration of bicycles at signalized intersections, departing
from stopped condition, until they reach their normal or desired speed.
The deceleration of bicycles at signalized intersections as they
approach a red traffic signal indication.
The interaction or response of a following bicycle to the actions of a
lead bicycle.
The decision to pass or follow
Behavior of bicyclists during passing
The arrival pattern and speed distribution of bicycles at an
intersection.
The stopped distances between motor vehicles and bicycles in mixed
traffic.
10
The startup lost time and saturation headway of bicycles in bicycle
motor vehicle mixed traffic.
Examine the performance of each submodel developed to represent bicycle
characteristics and bicyclist behavior.
Represent the static and kinematic characteristics of bicycles in a traffic
simulation model.
Validate the traffic simulation model.
Demonstrate its application
The various aspects of bicycle and bicyclist behavior are examined based on field
studies conducted in several cities in the United States. Submodules are developed to
represent the various aspects described above and are validated based on field data.
An integrated, comprehensive simulation model is developed based on these sub
models. The simulation is also validated based on a macroscopic measure of
effectiveness. The simulation will also be applied to study the impact of bicycle flow
on intersection capacity, operation, and design.
1.7 Main Contributions of Study
The main contributions of this dissertation work are as follows:
Static and kinematic characteristics of bicyclebicyclist unit and bicyclist
behavior in mixed traffic at signalized intersections are examined.
Several models are developed to represent various aspects of bicyclist
behavior at signalized intersections and validated based on field data. These
include following, passing, departing an intersection at the start of a green
phase, decelerating to stop at an intersection, stopping at an intersection and
flow through street or intersection.
11
A comprehensive microscopic bicyclemotor vehicle mixed traffic simulation
model is developed for signalized intersections in the United States. This
simulation is the first to represent the behavior of bicyclists based on field
studies. In previous efforts, the behavior of bicyclists was not represented in
simulation models, nor calibrated or validated based on field studies.
Detailed dynamic and kinematics characteristics of bicycle bicyclist (rider)
unit is studied and modeled.
1.8 Organization of the Dissertation
This dissertation presented in five chapters. Chapter 2 describes the study sites and
the data collection and data reduction techniques applied. The data collected include
bicycle turning and free flow speeds, acceleration and deceleration rates of bicycles,
passing of bicycles, following of bicycles, arrival distribution of bicycles, right
turning gap of motor vehicles with a conflicting through moving bicycle, stopped
distance between bicycle and motor vehicle, startup lost time of bicycles, and
saturation headway of bicycles at signalized intersections.
Chapter 3 presents, in each section, the bicyclebicyclist characteristics and bicyclist
behavior examined. Each section includes a review of the literature, the data
analyzed, and the findings relevant to each characteristic. Based on these findings,
several models to represent these characteristics are developed. The sections also
document the relevant model development and validation.
In Chapter 4, the main components of the simulation model are detailed. The results
on the validation of the model are presented in this chapter. Additionally, several
applications of the simulation model are demonstrated.
12
Chapter 5 presents the conclusion of the study and recommendations on areas for the
further research.
13
2.
Data Collection and Data Reduction
To study the dynamic and kinematic characteristics of bicycles and the behavior of
bicyclists at intersections, a research project was funded by the National Research
Council at University of Colorado at Denver. For this project, data was collected in
four cities in the United States. The investigation for this dissertation work is
conducted based on the data collected from this study.
Data was collected by 8 mm Hi8 video camcorders at seven locations in four cities:
(1) two signalized intersections in Davis, California, (2) a signalized intersection in
Boulder, Colorado, (3) a bicycle path and two signalized intersections in Denver,
Colorado, and (4) a signalized intersection in Fort Collins, Colorado. These seven
different sites have high volume of bicycles and allow the study of a variety of factors
that vary from site to site. The data was collected in the summers of the years 2000
and 2001. Traffic scenes were video recorded on sunny days and under dry pavement
conditions.
2.1 Study Sites
2.1.1 Intersection atRussell Boulevard and Sycamore
Lane in Davis, California
The intersection at Russell Boulevard and sycamore Lane in Davis, California, is near
the University of California at Davis campus. It is a Tsignalized intersection, with
two lanes in each direction on both northboundsouthbound and eastbound
westbound. As the bicycle volume is very high on Sycamore Street, the City of Davis
provides a bicycle signal indication phase, on the northbound direction. The bicyclists
14
on northbound wait for the bicycle signal to head towards to the university campus.
Bicyclists are typically students and commuters. The layout of this intersection is
illustrated in Figure 2.1.
Figure 2.1 Intersection at Russell Boulevard and Sycamore Street
2.1.2 Intersection at B Street and Third Street in Davis,
California
This intersection is located in Davis, California, close to the University of California
at Davis campus. This fourleg, 50ft wide signalized intersection, has one lane in
each direction on both the northsouth and the eastwest directions. Most bicyclists
use the Third Street to enter and leave the university campus. Bicyclists are typically
students and commuters. The layout of this intersection is illustrated in Figure 2.2.
15
Figure 2.2 Intersection at B Street and Third Street
2.1.3 Intersection at Folsom Street and Arapahoe Avenue
in Boulder, Colorado
This intersection is located in Boulder, Colorado, between downtown Boulder and the
University of Colorado at Boulder campus. It is a fourleg, 100fit wide fully actuated
signalized intersection. Most bicyclists use Folsom Street (10ft wide with a 6ft wide
bicycle lane) to enter and leave the university campus. The City of Boulder also
provides bicycle lanes in this street due to high volume of bicycles. The layout of this
intersection is illustrated in Figure 2.3.
16
Figure 2.3 Intersection at Folsom Street and Arapahoe Avenue
2.1.4 Cherry Creek Bicycle Path in Denver, Colorado
Cherry Creek bicycle path in Denver, Colorado is under and parallel to the Speer
Boulevard, one of the major streets in downtown Denver. It is a 10ft wide concrete
bicycle path that consists of both an exclusive and shared bicycle path sections. The
bicycle path runs northwest of downtown Denver from the Cherry Creek shopping
district, through lower downtown near the University of Colorado, Denver campus,
industrial areas, and sports arenas Coors Field and Pepsi Center and other recreational
areas. Bicyclists are typically students, recreational users and commuters. An
exclusive bicycle path section was selected to eliminate the conflict between bicycles
and pedestrians. This section is located between Arapahoe Street and Lawrence Street
as illustrated in Figure 2.4.
17
Speer Boulevard
Southbound
Figure 2.4 Cherry Creek Bicycle Path
2.1.5 Marion Parkway between Cedar Avenue and
Alameda Avenue in Denver, Colorado
Marion Parkway between Cedar Avenue and Alameda Avenue is a twoway street,
one lane in each direction, 12ft wide, with a 6ft wide bicycle lane on the right of the
motorvehicle lane. This bicycle route runs from a residential area to the Cherry
Creek bicycle path. This section of the Marion Parkway located between Cedar
Avenue and Alameda Avenue is illustrated in Figure 2.5.
@
BICYCLE LANE
MARION PARKWAY
BICYCLE LANE
Figure 2.5 Marion Parkway between Cedar Avenue and Alameda Avenue
18
2.1.6 Intersection at Lincoln Avenue and 12th Street
in Denver, Colorado
This intersection is located in downtown Denver, Colorado. The data was collected
on the eastapproach of the intersection, on the 12th Street. This section of the 12th
Street is a twoway street, one lane in each direction, as illustrated in Figure 2.6. This
bicycle route runs from residential area to the Cherry Creek bicycle path and
downtown Denver. Bicyclists typically are commuters and recreational users.
19
2.1.7 Intersection at Harmony Road and Minor Road
in Fort Collins, Colorado
This intersection is located near the office complex in Fort Collins, Colorado.
Bicyclists typically are commuters. They use both Harmony Road and Minor Road to
get in and leave their office. For the purpose of this study, the data was collected on
the northapproach of the intersection (on Minor Street) as illustrated in Figure 2.7.
Office Complex
Bicycle Lane
Harmony Road
Figure 2.7 Intersection at Harmony Road and Minor Road
20
2.2
Data Collection Techniques
Data on various aspects of bicyclist behavior were collected at seven locations. Each
location provides different types of bicycle characteristics since they include different
types of users, bicycle volumes, and roadway geometry. Table 2.1 presents a
summary of the bicycle characteristics and study locations, the data collected at
specific sites. Table 2.2 lists the location in the network where the data was collected.
For example, normal speed of bicycles is estimated based on data collected upstream
of an intersection.
Table 2.1 Data Collection and Locations
Bicycle Characteristics and Bicyclist Behavior Study Sites
1 2 3 4 5 6 7
Bicycle Speed
Normal Speed XX' m * V
Speed within an Intersection Ml
Turning Speed KiS.'
Acceleration Rate
Initial Accelration '
Acceleration during Normal Speed J
Deceleration Rates
Deceleration to Stop ~=\ 
Deceleration during Normal Speed a?;, m I*
Passing **
Following > m
Arrival Distribution mu SF ?.i 8P
RightTurning Gap of Motor Vehicle with a Conflicting Through Moving Bicycle * "
Stopped Distances
Startup Lost Time
intersection at Russell Boulevard and Sycamore Lane
intersection at B Street and Third Street
intersection at Folsom Street and Arapahoe Avenue
4Cherry Creek Bicycle Path
5Marion Parkway between Cedar Avenue and Alameda Avenue
intersection at Lincoln Avenue and 12th Street
intersection at Harmony Road and Minor Road
21
Table 2.2 Various Aspects of Bicyclist Behavior and Location on the Roadway
Network
Bicyclist Behavior Location on a Roadway Netwrok
1. Normal speed of bicycles
2. Turning speed and speed within
an intersection of bicycles
3. Deceleration and initial
acceleration rates
4. Passing and following
5. Bicycle arrival distribution
6. Rightturning gap of automobiles
with a conflicting through bicycle
7. Stopped distance between
automobile and bicycle
8. Startup lost time and saturation
headway of bicycles______________
On a roadway section upstream or
down stream of an intersection
At an intersection
At an intersection
On a roadway section upstream or
down stream of an intersection
Upstream of an intersection
At an intersection
At the stop line of an intersection
At the stop line of an intersection
2.2.1 Bicycle Speeds
The purpose was to study: (1) normal speed of bicycles, (2) speed of bicycles at the
signalized intersection, and (3) turning speed of bicycles. Therefore, bicycle
movements both upstream of the intersection and within an intersection area are
studied. Three camcorders, placed on the sidewalk (Figure 2.8), were used to record
bicycle movements at each intersection. The first two camcorders were used to record
bicycle movements over a 350fit section upstream of the intersection. Another
camcorder was used to record bicycle movements within an intersection area. This
third camcorder recorded both through and turning bicycles. The analysis based on
this data is presented in Chapter 3, Section 3.1.
22
ddsr
CAPTURED BY CAMCORDER #\ CAPTURED BY CAMCORDER #2 
ft
CAPTURED BY
CAMCORDER #3
I.
CAPTURED BY
CAMCORDER #4
100 ft
% r
Camcorder #1 Camcorder *2
Camcorder #4
Figure 2.8 Typical Data Collection and Locations of Camcorders
2.2.2 Deceleration and Initial Acceleration Rates
The purpose was to examine: (1) the acceleration rate of bicycles as they depart an
intersection at the start of a green phase or initial acceleration rate and (2) the
deceleration rate of bicycles as they approach an intersection and come to a complete
stop at the stop line during a red/yellow phase. Therefore, bicycle movements
upstream of an intersection, within an intersection area, and down stream of an
intersection were recorded. Four camcorders (Figure 2.8), placed on the sidewalk,
were used to record bicycle movements at each intersection. The first two camcorders
were used to record bicycle movements over a 350fit section upstream of an
intersection. The third camcorder recorded bicycle movements within an intersection
area. The fourth camcorder recorded bicycle movements over a 100ft section
downstream of an intersection as illustrated in Figure 2.8. The analysis based on this
data is presented in Chapter 3, Section 3.2.
2.2.3 Bicycle Passing and Following
To study bicycle passing maneuvers and following, video recordings were done at
three locations: (1) a section of the Marion Parkway between Cedar Avenue and
23
Alameda Avenue in Denver, Colorado, (2) a section of the Cherry Creek bicycle path
between Lawrence Street and Arapahoe Street in Denver, Colorado, and (3) a section
of the Folsom Street between Colorado Street and Arapahoe Avenue in Boulder,
Colorado. Three Hi8 video camcorders were placed at a sidewalk of each location.
The three camcorders captured the movement of bicycles over a 450ft section on the
southbound direction as illustrated in Figure 2.9. The analysis based on this data is
presented in Chapter 3, Sections 3.3 and 3.4.
Camcorder #3 Camcorder #2 Camcorder #1 < 450 ft 350 ft >. ds
; i i ^jÂ§
" i LAFTUkhU T L'AFiUkfcU : CAPTURED": I BY i BY i i BY i  CAMCORDER j CAMCORDER:  CAMCORDER : : #3 { : #2 : : #1 : Travel Direction
m
Figure 2.9 Typical Data Collection and Locations of Camcorders for Bicycle
Passing and Following
2.2.4 Bicycle Arrival Distribution
To study bicycle arrival distribution, video recordings were carried out at about 300
feet upstream of three intersections: (1) B Street and Third Street in Davis, California,
(2) Sycamore Lane and Russell Boulevard in Davis, California, and (3) Folsom Street
and Arapahoe Avenue in Boulder, Colorado. As discussed in Section 3.2, bicyclists
start decelerating at a distance less than 100 feet from the stop line in response to
24
traffic signals. Therefore, bicycle arrival at 300 feet upstream of an intersection is not
affected by the signal downstream. The analysis based on this data is presented in
Chapter 3, Section 3.5.
2.2.5 RightTurning Gap of Motor Vehicles with
a Conflicting Through Moving Bicycle
To study gaps for rightturning motor vehicles with opposing through bicycles, traffic
scenes were recorded at four intersections in the United States: (1) B Street and Third
Street in Davis, California, (2) Folsom Street and Arapahoe Avenue in Boulder,
Colorado, (3) 12 Street and Lincoln Avenue in Denver, Colorado, and (4) Harmony
Road and Minor Road in Fort Collins, Colorado. A Hi8 video camcorder was placed
on the sidewalk of each intersection to record bicycle and motorvehicle movements.
The camcorder covered the intersection area and 100ft section upstream of the
intersection as illustrated in Figure 2.10. The analysis based on this data is presented
in Chapter 3, Section 3.6.
2.2.6 Stopped Distance between Bicycle and Motor
Vehicle
Video recordings of stopped distances of bicycles and motor vehicles were collected
at two locations: (1) the south approach of intersection between Sycamore Lane and
Russell Boulevard in Davis, California, and (2) the south approach of intersection
between Folsom Street and Arapahoe Avenue in Boulder, Colorado. At the south
approach of Sycamore Lane, an 8ft wide bicycle lane is located between left and
right turn lanes, and a 6ft wide bicycle lane is located next to the curb of the south
approach of Folsom Street. Motorvehicle lanes on Sycamore Lane are 12ft wide and
are 10fit wide on Folsom Street. Typical stopped distances between bicycles and
25
motor vehicles are illustrated Figure 2.11. The analysis based on this data is presented
in Chapter 3, Section 3.7.
Figure 2.10 Typical Data Collection and Location of Camera for RightTurning
Gap of Motor Vehicles with a Conflicting Through Bicycle
(a) (b)
(a) Bicycle Lane at the Center
(b) Bicycle Lane at the Right Most Lane
Figure 2.11 Typical Stopped Distances of Bicycles and Motor Vehicles
26
2.2.7 Bicycle StartUp Lost Time and Saturation Headway
As intersections were surveyed to collect data on saturation flow rate of bicycles,
intersections with a minimum of five bicycles at the stop line during any red phase
were considered. The initial observations were made at several intersections in three
cities: (1) Davis, California, (2) Boulder, Colorado, and (3) Denver, Colorado.
However, only one intersection in Davis, California (intersection of Sycamore Lane
and Russell Boulevard) met this requirement.
The intersection of Sycamore Lane and Russell Boulevard is a signalized intersection
with 8ft wide bicycle lane between the left and right turn lanes for motor vehicles.
Since the bicycle volume at this intersection is fairly high (100300 bicycles per
hour), it has an exclusive signal phase for bicycles. Bicyclists stop at the stop line
during a red phase and wait for a green phase for bicycles. The bicycle traffic at this
intersection was video recorded using a camcorder. This camcorder captured bicycle
movements from about 100fit upstream of the intersection. During the data
collection, maximum of ten bicycles were in queue at the stop line during a red phase.
The typical bicycle traffic at a signalized intersection is illustrated in Figure 2.12. The
analysis based on this data is presented in Chapter 3, Section 3.8.
(a) (b)
(a) Bicycles in Queue During a Red Phase
(b) Bicycles Departing an Intersection at the Start of a Green Phase
Figure 2.12 Bicycles in Queue at a Signalized Intersection
27
2.3
Data Reduction Technique and Its Accuracy
This section presents a method to process full motion video of traffic scenes to
estimate bicycle location, speed and acceleration at a given rate of image processing.
The technique presented to estimate bicycle location data from video frames based on
transforming screen coordinates of video frames to ground or roadway coordinates, is
known as rectification. The numerical technique and the error analysis are presented.
This technique will be use to analyze the video recording of traffic scenes to estimate
various microscopic and macroscopic traffic flow measures. These measures may be
used to develop and validate traffic flow models. The data reduction technique
presented here should also allow researchers to collect bicycle flow data at very low
costs.
2.3.1 Study Site and Video Data Collection
The Cherry Creek mixeduse bicycle path lies between Market Street and Speer
Boulevard., located close to the University of Colorado campus in Denver, and was
selected as a test site. This section of the bicycle path is shared by bicyclists and
rollerbladers.
A video camera was placed at the test site on an overhead bridge, perpendicular to the
direction of bicycle traffic on February 5th, 2000 (Figure 2.13). The roadway recorded
is ten feet wide, straight, concrete section, with unrestricted sight distance, and level
terrain. Bright orange tiles measuring one square foot were used as markers. The tiles
were placed on both sides of the roadway at regular spacing. Total Station surveying
equipment (accuracy of 1.0 inch) was used to measure the location of the tiles. Four
tiles, placed at the two extreme ends of the roadway, were used as reference points,
and the intermediate tiles were used as known points (Figure 2.14). In addition, the
28
roadway length recorded was varied: 100 fit., 150 ft., and 200 ft. Traffic on this
section of the bicycle path was recorded for a few hours. During the data collection
period, the volumes of bicycles and skaters in both directions combined were
approximately 100 bicycles per hour and 40 skaters per hour.
Frames from full motion video were captured into Audio Video Image (AVI) file
format using a video capture card. The frame capture rate may be specified as number
of frames per second. For any frame from the AVI files, individual bicycle locations
may be identified on the screen in terms of x, y coordinates by using the Vehicle
Video Capture Data Collector (VEVID) software (Wei and Feng 1999). The rate at
which frames are captured from the video is termed frame capture rate and the rate at
which frames are processed to locate bicycles is termed the frame processing rate.
Figure 2.13 Bicycle Path Located by Cherry Creek in Denver, Colorado
29
Figure 2.14 Reference and Known Points on Roadway
As mentioned, the video capture card captures frames from the video at a specified
rate, for example two frames per second. However, the card is often unable to
maintain a constant interval between captures. For example, when two frames per
second is specified, the video capture software is often unable to maintain a constant
interval of 0.5 seconds between captures, although two frames per second are still
captured as specified. By increasing the frame capture rate, the error in the interval
between frames captured may be reduced.
For this study, the full motion video was captured into AVI files at a capture rate of
ten frames per second. However, to collect bicycle data every half second, the frame
processing rate was two frames per second, i.e. every first and sixth frame out of ten
captured per second were processed to locate bicycles.
2.3.2 Methodology
2.3.2.1 Coordinate Transformation Using Rectification
Technique
One of the primary purposes of recording traffic scenes is to obtain bicycle or vehicle
locations at regular intervals or at specific instants. Principles of projective geometry
30
were applied to transform screen coordinates to ground or roadway coordinates.
Projective geometry is derived from one of two fundamental operations in
photogrammetry projection. Geometric characteristics are transferred unchanged
from the original into an image (Ghosh 1979). The fundamental principle of the
general concept of projectivity is the theory of cross ratio. According to this theory,
the cross ratio AC/BC: AD/BD (written as ABCD) is equal to the cross ratio
A1B1C1D1 (Figure 2.15). If two figures are projective then their elements uniquely
correspond to each other and the cross ratio between any four elements in one figure
corresponds to the other. Projective figures can be arranged in a perspective position
and the process is known as relative orientation or rectification.
l
n
D
Cl
D1
Figure 2.15 Points that Lie in a Perspective Position
Based on this principle, coordinates can be transformed analytically between two
projective sequences. For projectivity between planes, i.e. in two dimensions, the
31
number of coordinates per point is two and two expressions are needed per point pair.
For every point pair with coordinates x, y in one plane, and x',y in the other plane;
or for every screen coordinate pair xs, ys and roadway coordinate pair xr, yr, the
following expression may be derived (Ghosh 1979):
C4Xs +C5>S +1
^ Cg + CjXs + CgXy
Vr~ ctx1+csy,+1
where,
xr, yr = Roadway x and y coordinates
xs, y* = Screen x and y coordinates
Ci to Q = Coefficients
The projectivity between the two planes is uniquely determined if a total of eight
coefficients are known. This requires at least four equations of types (2.1) and (2.2)
based on four known points. This equation system may be setup to solve for the
coefficients. Based on the coefficients estimated, the equations may be used to
transform any pair of screen coordinates to roadway coordinates. A condition
required for the expressions to remain valid is that three of the four points may not lie
in a straight line, or
C, C2 C3
Q C7 C8 *0 (2.3)
c< C5 1
(2.1)
(2.2)
Equations (2.1), (2.2), and four known points can be used to solve eight simultaneous
equations:
32
*>,1 i y>*
x,,2 i Xs,2 y>. 2
Xr,3 i Xs,3 y*. 3
Xr,4 i xsA
?r,l 0 0 0
yr. 2 0 0 0
yr, 3 0 0 0
yr, 4 0 0 0
~xsAXrA
~Xs,2Xr,2 ~ys,2Xr,2
~Xs,3Xr,3 ys,3Xr,3
~XsAXr,4 y*AxrA
ys,iy,A
~xs,2yr,2 ys,2yr,2
~Xs,3yr,3 ys,3yr,3
Wr.4 T.,4^,4
0 0 0 q c2
0 0 0
0 0 0 C3
0 0 0 C4
i x,,l y*.i q
i Xs,2 y*. 2 q
i Xs,3 ya, 3 q
i \4 y*A q
(2.4)
Rewriting this matrix in the following form,
[s]=[s][c]
And then inverting one matrix the coefficients are obtained,
[cHsRfM
(2.5)
(2.6)
The simultaneous equations are solved to determine the coefficients. Using these
estimated coefficients, any pair of screen coordinates may be transformed to roadway
coordinates. This procedure, defined earlier, is called rectification.
For different roadway lengths, the roadway coordinates of several points were
measured in the field to determine the accuracy of the measurements based on the
error propagation theory described in the next section.
2.3.2.2 Standard Error and the Law of Error Propagation
When the true values are known for a series of direct measurements xi, x2, x3,..., x of
a quantity x,, the true error of the measurements are as follows:
33
= X, X
s2=x2x (2.7)
6,=XX
The average error is defined as the arithmetic mean of the absolute values of the
errors:
(2.8)
where,
s = true error
n = number of observations
Standard error is determined as the square root of the arithmetic mean of the squares
of the true errors. Since true errors are not known, apparent errors or residuals (v) are
estimated from the best possible ground measurements.
m = lim
M
where,
m = standard error of measurements x
(2.9)
Standard error is the statistical expression for each of the errors. It may be assumed
that each measurement is afflicted by this standard error, and thus m is an expression
for the quality of a single measurement. From the special law of error propagation in
its simplest form, if
z = axXx + a2X2 + ...+anX
(2.10)
34
(2.11)
and the standard error for xj, %2 and X3 are mi, m2, andmj respectively, then,
2 2 2 2 2 2 2
mz =alml + 0^ +... + afimn
mz ^jaxmx + a\m\ + ...+a^m2 (2.12)
If a; = ci2 = <33= ... =a=l, and mi = m2 = m3... mn=m, then Equation (2.12)
reduces to
mz=mfn (2.13)
The law of error propagation is only valid for linear functions. But a nonlinear
function may be approximated by a Taylor's series, assuming the errors are small. For
an arbitrary function,
Z = f(XvX2,X2,...,X) (2.14)
where,
Xu X2,..., Xn are measured with errors Ej, E2, ..., E.
Z + E = f{Xx+Ei,X2+E1,....,Xn+Ea) (2.15)
E = f(Xi+El,X2+E2,....,Xn+En)f(Xl,X2,....,Xn) (2.16)
Using Taylor series,
E = ^Ei+^E2+... + ^En
dXx 1 dX2 2 dX
(2.17)
According to Equations (2.10) and (2.12),
M =
( \
mj
df
V^> j
+
df
ydX2 j
m.
+ ...+
\2
df
Kdx>, ny
m..
(2.18)
where,
M= the standard error of Z
35
2.3.2.3 Estimate of Distance Traveled
Screen coordinates may be transformed to roadway coordinates based on the
rectification procedure described in the previous section. Roadway coordinates for a
bicycle, estimated from screen coordinates of two consecutive frames processed at an
interval At, may be analyzed to estimate the distance traveled by a bicycle in time At.
If the roadway coordinates estimated from the first frame is (xj, yi) and the second
frame is fa, y2X distance traveled in time At is Z and may be estimated as follows
(Figure 2.16):
y
X2,y2
Y=y2yi
X1y! X=X2xi
X
Figure 2.16 Distance Traveled Based on Roadway Coordinates
(2.19)
36
If the standard error along the xdirection and the ^direction is mx and my
respectively, based on Equation (2.13), the standard error ofX= faxi) and 7= (}>2yi)
is mx and mf.
II J* (2.20)
II I1 (2.21)
The standard error of Z, Mz, may be analyzed as follows based on Equation (2.18):
Mz=.
df
m.
\2 / \2
' r df '
+
mv
KdXY Yj
r v ^2 (y V
x
my
V ^ J
+
mv
\Z Y j
(2.22)
44
2m2 + Y2mj
If mx = my = m, mx ~mY Jim, then,
Mz = sjX2m2x + Y2m2Y = ^yjlX2 + 272 = 4lm (2.23)
2.3.3 Analysis and Results
Table 2.3 presents the rectification coefficients for traffic scenes recorded with 100ft,
150ft and 200ft roadway sections in view. The average absolute errors and the
standard errors of several, regularly spaced known points marked by tiles at 20ft, 30
ft and 40ft spacing in the x direction are presented in Table 2.4.
37
Table 2.3 Transformation Coordinates for the Cherry Creek Bicycle Path
for Different Roadway Length in View
Longitudinal Roadway in View Rectification Coefficients
Cl C2 C3 C4 C5 C6 Cl C8
100 ft. 197.015700 0.000041 0.008663 0.000018 0.000259 75.186570 0.003110 0.029048
150 ft. 240.175600 0.002770 0.019393 0.000047 0.000455 46.502940 0.004926 0.051022
200 ft. 341.958600 0.002910 0.025403 0.000059 0.000670 20.905130 0.008716 0.075303
Table 2.4 Absolute Errors of Location Estimates for Different Roadway
Length in View
Longitudinal Roadway in View (ft) Maximum Error (ft) Minimum Error (ft) Average Error Standard Error (ft)
X y X y X y mx m v
100 1.86 0.32 0.01 0.01 0.82 0.16 0.89 0.14
150 1.72 0.92 0.04 0.14 0.85 0.55 1.10 0.60
200 2.47 1.36 0.78 0.57 1.69 0.86 1.82 0.89
As expected, Table 2.4 shows that for shorter roadway sections, the average absolute
errors along both the x andy directions are lower. The average error and the standard
error in the xdirection are higher than along the ydirection, because the spacing
between reference points is higher for the xdirection. For 100150 ft of roadway in
view, the average error along the length of the roadway is less than 1 ft. Figure 2.17
also shows that error is not systematic, i.e. does not vary based on the distance from
the camera and therefore shows that the rectification transformation technique
accounts for the perspective view of the roadway on the screen.
38
5
Including all points, except reference points
4.5 
4
3.5 
=0.05
p 2.5
M
u
W 2
1.5
1 
0.5 
0
0 20
Point closest to
Camera
40
60
80 100
Point furthest from
Camera
Percent Distance
Figure 2.17 Location Error as a Function of Distance from Camera
2.3.4 Speed and Acceleration Estimation from Video
Screen Coordinates
The previous section describes the methodology used to transform video screen
coordinates to roadway coordinates so that bicycle location can be estimated. Based
on the location data and the distance traveled by a bicycle at any point in time, its
speed and acceleration may be estimated. First the speed may be estimated as:
Average speed between tn and tn + At
x(t)x(t+At)
At
where,
x, = distance of bicycle from reference point at time tn
x, +AI = distance of bicycle from reference point at time tn + At
v( = velocity of bicycle at time tn
at = acceleration of bicycle at time tn
At = time interval
(2.24)
39
Assuming the average velocity occurs at midinterval, or velocity varies linearly,
v(tn 0.5At) = ^ ~~y (2.25)
and similarly,
v (tn + 0.5At) = (2.26)
Therefore, a constant acceleration between time interval (n0.5At) and (n+0.5At) may
be estimated as:
a(tn 0.5At)
v(tn +0.5At)v(t 0.5At)
(2.27)
Based on, Equations (2.26) and (2.27), the average, minimum, and maximum error of
speed and acceleration estimates are shown in Figure 2.18 and Figure 2.19 for the
case using a 100ft roadway section.
U)
.Q.
+*
C
S
"S
w
a
o
tZ)
u
o
In
W
<
Figure 2.18 Absolute Error of Speed Estimates for Different Video Frame
Processing Intervals, when 100ft Roadway Section is Used in
the Video Image
40
Video Frame Processing Interval (seconds)
Figure 2.19 Absolute Error of Acceleration Estimates for Different Video Frame
Processing Intervals, when 100ft Roadway Section is Used in
the Video Image
The figures (Figure 2.18 and Figure 2.19) show that if video images of 100ft
roadway section are processed every halfsecond, the average absolute error in speed
estimate is 1.64 fps and the average absolute error of the acceleration estimate is 3.28
fps2. Based on the standard error of location reported in Table 2.4, the standard errors
of speed and acceleration estimates are presented in Figure 2.20 and Figure 2.21.
These figures (Figure 2.20and Figure 2.21) show that as the video frame processing
interval increases, the standard error of both speed and acceleration converge to very
low values for different roadway lengths recorded.
41
14
Video Frame Processing Interval (seconds)
Figure 2.20 Standard Error of Speed Estimates for Different Video Frame Processing
Intervals
Video Frame Processing Interval (seconds)
Figure 2.21 Standard Error of Acceleration Estimates for Different Video Frame
Processing Intervals
42
2.3.5 Conclusions
This analysis shows that video recordings of bicycle traffic may provide accurate
estimates of distance traveled, speed, and acceleration. The average errors of bicycle
location, speed, and acceleration are less than 1ft., lfps and 1 fps2 respectively, if a
video camera records traffic scenes of 100fit roadway sections and the video frames
are processed at one second intervals. With up to 200 ft. section of roadway recorded,
the average error of bicycle location, speed, and acceleration is still less than 1 ft, 1
fps, and 1 fps2, respectively, if video frames are processed and analyzed every two
seconds. Also presented are detailed statistics of average error and standard error for
different roadway lengths and frame processing intervals used. As the video frame
processing interval (seconds) increases, the standard error of estimates (e.g. speed,
acceleration) converges. For simplification, the standard error along x and y were
assumed to be the same for error propagation. Therefore the standard error of
estimates of speed and acceleration may be considered the upper bound.
This technique will allow researchers to video record and analyze traffic scenes to
estimate various microscopic and macroscopic traffic flow measures that can then be
used to develop and validate traffic flow models. Very few studies have been
conducted to study bicycle flow characteristics. The data collection technique
presented here should allow researchers to collect bicycle flow data at very low costs.
The technique presented in this study has been applied to several studies (Maini and
Khan 2000; Maini and Khan 2000; Khan and Raksuntom 2001).
2.4 Data Reduction
All types of movements on videotapes were reviewed and captured into an Audio
43
Video Image (AVI) file format using a video capture card. This process breaks the
bicycle movements down to 10 frames per second. Positions of bicycles were
determined from the video images using the Vehicle Videotaping Data Collector
(Wei and Feng 1999). These positions or screen coordinates were converted into
roadway coordinates based on a coordinate transformation technique as discussed in
Section 2.3.
2.4.1 Normal Speed of Bicycles
The normal speed of bicycles were measured over a fixed distance, 50fit, at about
300fit upstream of the intersection where bicycles are not affected by the traffic
signal at the intersection. Each AVI file for traffic scene, further upstream of an
intersection, was viewed frame by frame in a personal computer, and the travel time
of each bicycle over the 50fit distance also recorded. Bicycle speeds were calculated
as distance divided by its travel time.
2.4.2 Speed of Bicycles at Signalized Intersections
Based on the bicycle positions, bicycle speeds within intersection were estimated
every 0.5 second. The signal stage, when bicycle crossed the stop line, was also
recorded.
2.4.3 Rightturning Speeds of Bicycles
In this study, only the rightturning bicycles were analyzed since few leftturning
bicycles were recorded on videotapes during the data collection. The rightturning
speed was measured based on a 30ft of distance traveled, 15 ft before and 15 ft after
the turning point, as illustrated in Figure 2.22. Based on this concept, the travel time
44
of each rightturning bicycle was extracted from the AVI files of traffic scenes
recorded. The data set was also categorized based on the signal stages, as right turns
occur during any signal phase, green, yellow, or red.
Travel Direction
Turning R>ii
.. Turning Route
Figure 2.22 Bicyclist makes a RightTurn at an Intersection
2.4.4 Normal Acceleration and Deceleration Rates
of Bicycles at Normal Speed
Normal acceleration and normal deceleration rates of bicycles are estimated as the
change in bicycle speeds as bicycle travels at its normal or desired speed, without any
interaction with other bicycles or a signal down stream.
2.4.5 Initial Acceleration Rate of Bicycles
Bicycle initial acceleration rate is defined as the rate at which a bicycle accelerates as
it departs an intersection at the start of green phase. Bicycles generally do not stop
behind each other. Instead, they stop next to each other and form more than one
45
queue within a lane. At the start of a green phase, bicycles in front of each queue may
depart an intersection at the same time. Therefore, bicycles in front of the queue were
selected to estimate initial acceleration rates. Based on bicycle positions on the video
frames, bicycle speeds, bicycle acceleration rates, and positions of bicycles from the
stop line were measured every 2.0 seconds.
2.4.6 Bicycle Deceleration Rate at Intersection
Bicycle deceleration rate is estimated as bicycles decelerate to stop at the stop line
during a red/yellow phase. If more than one bicycle arrive an intersection at the same
time, the bicycles in front of the queue were selected as an observation. Based on
bicycle positions on video frames, bicycle speeds, bicycle deceleration rates, and
positions of bicycles from the stop line were measured every 2.0 seconds.
2.4.7 Bicycle Passing Behavior
All passing events on videotapes were identified and captured using a video capture
card to an Audio Video Image (AVI) file format. This process captures the bicycle
movements at 10 frames per second. In this study, positions of bicycles were
extracted from the video images every 5 frames (or 0.5 second) using a video image
processing tool, VEVID (Wei and Feng 1999). These positions or screen coordinates
were transferred into roadway coordinates based on a coordinate transformation
technique described in Section 2.3.
2.4.8 Bicycle Following Behavior
A bicycle is considered to be in the following mode if it follows and responds to the
actions of a lead bicycle without any attempts to make a passing maneuver. All
46
following events on videotapes were identified and captured using a video capture
card to Audio Video Image (AVI) file format. This process captures the bicycle
movements at 10 frames per a second. Then positions of bicycles were extracted from
the video images every 10 frames or at 1second interval. The positions or screen
coordinates were transferred into roadway coordinates based on a coordinate
transformation technique described in Section 2.3.
2.4.9 Bicycle Arrival Distribution
Video recording of traffic scenes for bicycle arrivals captured into an audio video
image format (AVI) using a video capture card at 10 frames per second. The
headways of bicycles were obtained by recording the time each bicycles crossed a
section, about 300 feet upstream of the intersection. Time headway between bicycles
was estimated as the difference between the arrival times of consecutive bicycles.
2.4.10 Gap Acceptance of Motor Vehicles with
a Conflicting Through Moving Bicycle
All events were identified and captured into an audio video image format (AVI) at 10
frames per second. The AVI files were reviewed frame by frame to identify accepted
and rejected gaps.
The objective is to observe gap acceptance of righttuning motor vehicle with a
conflicting through moving bicycle. There are two types of rightturning gaps: (1) a
rightturning motor vehicle and a conflicting through moving bicycle in the same
approach, on an adjacent lane, during a green/yellow phase. This is referred to as a
following gap and is shown in Figure 2.23 (a), and (2) a rightturning vehicle and an
opposing, through moving bicycle, during a red phase. This is referred to as a lateral
47
gap and is as shown in Figure 2.23 (b). To estimate the critical gap for such
conflicts, following gaps are observed during the green or yellow phase and lateral
gaps during the red phase. The following gap in (1) is measured as the difference in
times between when a motor vehicle arrives at the stop line and when a bicycle on the
right lane passes the conflict point. This occurs because the through bicycle has a
right of way over the rightturning motor vehicle during a green phase. The lateral
gap in (2) is measured as the difference in times between when a righttumonred
motor vehicle comes to a complete stop at the stop line and when a bicycle passes the
conflict point. This occurs because the motorist waits for his/her acceptable gap
during a right turn on red.
,'3'J
Right Trnnnf Uatrr
Dninz Grat%m
CirJlkanf Biryh
Ti me Gap (seconds) 
l + l i
(a)
iÂ£j tXvuigml Dmm
Sk Conflicting
Cmci
 Time Gap (seconds*
BtCVCULANE
(b)
(a) following gap during green or yellow phase
(b) lateral gap during red phase
Figure 2.23 Typical RightTurning Gaps
2.4.11 Stopped Distance of Bicycle and Motor Vehicle
Based on the positions of bicycles and motor vehicles at the stop line, lateral and
longitudinal distances between bicycles and motor vehicles are determined. As
mentioned in the data collection section, the distances are categorized into four
groups based on type of stoppeddistances.
48
The four types of the stopped distances were: (1) stopped distance between motor
vehicles and the bicycle lane, (2) stopped distance between bicycles and an adjacent
lane, (3) lateral stopped distance between a pair of bicycles, and (4) longitudinal
stopped distance between a pair of bicycles. These four types of stopped distances are
illustrated in Figure 2.24.
Figure 2.24 Stopped Distances Measured at Intersections
2.4.12 Saturation Flow Rate of Bicycles
All videotapes of traffic scenes at 300 ft upstream of intersections were reviewed and
captured into an audiovideoimage format (AVI) using a video capture card at 10
frames per second. Only the AVI files with at least five bicycles in queue at the stop
line during the red phase were reviewed frame by frame. The headway between
bicycles departing the intersection at the beginning of green phase was measured as
the bicycles crossed the stop line at the intersection. The first headway is the elapsed
49
time, in seconds, between start of the green phase and the crossing of the front wheel
of the first bicycle over the stop line. The second headway is the elapsed time
between the crossing of front wheels of the first and the second bicycles over the stop
line. Subsequent headways were measured similarly.
The data analysis and results based on the data collection techniques discussed in this
chapter will be detailed in the next chapter, Chapter 3. In Chapter 3, a comprehensive
literature review for each bicycle characteristic is also detailed.
50
3. Bicycle Characteristics and Models to Represent
Bicyclist Behavior
As part of this dissertation research, bicycle characteristics and bicyclist behavior are
studied based on data collected from several signalized intersections in Davis
California; and Denver, Boulder and Fort Collins, Colorado. In this chapter, in each
section, a review of the literature, the data analyzed, and the findings relevant to each
characteristic are examined. Several models to represent these characteristics are
developed. The sections also documents the relevant model development and
validation based on field data collected.
3.1 Bicycle Speed
Generally, bicycles are smaller in size and travel at a lower speeds than motor
vehicles. Design variables for traffic control at signalized intersections including the
duration of the yellow phase are a function of the motorvehicle speed. Therefore, the
yellow phase designed based on motorvehicle speeds may be inadequate for bicycles
and result in conflicts between bicycles and motor vehicles at the intersection and
therefore cause a safety hazard. Bicycle speeds are also used to determine the LOS
for a bicycle lane and urban street. The current version of the Highway Capacity
Manual (HCM, 2000) (Transportation Research Board 2000) introduces a
methodology to determine the level of service (LOS) of a signalized intersection for
bicycles based on the uniform delay.
3.1.1 Literature Review
Bicycle speed distributions have been measured by several researchers (Opiela,
51
Snehamay et al. 1980; Botma and Papendrecht 1991; Liu 1991; Hoque 1994; Navin
1994; Taylor 1998; Wei and Feng 1999; Khan and Raksuntom 2001) on different
types of facilities in several countries. In the early 1980s, Opiela at el (Opiela,
Snehamay et al. 1980) observed approach speed of bicycles at seven intersections in
several cities in the US. The study reports that observed bicycle speeds are normally
distributed with a mean speed of 22 fps (24.99 km/h). This study, however, focused
mainly on university campus areas. Thus, the bicyclists were mainly students. A
study in the US (Taylor 1998) measured cruise speed of bicycles from a small group
of volunteers on a city street near an unsignalized intersection in Austin, Texas. The
reported mean cruise speed was 20.68 fjps (22.56 km/hr), but the standard deviation
was not reported. Navin (Navin 1994) studied a relationship between speed and flow
on a 13.12fit (4m) wide bicycle test track with radii of 9.84, 22.95, 39.35, and 52.46
ft (3, 7, 12, and 16 m) in Canada. The study reports that the mean speed of bicycles
reduces by 7% on a radius of 49.18 ft (15 m) or less.
Botma (Botma and Papendrecht 1991) studied bicycle speeds on a shared path used
by bicycles and mopeds in the Netherlands. He found that bicycle speeds are
normally distributed with a mean speed of 17.42 fps (19 km/hr) and remains
unaffected by volume over a large range of flow (50 to 1,500 bicycles per hour). A
recent study (Khan and Raksuntom 2001) conducted on passing maneuvers of
bicycles for an exclusive bicycle path in Denver, Colorado reports mean normal
speed of bicycles to be 22.63 fps (24.84 km/hr). The study also reports bicycle speed
distributions of both passing and passed bicycles during the entire passing maneuver.
The mean speed of the passing bicycles is 24.56 fps (26.97 km/hr) and for passed
bicycles is 16.02 fps (17.59 km/hr) during passing.
Liu (Liu 1991) and Wei (Wei and Feng 1999) measured bicycle speeds on streets in
Beijing, China, while Hoque (Hoque 1994) conducted his study in Bangladesh. The
52
reported mean speeds of bicycles in these three studies were less than 15 fps (16.47
km/hr) which is significantly lower than the reported mean speeds in the US. So far,
no research was found on bicycle turning speed or bicycle speed at signalized
intersection during green and red phases.
3.1.2 Objectives
A few studies have examined bicycle characteristics for onstreet bicycle facilities in
the US. However, these studies are based on a few observations using volunteers in
vacant parking lots or data collected in other countries. Therefore, the reported
bicycle speed distributions may not represent the bicycle population and the types of
bicycles used in the US. The objective is to examine normal speed of bicycles on on
street facilities, for the mix of trip purposes observed in the US. In addition, the
maximum speed of bicycles within an intersection during yellow and green phases,
relationship between normal speed and maximum speed, and bicycle turning speed is
also examined.
During a green phase, a turning bicycle decelerates as it approaches the signalized
intersection before making a turn. Therefore, the rightturning and leftturning
bicycles may experience delay caused by the intersection geometry. This impact may
be determined from the ratio of the turning speed and its normal speed. The study also
includes speed of rightturning bicycles.
3.1.3 Data Analysis and Results
Based on the data collected in four cities in the US, bicycle speeds in this study are
presented in three categories, depending on the type of movements. These are normal
speed, bicycle speed within the intersection during both the green and the yellow
53
phases, and rightturning bicycle speeds during the green/yellow and the red phase.
3.1.3.1 Bicycle Normal Speed, Bicycle Steady Speed, or
Free Flow Speed
Normal speed is defined as the travel speed of a bicycle as it enters a roadway section
and cruises a roadway section at constant or steady speed under low flow conditions.
It was measured at about 300 ft (91.5 m) upstream of the intersection where bicycles
are not affected by the traffic signal at the intersection downstream. As discussed in
Section 3.2, bicyclists start decelerating at a distance less than 100 ft (30.50 m) from
stop line in response to traffic signals. Therefore, bicycle speed at 300ft upstream of
an intersection was measured as normal speed. For all five locations, the bicycle
speeds range from 6.92 fps to 32.13 fps (7.59 to 35.28 km/hr). An analysis of data
shows that bicycle speeds at all locations are normally distributed. The mean normal
speed of bicycles at all intersection is 16.62 fps (18.25 km/hr) with a standard
deviation of 4.99 fps (5.48 km/hr).
The statistical analysis (comparison of means) shows that the mean normal speeds of
bicycles at all locations are significantly different, except the two locations in Davis,
California. The statistical summary is presented in Table 3.1 and the speed
distribution in Figure 3.1.
54
Table 3.1 Statistical Summary of Bicycle Speeds
Location Posted Speed no. of mph km/hr Observations Mean fps km/hr Minimum fps km/hr Maximum fps km/hr Standard Deviation fps km/hr
Sycamore Ln & Russell Blvd1 25 40 277 13.61 14.95 8.01 8.80 23.28 25.57 2.59 2.84
Third St &B St1 25 40 269 13.36 14.67 6.92 7.59 22.45 24.65 3.04 3.34
Marion PkWy & Cedar Ave2 25 40 84 18.95 20.81 8.36 9.18 31.94 35.07 5.27 5.79
Folsom St. & Arapahoe Ave3 30 48 247 20.44 22.44 8.36 9.18 32.13 35.28 4.21 4.62
Harmony Rd & Minor Rd4 40 64 100 22.34 24.52 18.18 19.97 30.06 33.01 2.60 2.86
Total 977 16.62 18.25 6.92 7.59 32.13 35.28 4.99 5.48
1 Davis, California 2 Denver, Colorado 3 Boulder, Colorado 4 Fort Collins, Colorado
The analysis also shows that the standard deviations of speeds at all locations are
significantly different. The ranking of locations based on the mean normal speeds,
from the highest to the lowest speed, is Harmony Road & Minor Road, Folsom Street
& Arapahoe Avenue, Marion Parkway & Cedar Avenue, and the two locations in
Davis. The data collected from these locations also show that 90% of the bicycle
trips in Davis are to school and 10% to work, 70% of the bicycle trips in Boulder are
55
to school and 30% to work, 100% of the bicycle trips in Denver are recreational and
100% of the bicycle trips in Fort Collins are to work. Therefore, the types of trips or
bicyclists have an effect on both the mean and standard deviation of the normal speed
of bicycles. This is more clearly shown in the data from Boulder and Davis both
near university campus with a different mix of bicyclists. The mean normal speeds of
bicycles for recreational and work trips are higher than for school trips. The
recreational trips, however, show the highest variation of bicycle speeds.
3.1.3.2 Maximum Speed of Bicycle within an Intersection
Area
Normally bicyclists accelerate as they cross an intersection during the green or the
yellow phase before the signal changes to the red phase. The data collected every
halfsecond includes both the speed and location of bicycles within intersection
during the green and the yellow phases. At the intersection at Third Street and B
Street, 36 and 22 bicyclists were observed during the green and the yellow phases
respectively. Another 47 and 21 bicyclists were observed, at the intersection between
Folsom Street and Arapahoe Avenue, during the green and the yellow phases
respectively.
A paired ttest performed on the data collected from the two locations in Davis and
Boulder shows that the maximum bicycle speed within the intersection area is
statistically significantly higher than the normal speed, and the results are presented
in Table 3.2. This suggests that bicyclists accelerate to cross the intersection area
before the signal indication changes to the red phase. After a bicyclist reaches his/her
maximum speed, he/she decelerates to return to his/her normal speed.
56
Table 3.2 A Comparison of Mean Speeds (paired ttest) of Through Bicycles
B St & Third St: 50ft wide intersection Folsom St & Arapahoe Ave: 100ft wide intersection
Maximum Speed Normal Speed Maximum Speed Normal Speed
Mean 25.78 15.30 29.40 21.20
Variance 21.49 5.49 21.43 14.98
Observations 58 58 68 68
Pearson Correlation 0.72 0.81
Hypothesized Mean Difference 0.00 0.00
df 57 67
tStat 23.67 25.06
P(T<=t) twotail <0.001 <0.001
t Critical twotail 2.00 2.00
Further analysis is conducted to test the hypothesis that the maximum speeds of
bicycles during the green and the yellow phases are significantly different. Since the
mean normal speed of bicycles are different for the two locations, a comparison of the
mean of the ratio of a bicyclists maximum speed within an intersection area and
his/her normal speed during the green and the yellow phases is conducted, expressed
as follows:
1 N
Rvo T7S
N i=1
V
K,
J Green Phase
(3.1)
1 N
^=T7l
N
V n>' J Yellow Phase
where,
Rra = mean of speed ratio for through bicycles during the green phase
Ryy = mean of speed ratio for through bicycles during the yellow phase
Vmax ( = maximun speed of ith bicycle within the intersection area (fps)
F' = normal speed of ith bicycle (fps)
N = number of observations
(3.2)
57
This analysis presented in Table 3.3 shows that the mean speed ratios of bicycles
during the green and the yellow phases are not significantly different at both
locations. The analysis presented in Table 3.4 suggests that the mean speed ratios are
significantly lower at a wider intersection during both the green and the yellow
phases. Table 3.4 also shows that irrespective of phasing, comparing the 50ft and the
100ft wide intersections, on average, bicyclists increase their speeds by 70 and 40
percent, respectively. Therefore, the rate of increase of bicycle speed or the average
acceleration rate is higher at the narrower intersection.
Table 3.3 A Comparison of Mean Speed Ratios of Through Bicycles during the
Yellow and Green Phases
At B St & Third St: 50ft wide intersection Folsom St & Arapahoe Ave: 100ft wide intersection
speed ratios during yellow phase speed ratios during green phase speed ratios during yellow phase speed ratios during green phase
Mean 1.71 1.68 1.45 1.38
Variance 0.04 0.06 0.02 0.02
Observations 22 36 21 47
Hypothesized Mean Difference 0.00 0.00
df 49 40
t Stat 0.46 1.90
P(T<=t) twotail 0.65 0.06
t Critical twotail 2.01 2.02
Table 3.4 A Comparison of Mean Speed Ratios of Through Bicycles for Different
Intersection Widths
B St & Third St: Folsom St & Arapahoe Ave:
50ft wide intersection 100ft wide intersection
Mean 1.69 1.40
Variance 0.05 0.02
Observations 58 68
Hypothesized Mean Difference 0.00
df 97
t Stat 8.41
P(T<=t) twotail <0.001
t Critical twotail 1.98
58
Analysis is also conducted on the location that bicyclists achieve their maximum
speeds. Since the widths of intersections are different for the two locations, a
comparison of the mean of the ratio of the distance between the stop line and the
location the maximum speed is achieved and the intersection width during the green
and the yellow phases is conducted, expressed as follows:
R
DG
t
Nm
( D_
W
J Green Phase
(33)
1 N
Ror=Z
N i=l
D
max,
1V
J Yellow Phase
where,
Rm = mean of distance ratio during the green phase
Rm = mean of distance ratio during yellow phase
Dmax= distance between stop line and the location
that maximum speed is achieve of bicycle ith (ft)
W = width of an intersection (ft)
N = number of observations
(3.4)
A paired ttest of mean of the distance ratio during the green and the yellow phases is
presented in Table 3.5. Table 3.5 shows that the distance ratios are not significantly
different for both the 50ft and 100ft wide intersections. Table 3.6 shows that for the
50fit and 100ft wide intersections, on average, bicyclists achieve their maximum
speeds at 35 and 60 feet from the stop line, respectively. Moreover, the mean of
distance ratios is significantly higher at the narrower intersection than the wider
intersection.
59
Table 3.5 A Comparison of the Mean of Distance Ratios during the Yellow and
the Green Phases
AtBSt& Third St: 50ft wide intersection At Folsom St & Arapahoe Ave: 100ft wide intersection
speed ratios during yellow phase speed ratios during green phase speed ratios duringyellow phase speed ratios during green phase
Mean 0.74 0.70 0.56 0.61
Variance 0.01 0.01 0.02 0.03
Observations 22 36 21 47
Hypothesized Mean Difference 0.00 0.00
df 45 44
t Stat 1.47 1.42
P(T<=t) twotail 0.15 0.16
t Critical twotail 2.01 2.02
Table 3.6 A Comparison of the Mean of Distance Ratios for 100ft and 50ft Wide
Intersections
B St & Third St: Folsom St & Arapahoe Ave:
50ft wide intersection 100ft wide intersection
Mean 0.72 0.59
Variance 0.01 0.03
Observations 58 68
Hypothesized Mean Difference 0.00
df 121
t Stat 5.05
P(T<=t) twotail <0.001
t Critical twotail 1.98
An analysis is also conducted to examine the relationship between maximum speed
and normal speed of a bicyclist. Since the speed ratios during the green and the
yellow phases are not significantly different for the 50ft and 100ft wide
intersections, bicycle speeds during both the phases at each location are combined.
The analysis shows that the maximum speed and the normal speed of bicyclists are
positively correlated for both 50ft and 100ft wide intersections. The linear
correlation between the maximum speed and normal speed at the 50ft and 100ft
wide intersections were 0.72 and 0.81 respectively. The relationship between normal
60
speeds and maximum speeds (with a zero intercept) within an intersection area of
bicycles may be expressed as:
for a 50ft wide intersection:
V r or V = 1.68V
mcrc_G max_Y n
; for 10
(3.5)
p value : 0.00
andR2 =0.50
for a 100ft wide intersection:
V r or V = 1.38V
max_G maxY n
p value: 0.00 and R1 =0.55
; for 10< Vn < 30
(3.6)
where,
Vmax q = maximum speed of bicycle within the intersection
during the green phase (fps)
V,ax y = maximum speed of bicycle within the intersection
during the yellow phase (fps)
Vn = normal speed of bicycle (fps)
3.1.3.3 Bicycle Turning Speed
Bicycle turning speed is defined as the speed of bicycle as it makes a turn at an
intersection. A bicyclist may make a right or left turn, depending on his/her
destination. Since a bicyclist may make a rightturn at the intersection during a green,
yellow, or red phase, the effects of signal stages are also investigated. In this study,
only rightturning bicycles were analyzed because very few observations of left
turning bicycles were available. The rightturning speed was measured based on the
fixed distance of 30 ft traveled as discussed in Chapter 2, Section 2.4.3. The data set
for analyzing turning speeds includes 43 bicycles during the red, yellow and green
phases.
61
Bicycle turning speeds are estimated for the red phase and the green or yellow phase.
A comparison of the mean of speed ratio of the turning speed and the normal speed of
bicycles during the red and the green or yellow phase was conducted using a ttest.
The mean of the speed ratios may be expressed as:
1 N
RTvc=Yr Z
N '=1
V
v RT,i
V
v y.i /
Green/Yellow Phase
(3.7)
1 N
N i=1
VD,
v .
\ /RedPhase
(3.8)
where,
RTvg = mean of speed ratios during the green/yellow phase
RTvr = mean of speed ratios during the red phase
VRr i = right turn speed of the ithbicycle (fps)
VH t = normal speed of the ithbicycle (fps)
N = number of observations
The analytical summary presented in Table 3.7 shows that the mean of speed ratios
during the red phase is significantly lower than the mean of speed ratios during the
green or the yellow phase for rightturning bicycles. In addition, on average, the right
turning speed of bicycles during red and green/yellow phases are about 68% and 78%
of the normal speed respectively.
62
Table 3.7 Comparison of the Speed Ratios for RightTurning Bicycles during the
Red and Green/Yellow Phases
Speed Ratio During Red Phase Speed Ratio During Green/Yellow Phase
Mean 0.68 0.78
Variance 0.01 0.01
Observations 21 23
Hypothesized Mean Difference 0.00
df 40
t Stat 3.21
P(T<=t) twotail 0.003
t Critical twotail 2.02
Further analysis shows that there is a significant relationship between rightturning
and normal speed of bicycles. The linear correlations between the rightturning speed
and the normal speed of bicycles are 0.64 and 0.88 during the red and the
green/yellow phases, respectively. The relationship between the turning speeds and
normal speeds (with a zero intercept) of bicycles may be expressed as:
y =n ygy
' RT GY XJ'/yYn
(p.values: 0.00
; for 12
andR2 =0.78)
(3.9)
VRTR = 0.65V
(p. values: 0.00,
; for 12
andR2 =0.22)
(3.10)
where,
VRT GY = bicycle right turn speed during green or yellow phases (fps)
Vrtr = bicycle right turning speed during red phase (fps)
V, = normal speed of bicycle (fps)
63
3.2 Acceleration and Deceleration of Bicycles at
Signalized Intersections
The bicycle deceleration model and the acceleration model presented here represent
the behavior of bicyclists as they approach and stop at a signalized intersection during
the red or yellow phase and as they depart an intersection at the start of a green phase.
Bicycle speeds, deceleration rates, and initial acceleration rates vary between
bicyclists.
The recent Highway Capacity Manual (HCM 2000) (Transportation Research Board
2000) introduces a procedure to evaluate the level of service (LOS) of a designated
onstreet bicycle lane at signalized intersections. The measure of effectiveness is
control delay and estimated based on the Websters uniform delay for motor vehicles
at signalized intersection. It assumes no overflow delay for bicycles for onstreet
bicycle lanes. According to the HCM, bicyclists will not normally accept an overflow
situation and will select alternate routes to avoid the excessive delay. In addition,
since bicycle volume on any onstreet bicycle lane is very low compared to the
capacity of bicycle lanes, bicycles in queue during a red phase clear the intersection
during the subsequent green phase. However, the bicycle delay estimated based on
the HCM methods does not include delay due to acceleration/deceleration. This delay
may be calculated based on the deceleration and initial acceleration models presented
in this dissertation. The deceleration and initial acceleration models may not only be
used to improve the delay estimates of the HCM procedure, but also to represent
acceleration and deceleration of bicycles in a microscopic simulation model.
3.2.1 Literature Review
A review of the literature (Taylor and Davis 1999) shows that very limited studies
have been conducted to examine the performance of bicycles on roadways.
64
Acceleration and deceleration rates of bicycles have been reported by several
researchers. They are reported in three categories: initial, normal and maximum rates.
As part of a doctoral dissertation research, Taylor (Taylor 1998) measured the
comfortable acceleration and deceleration rates under normal conditions for 12
volunteer bicyclists traveling at cruise speed in a city street in Austin, Texas. The
reported mean acceleration and deceleration rates are 3.8 fps (1.16m/s) and 7.5
fps (2.63 m/s ), respectively. Another study (Forester 1994) reported maximum
deceleration rate of bicycles based on the friction between tires and the pavement as
16.07 fps2 (4.9 m/s2).
Based on a few observations of data collected in two cities in India, Maini (Maini and
Khan 2000) reports mean initial acceleration and normal deceleration rates of 2.03
fps2 (0.62 m/s2) and 2.89 fps2 (0.88 m/s2), respectively for bicycles. Another study,
conducted in Bangladesh (Hoque 1994), recorded 2.78 fps2 (0.85 m/s2) as initial
acceleration rate, 2.78 fps (0.85 m/s ) as the normal deceleration rate, and 9.21
fps2 (2.81m/s2) as the maximum deceleration rate for bicycles.
3.2.2 Objective
The studies in the literature to date (Taylor 1998) report average initial acceleration
and deceleration rates for a group of bicycles. However, this dissertation has shown
that the initial acceleration and deceleration rates of bicyclists may vary based on
their normal speed. In addition, the initial acceleration and deceleration rates may also
depend on the width of an intersection. Therefore, the initial acceleration and
deceleration rates reported in the literature do not represent the variation in
acceleration and deceleration rates for bicycles at signalized intersections due to these
factors.
65
The main objective of this study is to present the findings of a study to examine the
acceleration and deceleration characteristics of bicyclists at signalized intersections;
and an initial acceleration and deceleration model developed to represent these
characteristics in a microscopic traffic simulation model. The results presented are
based on data collected from several intersections in two cities in the US.
Additionally, bicycle speed distribution, the distance to stop line as bicyclist make a
decision to stop, and the distance traveled as bicyclists achieve their normal speed
after crossing the stop line or the acceleration distance to achieve normal speed are
also presented.
3.2.3 Data Analysis and Model Development
Analysis of the data shows that acceleration and deceleration rates of bicycles at an
intersection are functions of the characteristics of a bicyclist, and the intersection
geometry. The following sections present the findings of this: (1) behavior of
bicyclists decelerating to stop at signalized intersections, and (2) behavior of
bicyclists accelerating to depart signalized intersections.
3.2.3.1 Behavior of Bicyclists Decelerating to Stop at
a Signalized Intersection
Based on the bicycle trajectory data collected every two seconds, as bicycles
approach an intersection to stop, several aspects of bicyclist behavior are studied.
These aspects include: a bicyclists decision to decelerate to stop during the red
phase, effect of the characteristics of a bicyclist or normal speed on its deceleration
rate, the rate of change of deceleration with respect to distance and a deceleration
model based on vehicle kinematic and the behavior of bicyclists to represent
deceleration of bicyclists as they approach and come to a complete stop at an
66
intersection during a red phase.
3.2.3.1.1 Decision to Stop
A nonmotorized bicycle uses human power as moving energy. The force from
peddling is transferred to a rear wheel to move a bicycle forward. The speed of a
bicycle is a function of the peddling rate or cadence. Therefore, a bicyclist is usually
unable to maintain a constant speed since it is difficult for a bicyclist to maintain a
constant rate of peddling. As discussed in Section 3.4.3.1, bicyclists apply
acceleration or deceleration rates while traveling at the normal speed. The reported
acceleration and deceleration rates range from 2.67 to +2.89 fps2 (0.81 to +0.62
m/s2). During a yellow or red phase, as a bicyclist approaches a signalized
intersection at a certain distance from the stop line, he/she makes a decision to stop
and bicycle speed decreases as it approaches the stop line at an intersection. The
relationship between bicycle speeds and the distance from the stop line is illustrated
in Figure 3.2.
40
35
30
/S
25 Â§
9
&>
u
Q,
20 #
2m
15 Â£
10
5
0
180 160 140 120 100 80 60 40 20 0
Distance To Stop Line (ft)
Figure 3.2 Bicycle Speeds and Distance to the Stop Line for All Locations
67
Figure 3.2 suggests that bicyclists start decreasing their speeds approximately 100
feet upstream of the stop line. A statistical analysis was performed to test this
hypothesis. For bicycles within 100 ft and upstream of 100 ft from the stop line, the
mean of the speed ratio or the normalized speeds of bicycles, expressed in Equation
(3.11), were compared to a common reference value (1.0). A summary of the
statistics is presented in Table 3.8.
1 n
^,=1
N >=1
v K Ji
where,
Vr = mean speed ratio
Vx = bicycle speed at X ft to the stop line (fps)
Vn = normal bicycle speed (fps)
N = number of observations
(3.11)
Table 3.8 Test of Normal Speed for Bicycles in the Deceleration Mode
Mean Standard Deviation Number of Data Points Standard Error Reference tvalue df P value
Less than 100 ft to the stop line 0.675 0.289 2281 0.006 1.000 53.79 2280 <0.001
Farther than 100 ft to the stop line 1.002 0.037 700 0.001 1.000 1.37 699 0.170
The analysis presented in Table 3.8 shows that mean of the speed ratios of bicycles
upstream of 100 feet to the stop line is not significantly different than 1.0. However,
the mean speed ratio for bicycles within 100 ft of the intersection is significantly
different than 1.0. Therefore, this analysis supports the hypothesis that a bicyclist
starts applying a deceleration rate when he/she approaches a distance of 100 feet to
the stop line.
68
3.2.3.1.2 Normal Speed and Deceleration Rate
Data for bicycle movement were collected not only from various locations, but also
for a diverse group of bicyclists. Their deceleration rates vary significantly. Figure
3.2 clearly shows that bicycle speed decreases as it approaches the stop line at an
intersection. The rate of decrease in speed depends on bicycle normal speed and
distance from the stop line. Thus, statistical analysis were conducted to test whether
deceleration rates were significantly different across locations or based on normal
speeds. To examine the affect of normal speed on the deceleration rate, the speed of
bicycles is normalized and the rate of change of the speed ratio (or normalized speed)
with respect to distance from the stop line is evaluated as follows:
(3.12)
where,
Vn = ratio of speed ratio with respect to distance to the stop line (ft"1)
Vx = bicycle speed at X ft to the stop line (fps)
Vn = normal bicycle speed (fps)
The t test and the analysis of variances presented in Table 3.9 reveals that the
average normalized speed or speed ratio with respect to distance to the stop line (Vrx)
at all three locations are not significantly different (at a=0.2T). This suggests that the
deceleration rate of bicycles at a signalized intersection depends on its normal speed
and distance to the stop line.
69
Table 3.9 Analysis of Variance of Speed Ratio With Respect to Distance to the
Stop Line
Groups Count Average (ft') Variance (ft'2)
Folsom St & Arapahoe Ave1: 100ft wide intersection 163 0.035 0.001
Sycamore Ln & Russell Blvd2: 50ft wide intersection 1601 0.037 0.001
B St & Third St2: 50ft wide intersection 517 0.039 0.001
ANOVA
Source of Variation SS df MS F Pvalue F critical
Between Groups Within Groups 0.003 2.509 2 2278 0.002 0.001 1.56 0.21 3.00
Total 2.513 2280
1 2
Boulder, Colorado Davis, California
3.2.3.1.3 Deceleration Rate of Bicycles Approaching an
Intersection
A model to represent the behavior of bicyclists as they approaching an intersection
was developed based on the relationship between normal speed of bicycles and the
distance from the stop line. A total of 429 bicyclists were observed at the three
intersections as discussed earlier. Approximately, 60 percent of these observations
were randomly selected to develop and calibrate a model, and the remaining
observations were used to validate the model.
As discussed in the previous section, a bicyclist decides to stop or initiates
deceleration at about 100 ft from the stop line. In other words, a bicycle at a distance
upstream of 100 ft from the stop line travels at its normal speed, begins to reduce its
speed as it arrives within 100ft of the stop line and comes to a complete stop at the
stop line. The data also shows that the relationship between bicycle speeds and
distances to the stop line is nonlinear as illustrated in Figure 3.2 and may be
represented as shown in Figure 3.3.
70
Travel Direction
Figure 3.3 Deceleration Model for Bicycles at a Signalized Intersection
As illustrated in Figure 3.3, the deceleration model may be developed using a
generalized linear modeling (GLM). Under a generalized linear modeling (GLM)
framework, the mean response is,
g(M) = P.+tfi* (313)
/=1
where,
g(ju) = monotonic differentiable link function
x = a fixed known vector of explanatory variables
J3:, ft, = vector of unknown parameters
71
The generalized linear modeling framework assumes that the observations are
independent. However, as bicycle trajectory data collected every two seconds for
each bicycle is used to develop the model, the assumption of independence of
observations is violated because measurements are repeated on the same subject
across time thus forming clusters of correlated observations. Consequently, there is
a need to account for the correlation among observations. Therefore, a generalized
linear model was developed based on the quasilikelihood estimation method, also
known as Generalized Estimating Equation (Liang and Zeger 1986; Zeger and Liang
1986). This technique is used to represent correlation between measurements on the
same subject. Therefore, the recently introduced generalized estimating equations
using quasilikelihood method is used to account for the correlation structure between
observations in the GLM. The Generalized Estimating Equation procedure may be
described as follows:
tVi tli
Let Yjj,j=l,...i = 1,... ,K represent the j measurement on the i subject. There
are nt measurements on subject i and total number of measurements, N, is estimated
as:
K
I>; (3.14)
;=l
Correlated data are modeled using the same link function and linear predictors
(systematic component) as the independence case. The random component is also
described by the same variance functions as in the independence case, but the
covariance structure of the correlated measurements must also be modeled. Let the
vector of measurements on the z'th subject be Y with corresponding vector of means pi\
, Vi be the covariance matrix of Yj, and Xy be the vector of independent, or
explanatory, variables for the/h measurement on the z'th. These vectors may be
represented as:
72
Y,=[yn> yj
Xy=[Xm,
V^^Rf^A)'2
where,
4 = ann. x. diagonal matrix with v ()
as the j,h diagonal element
R. (a) = an n. xn, working correlation matrix
= dispersion parameter
(3.15)
(3.16)
(3.17)
(3.18)
The working correlation matrix is unknown and must be estimated. It is estimated in
the iterative fitting process using the current value of the parameter vector /? to
compute appropriate functions of the Pearson residual. This residual, ey, is estimated
as follows:
eu
(3.19)
Based on the data collected for this study, the structure of the working correlation
matrix is known as Autoregressive (AR)\ The Autoregressive assumes that adjacent
correlations are higher in magnitude than nonadjacent ones. The relationship is given
by:
Corr (y.., yiJ+J) = a for t = 0, 1, 2, .... nH
1 A
a =
(iCj ~p)(j>
j'+>
(3.20)
(3.21)
73
(3.22)
And the dispersion parameter in Generalized Estimating Equation is estimated as:
A
(/> =
1
Np
(3.23)
where,
N = total number of measurements
p number of regression parameters
The Generalized Estimating Equation of Liang and Zeger (Liang and Zeger 1986) for
estimating the p x 1 vector of regression parameters /? is an extension of the
independence estimating equation to correlated data and is given by:
X
/=1
dp '
(r,n{P))
= 0
(3.24)
Since,
s(mv) = x,P
(3.25)
where,
g = link function
The p xrii matrix of partial derivatives of mean with respect to the regression
parameters for the z'th subject is:
dp
*711 ^,1
s'K)
Xil p XiiP
s'M
(3.26)
74
The iterative procedure for fitting a model using the Generalized Estimating Equation
is as follows:
Step 1: An initial estimate of P is computed with an ordinary generalized linear model
assuming independence.
Step 2: The working correlations R is computed based on the standardized residuals,
the current p, and the assumed structure of R.
Step 3: An estimate of the covariance is computed using Equation (3.18).
Step 4: P is updated using the following equation:
Pr+\ ~Pr +
f. dp 8a
kdp dp
(3.27)
Step 5: Steps 24 are repeated until convergence.
The Generalized Estimating Equation, as described above, is utilized in model
development. The goodnessoffit for the deceleration model of bicycles is presented
in Table 3.10.
Table 3.10 GoodnessofFit Measures for the Deceleration Model
Criteria For Assessing Goodness of Fit
Criterion DF Value Value/DF
Deviance 1085 1598.42 1.47
Scaled Deviance 1085 1086.00 1.00
Pearson ChiSquare 1085 1598.42 1.47
Scaled Pearson Chi Square 1085 1086.00 1.00
Log Likelihood 2014.68
Analysis of GEE Parameter Estimates: Empirical Standard Error Estimates
Parameter Estimate Error Standard 95% Confidence Limits Z Pr>]Z
Intercept 0 0 0 0
v x/3 0.216 0.002 0.219 0.227 115.76 <.0001
Vn = normal speed of bicycles (fps)
X = distance between bicycle and the stop line (ft)
75
The goodnessoffit criteria and the standard error on the parameter estimates
presented in Table 3.10 shows that the deceleration rate of a bicycle may be
represented as a function of the product of its normal speed and distance to the stop
line. The goodnessoffit measures also suggest a good fit, with low overdispersion
(ratio of value of the Deviance and degrees of freedom close to 1, ratio of value of the
Pearson ChiSquare and degrees of freedom close to 1). The empirical variance
covariance matrix is close to the modelbased variancecovariance for the most part.
In addition, standard errors and the pvalues of the estimated parameters show that the
predictors are significant at a=0.0001. As a result, the deceleration model may be
expressed as:
Vx = 0.216(X),/3 ;forX>100ft (3.28)
where,
Vx = bicycle speed at distance X to the stop line (fps)
Vn = normal bicycle speed (fps)
X = distance to the stop line (ft)
3.2.3.1.4 Deceleration Model of Bicycles Approaching
a Signalized Intersection
The deceleration model presented in (3.28) is developed based on the relationship
between bicycle speeds and distances from/to the stop line. It is difficult to implement
this model in an intervalbased microscopic traffic simulation. Therefore, its
corresponding deceleration model is developed as a function of time and distance.
Based on Equation (3.28), the relationship between bicycle speeds and distance to the
stop line is expressed as:
76
;for100
Since,
Or,
v.= 0.216 V.ixf
dX
dt
= V
< * dX x
)dt= J = J
0 100 V 100
dX
0.216 Vn(X)J/J
Hence,
21.S4]
(3.29)
The distance to the stop line (X) in Equation (3.29) may be rewritten as a function of
time (t) as follows:
m
X(t) = 
tV
+21.54
6.94
(3.30)
The first derivative of X(t), bicycle speed at time t, V(t), may be expressed as:
V(t) = = 0.216 V
dt
tV
'+21.54
6.94
y/2
(3.31)
The second derivative of X(t), bicycle deceleration rate at time t, a(t), may be
expressed as:
1++2U4
6.94
(3.32)
Based on Equations (3.29) to (3.32), the relationship between bicycle speed,
deceleration and distance or time to reach the stop line with respect to distance and
time is illustrated in Figure 3.4 for bicycles with normal speed of 10, 20 and 30 fps.
77
(e) (Q
Figure 3.4 Relationship between Distance to the Stop Line, Bicycle Speed, and
Bicycle Deceleration Rate
Figure 3.4 (a) shows that the deceleration rate bicyclists apply as they decide to stop
depends on its normal speed. Bicycles with a higher normal speed apply a higher
deceleration rate than bicycle with a lower normal speed. Figure 3.4 (e) shows that
bicyclists apply their highest deceleration rates approximately 10 ft from the stop line.
Additionally, bicyclists with a higher normal speed come to a complete stop at the
stop line faster than the bicyclists with a lower normal speed. In other words,
78
bicyclists with a higher normal speed also apply a higher deceleration rate than
bicyclists with a lower normal speed.
3.2.3.1.5 Model Validation
The deceleration model is validated based on 1,207 data points from 172 observations
not used in model development. The relationship between the predicted and observed
speeds has a slope of 0.94 with R of 0.91, without an intercept. It implies that the
predicted speeds from the deceleration model represent the observed speeds well in
the validation data set.
3.2.3.2 Behavior of Bicyclists Accelerating to Depart
a Signalized Intersection
This section presents the findings of an analysis of the variation of bicyclist behavior
as they depart an intersection based on the geometry of the intersection and their
characteristics. The initial acceleration model represents the behavior of bicyclists as
they accelerate to depart an intersection at the start of green phase.
3.2.3.2.1 Intersection Width and Acceleration Rate
Data was collected from two locations with different intersection widths. Initial
acceleration rates were expected to vary based on the width of the intersection. This
hypothesis was tested based on a data collected from: (1) 50fit wide intersection
between B Street and Third Street in Davis California and (2) 100fit wide intersection
between Folsom Street and Arapahoe Avenue in Boulder, Colorado. The relationship
between bicycle speed and distance from the stop line is illustrated in Figure 3.5 (a)
and (b) for the intersections in Davis, California and Boulder, Colorado respectively.
79
The plots clearly illustrate that the relationship between bicycle speed and the
distances from the intersection for both locations is different.
(a) (b)
Figure 3.5 Bicycle Speeds and Distances from the Stop Line of Bicycles at
Signalized Intersections, (a) Third St. & B St.: 50ft wide intersection
and (b) Folsom Ave. & Arapahoe St.: 100fit wide intersection
For the 50fit wide intersection in Davis, bicyclists reach their normal speed at the end
of the intersection or after they cross the intersection although they achieve speeds
higher than their normal speeds within the intersection area. However, for the 100ft
wide intersection, bicyclists reach their normal speed before crossing the full width of
the intersection.
One may argue that in order to reach the normal speed, a bicyclist with a higher
normal speed travels a greater distance than the one with a lower normal speed. The
data collected shows that the average speed is significantly higher at the Boulder
location; therefore a bicycle at this location is expected to travel a greater distance to
reach its normal speed. This study, however, shows that bicyclists for both locations
with the same normal speed, says 15 fps, reaches their normal speeds at different
distances. Additionally, the bicyclists at the wider intersection (100ft wide) do not
achieve speeds higher than their normal speed. Based on these observations, an
80
acceleration model for bicycles as a function of bicycle normal speeds, and
intersection widths is examined.
3.2.3.2.2 Acceleration Distance to Normal Speed
The acceleration distance, or the distance a bicyclist travels to achieve its normal
speed, is measured from the stop line to the location a bicyclist reaches his/her normal
or desired speed. Figure 3.5 clearly shows that the acceleration distance for a 50ft
wide and a 100ft wide intersection is a function of its width. A statistical analysis
was performed to test this hypothesis. The mean speed ratio of a bicycle speed and its
normal speed were compared to a common reference value (1.0). The analysis
presented in Table 3.11 suggests that, for a 100ft wide intersection, bicyclists reach
their normal speed downstream of 90 feet from the stop line and for a 50ft wide
intersection downstream of 50 feet from the stop line.
Table 3.11 Speed Ratio of Bicycles Accelerating at a Signalized Intersection
Mean Standard Deviation No. of Points Standard Error Reference tvalue df PValue
Folsom Street and Arapahoe Avenue1: 100ft wide intersection within 90 ft downstream of the intersection 0.552 0.310 215 0.021 1.000 21.17 214 <0.001
greater than 90 ft downstream of the intersection 0.995 0.086 106 0.008 1.000 0.589 105 0.557
B Street and Third Street2: 50ft wide intersection within 50 ft downstream of the intersection 0.903 0.399 221 0.027 1.000 3.626 220 <0.001
greater than 50 ft downstream of the intersection 1.023 0.107 45 0.016 1.000 1.460 44 0.151
'Boulder, Colorado 2Davis, California
3.2.3.2.3 Initial Acceleration of Bicycles Departing
a Signalized Intersection
This section presents a bicycle acceleration model developed to represent bicyclist
behavior as they accelerate to achieve normal speeds at an intersection. The model is
developed representing the relationship between bicycle speeds and the distance from
81
the stop line. Based on the differences in bicyclist behavior as a function of both their
normal speed and intersection geometry discussed in the previous section, two
acceleration models were developed: (1) for a 100ft wide intersection and (2) for a
50ft wide intersection.
1) Acceleration Model for a 100ft Wide Intersection
A total of 52 bicyclists were observed at the intersection between Folsom Street and
Arapahoe Avenue. Sixty percent of the observations were randomly selected to
develop the model, and the remaining observations were used to validate the model.
As discussed in the previous section, a bicyclist departs an intersection at the start of
green phase and reaches his/her normal or desired speed at a distance of 90 ft from
the stop line. Furthermore, the relationship between bicycle speed and distance from
the stop line is nonlinear and may be represented as shown in Figure 3.6.
h
100 feet
Figure 3.6 Acceleration Model for a 100ft Wide Intersection
82
