The Dissertation Committee for Nguyen Xuan Long Certifies that this is theapproved version of the following dissertation:

A Concept of Safety Space for Describing Non-lane-based
Movements of Motorcycles

Committee:
Shinya Hanaoka, Supervisor
Associate Professor
Manabu Kanda
Professor
Kunio Takahashi
Associate Professor
Yasuo Asakura
Professor
Daisuke Fukuda
Associate Professor
Tetsuo Shimizu
Professor, Tokyo Metropolitan University

A Concept of Safety Space for Describing Non-lane-based
Movements of Motorcycles

by
NGUYEN XUAN LONG

Dissertation
Presented to the Department of International Development Engineering
Tokyo Institute of Technology in Partial Fulfillmentof the Requirements for the Degree ofDoctor of Philosophy

Tokyo Institute of Technology
September 2012

Acknowledgements

I would like to express my heartfelt gratitude to my supervisor, Associate
Professor, Shinya Hanaoka. His full support enabled me to work on my favorite topic
under a perfect research environment. I also appreciate his warm encouragement which
helped me overcome many difficulties and anxieties during my research activities. In
addition, his trust in me was a great motivation for me to finish my PhD research in three
years.
I would like to thank JGC-S Scholarship Foundation and Kubota Foundation for
their financial support.
I would like to send my deep appreciation to the committee members, Professor
Yasuo Asakura, Professor Manabu Kanda, Professor Tetsuo Shimizu, Associate
Professor Daisuke Fukuda, Associate Professor Kunio Takahashi for their valuablecomments and suggestions.
Great thanks go to Doctor Kawasaki Tomoya, Doctor Tzu-Chang Lee, and Doctor
Vu Anh Tuan for their useful advices on my research progress, and my lab-friends fortheir support and friendship that gave me happy memories.
Sincere thanks also go to my family in Vietnam who supported me all the timeand my friends who kept in touch and shared emotions with me during the time I lived
away from my country.

iii

ABSTRACTThe motorcycle is the main transport mode for commuters in Vietnam owing to
its lower cost and higher mobility compared to the car when running on congested city
roads. A better understanding of the characteristics of the motorcycle traffic flow can bevery helpful in formulating proposals for traffic management policies.
The basic difference between the car and the motorcycle is in their movement.
The former is lane-based, whereas the latter is non-lane-based. Under congested
conditions, cars tend to stay in a single lane, while a motorcycle often swerves to the rightor left without following a lane; making the interactions in the longitudinal direction
between cars the important concern and interactions in both longitudinal and lateral
directions the important concern for motorcycles. Thus, this study was conducted toinvestigate the effects of the zigzag movements of motorcycles on issues of traffic
congestion and traffic safety as detailed below:
Firstly, the study researched the characteristics of non-lane-based movements
considering the effect of the lead motorcycles’ velocity changes on the two behaviors of a
subject motorcycle: acceleration and deceleration. A concept of safety space wasintroduced to describe the changes of these behaviors in response to the safety level ofthe safety space which boundary is determined by the influence of other motorcycles.
Secondly, models based on the proposed safety space concept was developed andcalibrated using data extracted from video clips taken at road segments in Ho Chi Minh
City, Vietnam. Non-linear regression analysis was used for calibration. The model was
validated by calculating the root-mean-square error of both estimated and actual fieldvalue, which consequently showed that the model reproduced good values of motorcycle
speed and direction.

iv

Thirdly, the research developed a microscopic simulator to further verify the
zigzag movements of motorcycles. The simulation program was written in the C
language and run under the Linux operating system. The calculation process combines
two different models (1) a free acceleration model for describing the acceleration
behavior to achieve free speed when no influential motorcycle is running in front of a
subject motorcycle and (2) the proposed non-lane-based model for describing the
behaviors of acceleration or deceleration when influential motorcycles exist. The
computer simulation was used to reproduce two basic types of non-lane-based
movements, namely, oblique following and swerving movement and to verify thedifference in the fundamental diagrams between lane-based and non-lane-based
movements.
Fourthly, the study aims to investigate the characteristics of the mixed traffic flowthat affect traffic safety, also applying the concept of safety space. The research questions
are formulated as: (1) how long is the safety distances that the car and the motorcycle
keep with their surrounding vehicles, (2) how the safety distances differ when theinfluential vehicle ahead is a car or a motorcycle. The parameters were also estimatedfrom the mixed traffic flow data collected in Ho Chi Minh City. The safety spaces of the
car and the motorcycle were calculated and results were discussed.
Finally, the developed simulator which follows the concept of safety space wasapplied to assess the motorcycle conflict caused by non-lane-based movements on a roadsegment. For each time step in the simulation, speed, distance, driver reaction time andmotorcycle's physical size were the essential factors considered to calculate the safetylevels of the safety spaces for different motorcycle flow densities.

v

The results from this research are expected to be very useful in understanding thecharacteristics of driving safety for the motorcycle traffic flow in the developing
countries.

vi

Table of Contents
List of Tables ...........................................................................................................x
List of Figures ....................................................................................................... xii
Chapter 1 INTRODUCTION .................................................................................14
1.1 Background .............................................................................................14
1.2 Research objectives .................................................................................18
1.3 Scope and limitations of the research .....................................................18
1.4 Outline of the thesis ................................................................................20
Chapter 2 LITERATURE REVIEW ......................................................................22
2.1 Introduction .............................................................................................22
2.2 Characteristics of non-lane-based movements........................................22
2.3 Models of motorcycle driving behaviors ................................................25
2.3.1 Statistical analysis on motorcycle characteristics .......................25
2.3.2 Car-following models .................................................................26
2.3.3 Mixed traffic flow models ..........................................................29
2.3.4 Pedestrian movement models .....................................................31
2.3.5 An application of the social force model to motorcycle traffic ..32
2.4 The application of traffic simulation models to traffic safety.................33
2.4.1 Accident prediction models ........................................................34
2.4.2 Measures for traffic safety assessment .......................................35
2.5 Summary .................................................................................................38
Chapter 3 MODEL DEVELOPMENT ..................................................................40
3.1 Introduction .............................................................................................40
3.2 Concept of the safety space.....................................................................41
3.3 Model Formulation .................................................................................44
3.4 Model discussions ...................................................................................47
3.5 Data collection ........................................................................................49
3.5.1 Survey location ...........................................................................49vii

3.5.2 Data extraction ............................................................................53
3.5.3 Data description ..........................................................................54
3.6 Parameter calibration ..............................................................................59
3.7 Model validation .....................................................................................60
3.8 Summary .................................................................................................63
Chapter 4 THE TRAFFIC SIMULATOR .............................................................65
4.1 Introduction .............................................................................................65
4.2 Traffic simulation technique ...................................................................65
4.2.1 Agent-based microscopic simulation models .............................66
4.2.2 Tools for building traffic simulator.............................................68
4.3 The simulator ..........................................................................................70
4.3.1 Overall design .............................................................................70
4.3.2 Components ................................................................................71
4.4 Verification .............................................................................................81
4.4.1 Reproduction of non-lane-based movements..............................81
4.4.2 Differences from lane-based movements....................................87
4.5 Summary .................................................................................................93
Chapter 5 SAFETY SPACE FOR CAR AND MOTORCYCLE IN THE MIXEDTRAFFIC FLOW ..........................................................................................94
5.1 Introduction .............................................................................................94
5.2 A model for the mixed traffic flow .........................................................95
5.3 Parameter calibration ..............................................................................99
5.4 Discussions on safety spaces of the motorcycle and the car .................102
5.4.1 Threshold safety space for motorcycle and car.........................102
5.4.2 Comparison of acceleration between motorcycle and car ........105
5.5 Summary ...............................................................................................108
Chapter 6 MOTORCYLE SAFETY ASSESSMENT IN VIETNAM .................109
6.1 Introduction ...........................................................................................109
6.2 A model for motorcycle traffic safety assessment ................................109
6.2.1 Acceleration and deceleration ...................................................109viii

6.2.2 Conditions of choosing a lead vehicle to accelerate .................112
6.3 Model calibration ..................................................................................113
6.3.1 Parameter calibration ................................................................113
6.3.2 Model validation .......................................................................115
6.4 An application to traffic safety assessment ...........................................116
6.4.1 Conflict situations at a road segment ........................................116
6.4.2 Safety index: Deceleration Rate................................................117
6.4.3 Scenario settings for computer simulation ................................117
6.4.4 Effects of flow density on traffic conflict .................................118
6.5 Summary ...............................................................................................120
Chapter 7 CONCLUSIONS AND FUTURE WORK .........................................121
7.1 Conclusions ...........................................................................................121
7.2 Future work ...........................................................................................124
Appendix A ..........................................................................................................126
A.1 Social force model for the motorcycle .................................................126
A.2 Parameter calibration ...........................................................................130
References ............................................................................................................134ix

List of Tables
Table 2.1 Behaviors of the non-lane-based movements .................................................... 23
Table 2.2 Behaviors of the motorcycle in the scope of this research ................................ 25
Table 2.3 Types of traffic conflicts .................................................................................... 36
Table 3.1 Resolution of the video image at two locations ................................................. 53
Table 3.2 Given parameters for the motorcycle-only flow ................................................ 59
Table 3.3 Derived parameters for the motorcycle-only flow ............................................. 60
Table 3.4 Statistical measures for the speed and the ratio of swerving maneuvers forthe motorcycle-only flow .............................................................................. 63
Table 4.1 Agent-based models for the microscopic traffic simulation .............................. 67
Table 4.2 Open source software packages .........................................................................69
Table 4.3 Parameters for simulations................................................................................. 83
Table 5.1 Given parameters for case 1: the subject vehicle is a motorcycle, theinfluential vehicle is a car ........................................................................... 100
Table 5.2 Given parameters for case 2: the subject vehicle is a car, the influential
vehicle is a motorcycle................................................................................ 100
Table 5.3 Derived parameters of acceleration for the motorcycle and the car in themixed flow ..................................................................................................101
Table 5.4 Statistical measures for the speed and the ratio of swerving maneuvers ofthe motorcycle and the car in the mixed traffic flow ..................................102
Table 6.1 Given parameters when distinguishing acceleration and deceleration ............ 114
Table 6.2 Estimated parameters when distinguishing acceleration and deceleration ......115
Table 6.3 Statistical measures of speed, ratio of swerving and acceleration modeled
correctly when distinguishing acceleration and deceleration ..................... 116
Table 6.4 Simulation parameters ..................................................................................... 118
xTable A.1 Given parameters for motorcycles in the social force model ......................... 131
Table A.2 Parameter estimates for motorcycles in the social force model ...................... 132
Table A.3 Statistical measures for the speed of motorcycles in the social force
model........................................................................................................... 133

xi

List of Figures
Figure 1.1 Modal split in six Asian cities (Source: Hung, 2006) ......................................15
Figure 1.2 The number of traffic fatalities 100.000 persons by country(IRTAD, 2007) .............................................................................................. 16
Figure 1.3 Organization of dissertation ............................................................................. 21
Figure 3.1 Framework of methodology for the motorcycle-following model ................... 41
Figure 3.2 Equipotential lines of safety space ...................................................................42
Figure 3.3 Threshold safety space ..................................................................................... 43
Figure 3.4 Direction of the acceleration vector .................................................................46
Figure 3.5 Two survey locations in Ho Chi Minh City. .................................................... 52
Figure 3.6 Histogram of the speed at two locations........................................................... 55
Figure 3.7 Scatter plots of longitudinal distance against lateral distance .......................... 57
Figure 4.1 Flow chart of the traffic simulation model ....................................................... 71
Figure 4.2 Screenshot of the simulator .............................................................................. 73
Figure 4.3 Time-space diagram of the trajectories ............................................................ 84
Figure 4.4 Time-space trajectories of the oblique following ............................................. 85
Figure 4.5 Time-space trajectories of the swerving movement .........................................86
Figure 4.6 Fundamental diagrams: (a) reaction time = 0.3 s, (b) reaction time = 0.5s, and (c) reaction time = 0.7 s. .....................................................................92
Figure 5.1 Safety spaces for a motorcycle when an influential vehicle is a car ................ 96
Figure 5.2 Safety spaces for a car when an influential vehicle is a motorcycle ................ 98
Figure 5.3 Threshold safety space for the motorcycle and the car in the mixed
traffic flow ..................................................................................................104
Figure 5.4 Relationships between acceleration and distance in 3 cases of interaction ....107
Figure 6.1 The critical following angle of the motorcycle .............................................. 112
xii

Figure 6.2 The following route for the motorcycle to follow a leader ............................ 113
Figure 6.3 Non-lane-based road segment for simulation ................................................. 117
Figure 6.4 Effects of flow density on probability of sudden braking .............................. 119
Figure A.1 Equipotential lines of repulsive force ............................................................ 127
Figure A.2 Angle of sight for motorcycle ........................................................................129xiii

Chapter 1 INTRODUCTION
1.1 BACKGROUND
Although the characteristics of the car traffic flow have been extensively studied,
there is little knowledge on the motorcycle traffic flow despite the motorcycle’s
popularity in developing countries. Figure 1 shows that several big cities in Asia use themotorcycle as the main transportation mode. In Vietnam, motorcycles are mainly usedamong cars, buses, and non-motorized transportation modes. They make up 50% and
60% of traffic flow in Ha Noi and Ho Chi Minh City, respectively, whereas, the ratio ofbus usage are very low, with only 5% ~ 6%.
There are two main reasons why people prefer to use the motorcycle. The first is
its high mobility. Its smaller size and shape relative to car and bus enable it to navigate
urban roads easier and faster. It also requires only a small parking space, so people areusually able to park their motorcycles in their houses or offices’ garages, making it aneffective door-to-door transportation mode. The second reason is economy. Motorcycle
costs less than a car, thus it is the optimum choice for low- or middle-income families
where each working member could own one.
It is difficult to change the habit of using the motorcycle if people have beenusing it before. Thus, it is predicted that the motorcycle traffic flow will continue to exist
for a long. Like in Taiwan, a strong motorcycle market developed because of thevehicle’s high mobility and accessibility. And though Taipei has now become a highincome city, still a high density of motorcycle use can be seen.

14

44%
1%
5%
50%

31%
1%
6%

62%

23%
39%
18%

Hochiminh

10%

33%

26%

42%

Delhi

Non-motorised
transport
Private car

6%

13%
Hanoi

10%

35%

36%

30%

23%

27%

29%

JakartaBangkok

TaipeiPublic transport

Motorcycle

Figure 1.1 Modal split in six Asian cities (Source: Hung, 2006)

In Vietnam in recent years, the number of accidents and fatalities related to
motorcycle transportation has increased rapidly. Vietnamese government has beenpromoting policies to help minimize the number of these incidents. Figure 1.2 shows thenumber of traffic crash fatalities per 100,000 persons in Vietnam and other countries in2007. It was found that the number of fatalities in Vietnam is relatively high in the world,with that of Hanoi being higher compared to the average number in Vietnam during aninterval of 4 years (2005 – 2008).
Not keeping the safety distance and reckless driving are the main reasons for theaccidents in the capital Hanoi (Hung, 2008).

15

15
10
5

19.6
15.3
19.1

20

4.2
4.6
4.9
4.9
5.5
5.5
6.1
6.2
6.5
6.5
7.2
8
8.8
9.1
9.3
9.3
9.7
9.9
10.2
10.4
11.1
11.8
12.6
12.7
12.9
13.2
14.3
14.7
15
15.2
15.3

25

Singapore
Netherlands
NorwaySwedenUnited Kingdom
Switzerland
DenmarkJapan
Ger m a ny
IcelandFinland
Australia
FranceCanadaAustria
IrelandItaly
New Zealand
Spain
Belgium
L uxem bo ur g
Portugal
Czech RepublicHungary
Slovenia
Korea
PolandAmerica
GreeceVietnamHanoi Capital (2005)
Hanoi Capital (2006)
H a no i C a pi t a l ( 2 0 0 7 )Hanoi Capital (2008)

0

Figure 1.2 The number of traffic fatalities 100.000 persons by country(IRTAD, 2007)
To reduce motorcycle accidents, the first step would be to better understand theproperties of the motorcycle movement and how it differs from that of the car.
Consequently, policy makers could propose and implement useful traffic management
policies based on these understandings.
The basic difference between the car and the motorcycle is in their movement.
The former is lane-based, whereas the latter is non-lane-based. Under congested
conditions, cars tend to stay in a single lane while a motorcycle often swerves to the rightor left without following a lane. While for the car, the interactions of motion between
vehicles in the longitudinal direction are the important concerns; for the motorcycle,
interactions in both longitudinal and lateral directions need to be taken into consideration.
In this research the effects of the non-lane-based movement of the motorcycle on theissues of traffic safety are investigated.
How to describe the non-lane-based movement of the motorcycle is a big
challenge in many previous researches. There are many arguments on the acceptable16assumptions. Most of the studies divided the non-lane-based movement into thelongitudinal movement and the lateral movement, and modeled the separate movementswith an assumption on a relationship between them. For the longitudinal movement, thetraditional car-following model has been typically used. The lateral movements, however,are modeled with many different assumptions made to consider the relationship between
the movements in the longitudinal and lateral directions.
In the model of Cho and Wu (2004), longitudinal positions with respect toinfluential vehicles affect the lateral position of a subject motorcycle. This is based on thesimple assumption that the lateral position of a motorcycle is determined by the averagelateral position of surrounding vehicles weighted by their longitudinal positions. Lee etal. (2009) also introduced the “virtual motorcycle lane” concept to identify the leader
motorcycle who is leading the subject motorcycle in a virtual motorcycle lane. A
motorcycle can change lanes to overtake its leader. The random choice of alternative
virtual lanes depends on the utility function, with explanatory factors that include speed
and gap acceptance, among others. However, for investigators who assumed that a
motorcycle runs in a virtual lane and changes to the next virtual lane randomly, they
faced difficulties in determining the width of a virtual lane and in differentiating lanechanging behavior from oblique following behavior just by observing a traffic recording
video. Minh et al. (2010) assumed that motorcycles run on the “dynamic lane of
motorcycle” and follow another preceding motorcycle on the same dynamic lane. The
research calculated the width of the dynamic lane using linear relationship with average
speed. Here, average speed of a motorcycle affected its own lateral position.
These approaches above, which modeled the longitudinal movement and thelateral movement separately, led to many arguments on acceptable assumptions. In thisstudy, the introduction of the safety space integrated the longitudinal movement and the17lateral movement into one. Safety space is the space that surrounds a single subject
motorcycle when it is running along a road. The boundary of the safety space isdetermined by the influence of other surrounding vehicles that affect the driving
behaviors of the subject vehicle. The subject vehicle will control its speed in response to
the changes in the safety level of the safety space, to avoid an accident with surrounding
vehicles.
1.2 RESEARCH OBJECTIVES
The aim of the study is to develop a concept of safety space that is capable ofdescribing the non-lane-based movements under congested situations, and apply the
proposed concept in assessing the motorcycle traffic conflict caused by these movements.
To achieve the aim, the study designs five objectives as below:
1) To investigate the characteristics of non-lane-based movements of motorcycles
by considering driving behaviors in the congested conditions.
2) To propose a concept of safety space to describing these behaviors, i.e.,
dynamic movements of motorcycles in traffic made up only of motorcycles.
3) To develop a microscopic traffic simulator based on the concept of safety space
to verify the zigzag movements of the motorcycle.
4) To investigate the characteristics of the mixed traffic flow that affect traffic
safety.
5) To assess the motorcycle traffic conflict brought by the non-lane-based
movements.
1.3 SCOPE AND LIMITATIONS OF THE RESEARCH
The study attempts to investigate the non-lane-based movements of motorcycles
on straight road segments under congested situations. Road segments are selected rather

18

than road intersections because driving behaviors here are simpler due to reduction on theeffects of road designs such as size of intersection, position of stopping line, signal
system and turn-left or turn-right lane. Moreover, congested situations are considered
because vehicles zigzag movement is emphasized in these situations. Motorcycles infront change their speed and direction and other motorcycles behind them decelerate or
accelerate in response to these changes.
This research focuses solely on heterogeneity in the motorcycle driving behaviors
based on the non-lane-based movements under congested situations such as alongside
travelling, oblique following and swerving. The other driving behaviors showed under
uncongested situations such as free-speed travelling, overtaking and filtering; or at theintersections such as free deceleration, oblique following and left or right turning; orthose taking place in different environment conditions such as pair driving, alignment,sight distance, delineation, weather and visibility are not in the scope of this research.
The study explores firstly the characteristics of the homogeneous motorcycle
drivers. The future analyses should show differences between homogeneous drivers andheterogeneous drivers. In reality, different drivers react differently to types of stimuli.
Hence, heterogeneity in driving styles of different drivers such as different reaction time,
aggressive or non-aggressive, knowledge of traffic laws, training and driving skill could
make an impact on stability of the analysis results.
For the case study, the research conducted a survey of traffic flow in two roadsegments in Ho Chi Minh City, Vietnam. Data on motorcycle movement trajectories wereextracted from video clips capturing the movements of motorcycles at these 40-m-longroad segments. The survey was conducted in the period of December 30–31, 2010, from6:00 am to 8:00 am and 3:30 pm to 5:30 pm, to record movements of motorcycles during
peak hours.

191.4 OUTLINE OF THE THESISThe thesis comprises of seven chapters, as shown in Figure 1.3. Each chapter isdetailed as follows:
Chapter 1 introduces the background, the research objectives and the outline of
the thesis.
Chapter 2 provides the literature reviews. Reviewed papers are categorized into
two groups, namely, models for describing the driving behaviors of motorcycles, andapplications of microscopic simulation models to analyze the issues of traffic accidents.
Chapter 3 proposes the concept of safety space to describe non-lane-based
movements of the motorcycles with good potential to analyze traffic safety. The model
development based on the proposed concept is presented. The results of the model
calibration using survey data and the validation process are presented in the end of thechapter.
Chapter 4 develops a microscopic simulator to verify the zigzag movements ofmotorcycles based on the proposed model.
Chapter 5 applies the concept of safety space to investigate the characteristics ofthe mixed traffic flow, i.e., the traffic flow with cars and motorcycles that affect traffic
safety. Same as in Chapter 3, but for the mixed traffic flow, this chapter presents theestimation of the model parameters using survey data collected in Ho Chi Minh City. The
resulting safety spaces for the car and the motorcycle are also discussed.
Chapter 6 introduces an application of the microscopic simulator to assess theaccident potential for non-lane-based movements of the motorcycle at a road segment.
The study computes the safety levels of the safety spaces at each time step according todifferent densities of the motorcycle flow.

20Chapter 7 summarizes the new findings in this research and detailed suggestions
for the further research.

Chapter 1 Introduction

Chapter 2 Literature review

Objective 1

Chapter 3 Model development
Chapter 5 Safety spacefor car and motorcyclein the mixed flow

Objective 2
Chapter 4 Traffic simulator

Objective 3

Chapter 6 Motorcycle
safety assessment in
Vietnam

Objective 4

Objective 5
Chapter 7 Conclusion
Figure 1.3 Organization of dissertation

21

Chapter 2 LITERATURE REVIEW
2.1 INTRODUCTION
This chapter provides a detailed description of the characteristics of non-lanebased movements. The patterns of driving behaviors related to non-lane-based
movements are classified. Review of models describing motorcycle driving behaviors
follows. Finally, literatures on the application of these models to analyze traffic safety arepresented.
2.2 CHARACTERISTICS OF NON-LANE-BASED MOVEMENTS
Compared with the car, the motorcycle on the road possesses a smaller size and abetter ability of turning left or right. Because there is no road designed as motorcycle
lane, the motorcycle does not need to follow any lane disciplines. Moreover, as the roadlaws do not restrict a motorcycle to run on a car lane, a motorcycle can change to any
lane that it feels convenient. Even two motorcycles can travel alongside on the same carlane. Therefore, motions in a longitudinal direction are the main concern for the case of
the car, whereas for the motorcycle, both longitudinal and lateral directions should beconsidered. Investigations on the zigzag movements of motorcycles will contribute to theunderstanding about the effects of non-lane-based movements on the issues of traffic
congestion and traffic safety.
The observed motorcycle driving behaviors related to the non-lane-based
movements are categorized by traffic situation and road geometry, as illustrated in Table
2.1. Detailed explanations on these behaviors are given as follows:

22

Table 2.1 Behaviors of the non-lane-based movements
Congested situation
Alongside travelling
Road segment
Oblique following
Swerving
Road intersection Free deceleration
Oblique following
Turning left/rightNon-congested situation
Free-speed travelling
Overtaking
Filtering

Alongside travelling
A motorcycle travels alongside another motorcycle on the same car-lane(Branston, 1977). The standard width of the car-lane, 3.65 m, is designed to fit the
average width of the car which is 1.6 m. A motorcycle with an average width of 0.8 m
can share the lane easily. Alongside travelling movement is easily observed in congested
situations when the density of traffic flow is high.
Oblique following
A motorcycle follows a preceding motorcycle at an oblique position (Robertson,2003). As a result, motorcycle riders are situated in an angle with a good view of othersurrounding vehicles. This helps riders avoid a possible accident and find a chance toovertake lead vehicles.
Swerving
A motorcycle changes its direction quickly to the left or right in response to thesudden braking of a preceding motorcycle (Robertson, 2002). To avoid a rear-end
collision with a lead motorcycle, a following motorcycle can decelerate its speed andswerve away from the original position. It is often observed that a motorcycle
simultaneously performs these two actions.

23Free-speed travelling
A motorcycle travels at a free speed. Free speed refers to the speed at which a
motorcycle desires to travel. Under non-congested situation, a rider wishes to run as fast
as possible to finish a trip on time.
Overtaking
This behavior happens when a following vehicle decides to pass another vehicle
travelling at a lower speed (Minh, 2005). It includes a series of actions: moving laterally,
speeding up to pass a lead vehicle, and moving back to the lane. Such behaviors areobserved in non-congested situations. Motorcycles often overtake towards an outer lanenear a median where vehicles can travel at a higher speed.
Filtering
Filtering refers to the behavior of a motorcycle as it moves through lateralclearances between other vehicles (Oketch, 2000). Filtering behavior often occurs when ahigher speed motorcycle overtakes two lower speed motorcycles travelling ahead bymoving to the lateral spaces between the two vehicles.
Free deceleration
A motorcycle decelerates its speed freely until it stops at a stop line or at the endof the queue waiting for a green light at the intersection (Minh, 2006). When riders feel
free from the influences of the leaders, they will loosen their hand on the acceleration
gear and enjoy the free deceleration.
Turning left/right
A motorcycle on the main street changes from the current lane to another lane inorder to turn left or right onto the cross-street.

24

The research focuses on the driving behaviors at a road segment under congested
situation; namely alongside travelling, oblique following and swerving. In this study,
these behaviors are described by the motorcycle-following model shown in Table 2.2.

Table 2.2 Behaviors of the motorcycle in the scope of this research
Road segment

Congested situations
Motorcycle-following model
Alongside travelling
Oblique following
Swerving

Road intersection

Non-congested situations
Free-speed travelling
Overtaking
Filtering

Free deceleration
Oblique following
Turning left/right

2.3 MODELS OF MOTORCYCLE DRIVING BEHAVIORSThis section discusses the statistical analysis of many basic characteristics of the
motorcycle flow, and the models which describe the behaviors of motorcycle, car, mixed
flow and pedestrian.
2.3.1 Statistical analysis on motorcycle characteristics
Motorcycle refers to the two-wheeled vehicle equipped with engine. Motorcycles
include scooters, mopeds and motorized bicycles. Their average size is 0.7 m ~ 0.8 m
wide by 1.6 m ~ 1.9 m long. A motorcycle rider accelerates using the right handle bar,and decelerates by simultaneously loosening the handle bar and applying a leg brake. The
maximum deceleration is measured at around -6.19 m/sec2 in an experiment conductedby Ecker et al. (2001).

25

Several researchers have investigated the properties of the motorcycle traffic
flow. Minh et al. (2005, 2006) investigated some basic characteristics of the motorcycle
flow, such as the speed-flow relationship and the distribution of headway. The meanvalue of a motorcyclist’s reaction time has been measured to be ~0.5 s. The headway of
motorcycles is found to be 0.5 s to 1.0 s.
Because of its small size and shape, a motorcycle needs less surrounding space tomove than does a car. The passenger car unit values for a motorcycle (Lee et al., 2010)
were estimated in different speed ranges in congested flow using a simulation model. The
results showed that PCU values of motorcycles are 0.4 and 0.5 at flow speeds of 10km/h
and 20km/h, respectively. Y et al. (2010) proposed the motorcycle equivalent unit values(MCU values) for the mixed flow with the predominance of motorcycles. MCU value has
been found to be related to the mean speed and the effective space of each vehicle type,which is defined as the space needed to maintain the desired speed. The estimation results
indicated that MCU values of car, bus and bicycle at a road segment are 3.43, 10.48 and
1.38, respectively.
A motorcycle’s speed, like that of a car, decreases when traffic becomescongested. Kov and Yai (2010) reported that the mean speed of the mixed traffic flow
decreases tremendously when the number of cars increases. The speed of the car in heavy
traffic is less than that of the motorcycle.
2.3.2 Car-following models
Motorcyclists display several kinds of behavior that resemble those of car drivers.
Motorcyclists follow their leader and accelerate or decelerate in response to the changes
in the speed of the preceding vehicles.
The General Motors model (GM model), which was developed at General Motors
research labs by Chandler et al. (1958) and Gazis et al. (1959), assumes that the26

acceleration of the following car is non-linearly related to three factors: speed of thepreceding car, relative speed between the following and the preceding, and the head way
between them as shown below:

an (t ) DvnE (t )'vn (t  W )'xnJ (t  W )(2.1)( ): the acceleration of vehicle n at time t( ): the speed of vehicle n at time t( ): the speed difference at time t between vehicle n and vehicle n-1( ): the position difference at time t between vehicle n and vehicle n-1: the car driver reaction time
: parameters

GM model is simple with only three parameters which are also easy to calibrate.
Although there are a large number of different calibration results under different traffic
conditions (Brackstone and McDonald, 1999), GM model is still applied to microscopic
simulation (MITSIM) due to its simplicity. When applying GM model to the motorcycle,
it is important to note that the lateral motorcycle movement is described poorly because
GM model only focuses on the longitudinal movement (Lan and Chang, 2005).
For the car, collision avoidance model is an alternative approach for the following
behavior. The models of Kometani and Sasaki (1959) and Gipps (1981) assume that
following vehicles control their speed to ensure that they can stop safely in order to avoid
a possible accident if the preceding vehicle suddenly brakes. From the viewpoint ofsafety driving, Gipps (1981) introduced the constraints of braking in the emergency
regime, extra safety reaction time and safety headway margin. The model has also been27

applied to many micro simulation programs such as MULTSIM (Gipps, 1986), AIMSUN(Barcelo, 2001). However, collision avoidance models have difficulties in applying to themotorcycle. These models were developed on the systems of motion equations forinteractions between a preceding vehicle and a following vehicle. Hence, a limitation
exists when considering the interaction of more than two vehicles, which is common in
the congested conditions.
Psychophysical model or “Action point” model is a different approach for carfollowing behavior. The earliest versions of the model (Michaels, 1963; Leutzbach andWiedemann, 1986) developed a concept that drivers can control their speed by perceptual
thresholds. These thresholds are limitations related to changes in distance
two vehicles, their relative speed

x betweenv and rate of divergence of the visual angle of thehead vehicle (~ v/ x2). When one of these thresholds is exceeded, drivers will change
their acceleration, typically in the order of 0.2 m/s2 (Montroll, 1959) until they cannot
perceive that these thresholds are not re-exceeded. The model produced the phenomenonof “spiral plots” which were founded by other studies (Gordon, 1971; Brackstone et al.,2002). “Action point” model has been employed in many traffic simulation programs
such as PARAMICS (Cameron and Duncan, 1996), VISSIM (Fellendorf and Vortisch,2001). Calibration of perceptual thresholds has been less successful because ofdifficulties in estimating parameters related to human factors, such as recognizing orperceiving the changes of distance and relative speed. Nevertheless, the model is basedon the understandable assumptions of perceptual thresholds related to distance andrelative speed; hence, can still be used to describe the driving behaviors in a proper way.
The concept of this model is a very useful reference for developing a model for
motorcycles.

28

2.3.3 Mixed traffic flow models
In the mixed traffic flow, the car and the motorcycle run on the same lane. The
basic difference between the car and the motorcycle is related to the lane-based
movement of the former and the non-lane-based movement of the latter. A car runs inlanes and seldom changes lanes. However, a motorcycle changes its direction very often
especially under congested conditions. How to describe the non-lane-based movement of
the motorcycle is a big challenge for the mixed traffic flow models.
Many researches represented the non-lane-based movement by dividing it into thelongitudinal movement and the lateral movement. As the longitudinal movement issimilar to the car following, the traditional car-following model has been applied todescribe this movement. Example applications are those of Cho and Wu (2004) whichdeveloped the “spacing model”; Minh et al. (2006) which used the GM model; and Lee etal. (2009) which applied the Gipps model.
However, the lateral movement is more complex to be modeled. The complexity
is in making the assumptions of the relationship between the longitudinal movement andthe lateral movement. Cho and Wu (2004) assumed that lateral position of a motorcycle
was determined by an average lateral position of the surrounding vehicles weighted by
the longitudinal positions of these vehicles. In this model, longitudinal positions withrespect to influential vehicles have an effect on lateral position of a subject motorcycle.
Minh et al. (2010) assumed that motorcycles run on the “dynamic lane of motorcycle”
and follow a preceding motorcycle on the same dynamic lane. The dynamic lane is avirtual lane that motorcycle drivers perceive when running. The research calculated thewidth of the dynamic lane using linear relationship with the average speed. Here, theaverage speed of a motorcycle is affected by its own lateral position. Lee et al. (2009)
introduced the “virtual motorcycle lane” concept to identify a motorcycle leading the29subject motorcycle in the virtual motorcycle lane. A motorcycle can change lanes toovertake its leader. The random choice of alternative virtual lanes depends on the utility
function, with explanatory factors that include speed and gap acceptance, among others.
However, for investigators who assumed that a motorcycle runs in a virtual lane andchanges to the next virtual lane randomly, they faced difficulties in determining the widthof a virtual lane and in differentiating the lane-changing behavior from oblique following
behavior when only observing a traffic recording video.
Cellular automata model provides a calculation technique for simulating two
dimensional motorcycle movements based on the simplicity of moving rules developed
for the motorcycle such as car-following, lane-changing or overtaking. The model
assumes that a vehicle with a certain type of transportation mode is assigned a certain
number of cell units to be equal to the real physical size of the vehicle. Ahuja (2001) set
the size of a cell unit as 0.6 m, which is exactly equal to the width of the bicycle
considered in this study. Lan and Chang (2005) used a cell unit of 1.25 x 1.25 m2 so as torepresent the size of the car and the motorcycle as 6 x 2 cell units and 2 x 1 cell units,
respectively. The time step in updating positions of vehicles is often set as one sec so thatvehicles move in a longitudinal distance which is equal to their speed. The model issuccessful to reproduce fundamental diagrams of the mixed traffic flow. It has been used
to analyze the characteristics of traffic congestion caused by the effects of various typesof vehicles and the lane width on the mixed traffic flow (Lan and Hsu, 2006).
Both aforementioned conventional models and the cellular automata model havethe same problem of deciding the width of motorcycle lane or cell. The lane width that
directly affects the flow density through lateral movements can be calibrated using fielddata. However, this model has a low potential to analyze the issues of traffic safety
because the updated accelerations in each time step are given by the fixed values.

30

2.3.4 Pedestrian movement models
Walking movements of the pedestrian can be categorized as non-lane-based
movements. The basic behaviors of the pedestrian under congested conditions, like thatof the motorcycle, include (1) accelerating to move in the desired direction, (2)decelerating and turning left or right to avoid a possible collision.
The basic behaviors mentioned above can be represented by the decision making
process. Pedestrians choose their direction and speed at each time step so as to maximize
their utility function. Antonini et al. (2006) developed a discrete choice model andassumed that the utility function can be explained by influential factors such as desired
direction and speed of a subject pedestrian, the number of other influential pedestrians,
their positions and moving directions. The advantage of the discrete choice model is inproviding a sufficient method to calibrate parameters which considers variability of
behaviors according to individual pedestrians. The discrete choice model has been
employed to describe the lane-changing behavior of the motorcycle (Lee, 2009).
However, the behavior is explained using the virtual lanes for the motorcycle based on
the lane-based movement of the car.
Asano et al. (2009) applied the multi-player game theory to describe the decision
making process of pedestrians. The study assumed that pedestrians choose their direction
and speed at each time step so as to minimize their travel times to the destination while
avoiding collisions, corresponding to game theory. However, the model does not consider
safety factors such as reaction time, and safety distance related to the description ofcollision avoidance behavior. Hence, such factors should be taken into account when
applying the model to the motorcycle.
Helbing et al. (1995, 1998, 2001) introduced the social force approach to describe
the non-lane-based movement of the pedestrian. They assumed that pedestrians do not31usually make complicated decisions between alternative behaviors, but rather follow
optimized behaviors learned from experience. For example, pedestrians walk at their
desired speeds. Sometimes, if they feel uncomfortable with their current position, they
may change direction to move to wider spaces. The psychological behaviors can beconsidered as social forces that cause them to move, and these forces can be entered into
an equation to describe the changes of motion. This model explained the influence ofdensity on pedestrian movements. A similar influence should be taken into account when
considering the non-lane-based movement of the motorcycle.
2.3.5 An application of the social force model to motorcycle traffic
This research attempted to apply the social force model in modeling the non-lanebased movement of the motorcycle (Appendix A). The results of parameter calibration
showed that several estimation parameters do not differ from 0 at the significance level of
0.05. The reasons for the failure are listed below:
1) Acceleration force is a function of desired speed. Desired speed is assumed tobe constant in the early papers of the author, and to be an increasing function of timedelay in the latter papers. Therefore, how to make an acceptable assumption of desired
speed is a difficult problem. Moreover, there is a strong relationship between acceleration
force and repulsive force because acceleration is the sum of the two forces. Hence,parameters of acceleration force have a strong correlation with parameters of repulsive
force.
2) Repulsive force is not related to the speed difference. Speed difference is themost important factor affecting the magnitude of the acceleration. However, repulsive
force is assumed to be a derivative of an exponentially decreasing function of speed anddistance with respect to the distance between two vehicles. This point should be paid
attention to when modifying the equation of repulsive force.
323) It is difficult to explain the concept of vector addition of social forces which
represents the real behaviors. When considering the interaction of two or more influential
motorcycles on a subject motorcycle, the acceleration of the subject vehicle changes inlarge range because of taking the vector addition of these forces generated by influential
motorcycles. For example, if there are two influential vehicles in front, the repulsive
force will increase twice than that of the case of only one vehicle in front. If the twovehicles approach the subject vehicle, one from both sides, the repulsive force will be
zero. This led to unpredictable trajectories of motorcycles which differ from the real data.
4) The condition for modeling the collision avoidance behavior is too simple. The
model assumed that repulsive force is an exponentially decreasing function of speed anddistance. When two vehicles approach closer, the repulsive force becomes larger andpushes these two vehicles farther. Therefore, it is necessary to provide more conditions
for accident prevention such as safety distance and maximum deceleration. Such
conditions are taken into account in this study.
5) When reviewing papers of social force model, it was found that there are little
papers published in journals showing results of parameter calibration or model validation.
In conclusion, social force model is a good approach when the “force” is assumed
to explain an “action” happening. Taking the sum of all the forces may not explain well
the moving trajectory of the vehicle. The research tries to develop a better approach thatcan provide a good estimation of the motorcycle trajectories.
2.4 THE APPLICATION OF TRAFFIC SIMULATION MODELS TO TRAFFIC SAFETY
This section provides literation review on models which are used for predicting
traffic accident, especially focusing on traffic simulation models. Also, the traffic
simulation measures to assess the safety of vehicles are discussed.

33

2.4.1 Accident prediction models
The safety level of a vehicle or a facility refers to the number of accidents or rateof accidents involved with the vehicle or the facility. An accident here is defined as acrash between two or more vehicles. There are two popular approaches to estimate thesafety level of a vehicle: (1) develop safety performance functions that relate the numberof accidents, or rate of accidents, to the explanatory variables using regression analysis,(2) develop simulation models to calculate the safety level using measures for traffic
safety assessment.
In the former approach, the correlations among variables are found by analyzing
the dispersion and approximated by deriving regression formulas. Neuman and Glennon(1983) found the correlations between the road environment of road design, infrastructure
and accident causes. Warshawsly and Shinar (2002) found the relationship between
reaction time to a brake light and driver’s gender, age, level of expectancy for the brakelight, and number of times that a task was performed. This approach requires consensus
data on traffic accidents which are very difficult to collect. In reality, probability of traffic
accident is very low and varies across the times of day, days of week, locations andspecial events.
The latter approach has a potential to address the aforementioned problems oflack of observation data. The simulation models were developed on the basis ofbehavioral modeling of vehicles as mentioned in Section 2.3. Although the models cannot
estimate the number of accidents, they can be used to reflect the safety or the increased
probability of higher-than-average accident rates (Gettman and Head, 2003). Microscopic
models simulate position, speed and acceleration of every vehicle in the traffic flow andupdate it in every second. Hence, simulation models can produce a larger amount ofanalysis data than observation data, and with time savings. Lastly, these models cover34

many scenarios such as night time, weekend, and special locations that observers meetdifficulties in data collection.
2.4.2 Measures for traffic safety assessment
Conventional researches focused on measures related to the traffic conflict
techniques (Perkins and Harris, 1967; Glauz and Migletz, 1980; Parker and Zegeer,1988). A traffic conflict is defined as an event involving two or more road users, in which
the action of one user causes the other user to make an evasive maneuver to avoid acollision (FHWA, 1990). Road users refer to motorists, motorcyclists, cyclists andpedestrians. According to the definition, conflicts are vehicle interactions which can leadto accidents. A conflict occurs when an action of the first user places the other user in an
accident unless the other user does not take an evasive action.
Traffic conflicts can be categorized by types of maneuvers. Definitions of various
types of conflicts and the corresponding types of accident are summarized in Table 2.3(FHWA, 1990). Many studies investigated the connection between the number ofobserved conflict counts and the number of traffic accidents (FHWA, 1985; Kaub, 2000).
They concluded that conflict counts and traffic volume tend to track the accident trends
fairly well.

35

Table 2.3 Types of traffic conflicts
Type of

Definition (for right-hand driving)

conflicts

Type ofcollisionSame

The vehicle in front slows down or turns left/right, and the

direction

following vehicle brakes or swerves to avoid the collision.

Lane-change

The vehicle in front changes from one lane to another lane,

Rear-end

Rear-end

then the following vehicle brakes or swerves to avoid thecollision.
Opposing

An incoming vehicle in the opposite direction turns left,

Head-onleft turnthen another vehicle in the other direction applies a brake.

Side-swipe

Cross traffic

A vehicle on the cross-street turns into the path of a second

Rear-end

vehicle on the main street which has the right-of-way toSide-swipe

proceed, then the second vehicle brakes or swerves to avoid
an accident.
Right-turn-A right-turn-on-red vehicle turns right into the lane of aRear-end

on-redsecond vehicle which has the right-of-way, then the second

Side-swipe

vehicle brakes to avoid a collision.
Pedestrian or

A pedestrian or bicycle crosses in front of a vehicle whichbicyclehas a right-of-way then the vehicle applies a brake.

Secondary

When the first vehicle causes the second vehicle to apply a

Rear-end

brake, the third vehicle also brakes or swerves away in

Side-swipe

response to the second.

36

The primary measures to determine a conflict using microscopic simulation wereintroduced by Gettman and Head (2003) in the following list.
Time to collision (TTC)
TTC is the time to collision at the area of potential collision between two vehicles
if they continue to run with the same speed without placing evasive actions. It can bemeasured by dividing the distance by the speed between the two road users at the time ofevasive action.
Post-encroachment time (PET)PET is defined as the time difference between the time the first vehicle passes outof the area of potential collision and the time the second vehicle with right-of-way arrives
at the area of potential collision (Allen et al., 1978). Therefore, it is the time difference
between vehicles passing through the same conflict area.
Maximum of the speeds of two vehicles involved in the conflict event (MaxS)
MaxS is the maximum speed recorded for each vehicle during the time of evasive
action. Then, the maximum speed of those vehicles is determined to be MaxS.
Maximum relative speeds of two vehicles involved in the conflict event (Deltas)
DeltaS is the maximum relative speed recorded for each vehicle during the timeof evasive action. Then, the maximum relative speed of those vehicles is determined to be
DeltaS.
Deceleration rate (DR)DR is the deceleration rate of the evasive action taken by a vehicle. Deceleration
rate is a measure to indicate the severity of the conflict event. The reason is that when themasses of conflict vehicles are known, it is easy to calculate the momentum values which
represent the damage of the resulting collisions.
37

MaxS, DeltaS and DR can estimate the severity of collisions. These values areavailable from the output of simulation model at every each time. Because of this reason,
this study uses DR as an efficient measure to assess traffic safety of the motorcycle at aroad segment.
2.5 SUMMARY
This chapter provides a detailed description of the characteristics of motorcycle
non-lane-based movements. Because there is no motorcycle-lane on the road, themotorcycle does not need to follow the lane disciplines. The observed driving behaviors
related to the non-lane-based movements were categorized by traffic situation and roadgeometry. This research focuses only on the behaviors at the road segment undercongested situations such as alongside travelling, oblique following and swerving. In thisstudy, these behaviors are described by the motorcycle-following model.
What follows is the review of the models describing the driving behaviors.
Results from statistical analysis on many basic characteristics of the motorcycle flow
were discussed. A motorcycle needs less surrounding space to move than does a car due
to its small size and shape. A motorcycle’s speed, like that of a car, will decrease whentraffic becomes congested. Car following models were reviewed because motorcyclists
display several kinds of behaviors that resemble those of car drivers. For example, amotorcyclist follows its leader and accelerates or decelerates in response to the changes
in the speed of the leader. In the mixed traffic flow, the car and the motorcycle can run on
the same lane. The car follows the lane-based movement and the motorcycle runs on thebasis of the non-lane-based movement. Many researches attempt to represent the nonlane-based movement by separating it into the longitudinal movement and the lateral
movement. As the longitudinal movement is similar to the car following, the traditionalcar-following model has been applied to describe this movement. However, the lateral38

movement is more complex to model. The complexity comes from the way of making
assumptions in the relationship between the longitudinal movement and the lateral
movement.
In the pedestrian flow, walking movements of the pedestrian can be considered as
non-lane-based. However, almost all of the models for describing movements ofpedestrians do not consider safety factors such as reaction time, safety distance, andspeed difference related to the description of collision avoidance behavior. Therefore,such considerations should be taken into account in the case of the motorcycle.
Finally, literatures on applications of models for traffic safety were presented.
There are two approaches to estimate the safety level of a vehicle. The first is to develop
safety performance functions that relate the number of accidents or rate accident to the
explanatory variables using the regression analysis. The second is to develop microscopic
simulation models to calculate the safety level using traffic conflict measures for traffic
safety assessment. The first approach requires the consensus data on traffic accidents
which are very difficult to collect. The latter approach has a potential to address theaforementioned problems of lacking observation data. Traffic conflict is an observablesituation, in which the action of a user causes the other user to make an evasive maneuverto avoid a collision. Many researches concluded that there is a connection between thenumber of observed conflict counts and the number of traffic accidents. Traffic conflicts
were categorized by types of maneuvers; and the primary measures to determine a
conflict situation using microscopic simulation were introduced. This study will use
Deceleration Rate (DR) to assess the traffic safety level of the motorcycle at a roadsegment.

39

Chapter 3 MODEL DEVELOPMENT
3.1 INTRODUCTION
This chapter develops a methodology for describing the non-lane-based
movement of the motorcycle. In the second section, a concept of safety space for the
motorcycle is introduced. In the third section, the motorcycle-following model isdeveloped based on the concept. Detailed discussions about the limitations of theprevious models are summarized in the fourth section. The fifth section introduces thedata collection, including the survey locations and data extraction. Then, calibration is
performed to estimate values of parameters for the proposed model in the sixth section.
The seventh section compares the estimated results to field data so as to validate themodel using statistical measures to calculate the value of errors. The eighth section
introduces a microscopic simulator to verify the non-lane-based movements ofmotorcycles.
The framework of methodology for developing the motorcycle-following modelis shown in Figure 3.1.

40

Motorcycle-following model
Concept of safety space
Model formulation• Acceleration• The rule of determining themost influential vehicle
Data collection• Survey location• Data extraction

SEV computer software

Parameter calibration• Parameters of acceleration

Non-linear regression

Model validation• A new sample at another location• Comparison of observed andestimated speeds

Root-mean-square error
Mean error

Figure 3.1 Framework of methodology for the motorcycle-following model

3.2 CONCEPT OF THE SAFETY SPACE
Safety space is the space that surrounds a single subject motorcycle when it isrunning along a road. It has the form of a physical space whose boundary is determinedby the influence of other vehicles that affect the driving behaviors of the subject vehicle.
A motorist is assumed to perceive this physical space as an approximate half ellipse, as
illustrated in Figure 3.2. The boundaries of safety spaces are equipotential lines, meaningthat all vehicles on the same line represent the same level of safety, as perceived by thedriver of the subject vehicle. When another vehicle moves closer to or farther away from41

a subject vehicle, the safety space becomes smaller or larger; as a result, the perceived
level of safety decreases or increases.

Left

Y

Safetyspace V2

Subject

Safetyspace V1

X

Right
Head
Figure 3.2 Equipotential lines of safety space

Numerous observations of the zigzag movements of the motorcycle have shownthat non-lane-based movements can be explained by two behaviors. The first isacceleration in order to achieve a free speed. When a leader motorcycle in front speeds
up, the safety space of a subject motorcyclist expands, which then increases speed andmoves toward the influential motorcycle so as to enjoy the free speed. The second
behavior is deceleration to avoid a collision. When another motorcycle approaches, thesafety space becomes smaller and the motorcycle’s speed is reduced, while it may also
swerve to the right or left. Therefore, there is a very close relationship between changes
in a motorcyclist’s speed and direction of motion and the changes in the size of the safety
space. Furthermore, as the level of safety for a certain safety space is easily expressed bya density equation, it can be used to evaluate how the behavior of a motorcycle changes,
depending on a high or low density of traffic flow. Based on these observations, thepresent study applies the concept of safety space to the motorcycle in order to describe42motorcyclists’ behaviors. It is assumed that the behavior of a motorcycle driver is notcomplex, but consists simply of acceleration or deceleration in response to changes in thesize of the safety space with a view to achieving a higher safety level.
The safety space for a subject motorcycle is assumed to be determined by the
combination of a half ellipsoidal boundary and two parallel lines (see Figure 3.2). The
ellipsoidal boundary with its center is placed at the middle point of the front side of thesubject motorcycle and crosses the middle point of the back side of the influential
motorcycle. The two parallel lines connect to the ellipsoidal boundary and expand to theback of the subject motorcycle. These boundaries make up the whole space surrounding
the motorcycle. The ellipsoidal boundary shows the space when the preceding motorcycle
runs in front of the subject. Two parallel lines make the clearances on the both side of thesubject when two vehicles run side-by-side.

Y

Safety space

Threshold safety space

WD  d yWD

W D vDXdydx
 2d x( x, y )Figure 3.3 Threshold safety space

There are many safety spaces for a given motorcycle. The safety level of a safety
space varies according to physical traffic conditions, such as distances between vehicles,
43

their speeds, the sizes of the vehicles and the various reaction times of the drivers.
Therefore, the concept of “threshold” safety space is introduced to define the minimal
safety level that the motorcyclist considers acceptable for driving and avoiding a possible
accident. As shown in Figure 3.3, the threshold safety space of a subject vehicle α isassumed to have an ellipsoidal shape, with the vehicle placed at the center and the
direction of its velocity vα determining the direction of the major axis, and two parallellines connecting to the ellipsoidal boundary and expand to the back of the subject
motorcycle, with the length of two parallel lines being equal to two times of the length of
the subject motorcycle. The physical size of a motorcycle on each axis is denoted by dx,
dy. The length of the semi-major axis is the safety distance on the x-axis, measured fromthe front side of one motorist to the rear side of another and expressed as ταvα, where τα isthe relaxation time on the x-axis. Relaxation time is defined as the time needed tocomplete a series of actions to avoid a collision: perceive the leading vehicle braking
suddenly, swerve left or right, and brake to reduce speed. The length of the semi-minor
axis is the safety distance on the y-axis, given by Wα+dy, where Wα is the lateral distanceon the y-axis between two motorcycles. This is also the lateral safety distance when two
vehicles are riding side by side. A motorcycle rider is assumed to control the speed anddirection of motion so as to keep other motorcycles outside the vehicle’s threshold safety
space for the collision avoidance.
3.3 MODEL FORMULATION
Suppose that a subject vehicle α travels at speeds vα at time t. If an influential
vehicle β increases or decreases its speed to vβ at time t, then vehicle α will adjust its
acceleration aα, with a lag of reaction time Tα, to be equal to a gradient ∇ of a level ofsafety Vβ for the current position of β with respect to a relative speed vector ⃗⃗ , as follows:44⃗

aD (t  TD ) v&DE VE (t )(3.1)

The negative sign on the right-hand side of Equation (3.1) means that aα isnegative or positive when β moves in or out of the safety space, respectively. The level ofsafety Vβ for vehicle β can be expressed by an exponential function of the distance
between two vehicles. If Vβ is assumed to be the equipotential curve of the ellipse andtwo parallel lines connecting to the ellipsoidal boundary with the length of two parallellines being equal to two times of the length of the subject motorcycle, then Equation (3.1)
can be rewritten asaD (t  TD )

­
§
2
§ §
··
·
y2
¸ B ¸ ¸ if x t 0°  v& ¨ A exp¨  ¨ x
DE ¨¨ ¨ W v 2 W d 2 ¸
¸¸
°°
D
y
¹
© © D D
¹¹
©
®
§
2
·
§ §
·
·
°
y
¨
¨ ¨
¸ B¸¸
if  2d x d x d 0°  v&DE ¨ A exp¨  ¨
2 ¸
¸¸
W

d
D
y
°¯
©
¹
©
¹¹
©

(3.2)

where A and B are parameters. Parameter A represents the magnitude of the safety level,
while parameter B represents the effect of stretching out the value of safety level; x, y are
the distances between vehicles α and β measured on the x-axis and y-axis, respectively.
Equation (3.2) allows the threshold safety space to change its size according to the speedof the subject vehicle: at higher speeds, a larger threshold safety space is needed tomaintain the same level of safety.
The direction of the acceleration vector ⃗ , which shows the direction of motion,is related to the gradient direction of the safety space as

45

&
aD
&
aD

where ‖ ⃗ ‖ and ‖­  VE
if aD d 0°V°E®  VE°
if aD ! 0
°  VE¯(3.3)‖ denote the magnitude of the acceleration vector and thegradient vector, respectively (Figure 3.4). Equation (3.3) shows a simple assumption.
When β moves closer to α, α will decelerate () and keep farther away from β in thegradient direction to avoid a collision. When β moves farther away from α, α will
accelerate () to follow β in the reverse gradient direction.

Y

VehicleSubject

X

Figure 3.4 Direction of the acceleration vector

Under heavy traffic conditions, a motorcycle driver may not be able to respond to
all the influential motorcycles. Hence, it is important to specify which motorcycle is themost influential. Suppose there are N influential motorcycles affecting the driving
behavior of a subject motorcycle α and its acceleration for the influential vehicle i isdenoted by ⃗. Then it can be assumed that the influential vehicle i is chosen to be the46most influential if the subject vehicle responds to it with the maximum magnitude of theacceleration, as follows:&&&&max ^ aD 1 , aD 2 ,..., aDi ,..., aDN `
i

(3.4)

This assumption is reasonable because a subject vehicle cannot respond to many
influential vehicles at the same time. It will focus on decreasing speed to avoid a collision
with the most influential vehicle, while paying lesser attention to other vehicles. It also
increases speed to follow the most influential vehicle in order to achieve the highest
acceleration. Obviously, a subject motorcycle responds to many different “mostinfluential vehicles” during the course of a journey. This explains the right/left swerving
behaviors of motorcycle under heavy traffic conditions.
3.4 MODEL DISCUSSIONSThe proposed concept can deal with the limitations of the previous models as
follows:
1) The model embodies reasonable assumptions which directly relate acceleration
to the distance and relative speed between vehicles based on the concept of safety space.
This connects the proposed motorcycle-following model to the conventional carfollowing model. Hence, the model is able to describe the driving behaviors of
motorcyclists in a proper way.
2) There are many arguments regarding acceptable assumptions on the non-lanebased movement. Most of the studies divided the non-lane-based movement into thelongitudinal movement and the lateral movement, and modeled the separate movementswith an assumption on a relationship between them. However, these approaches made themodels complex. In this study, the introduction of the safety space integrated the47

longitudinal movement and the lateral movement into one. Here, the direction of theacceleration vector is assumed to be perpendicular to the boundary of the safety space.
The assumption ensures that a motorcycle tends to move on the boundary of the safety
space and keeps the safety space from another vehicle.
3) The motorcycle has more freedom of the lateral movements than the car. The
more freedom it gets, the more safety it pays attention to. However, many models do notconsider safety factors such as reaction time and safety distance related to the descriptionof collision avoidance behavior. Hence, such factors should be taken into account when
applying the model to the motorcycle. The proposed model provided a threshold safety
space for accident prevention calculated by reaction time, relaxation time, and speed, sizeof a vehicle.
4) A big limitation exists in almost all conventional models when consideringinteractions of more than two vehicles in the very congested conditions. The present
model assumes that a subject rider responds to the most influential rider. In general, asubject motorcycle decelerates to avoid a collision with the most influential vehicle,
while paying lesser attention to other vehicles. When a rider wants to accelerate, it also
follows the most influential vehicle to get the highest value of acceleration. Hence, theseassumptions are understandable for congested situations. In the non-congested
conditions, maybe the behaviors of free-speed travelling, overtaking and filtering are notdescribed appropriately using these assumptions.
5) The biggest advantage of the motorcycle-following model related to the abilityof application is its simplicity, with only three parameters, and ease in calibration using
non-linear regression analysis. Although there could be different calibration results under
different traffic conditions, the model can be applied to microscopic simulation undermany different situations due to its simplicity.

486) This model has a high potential to analyze the issues of traffic safety because
the acceleration in each time step is updated continuously in the simulation progress. This
study uses Deceleration Rate (DR) to assess the safety level of motorcycles.
3.5 DATA COLLECTION
To calibrate the proposed model, data of the trajectories of vehicles over time arenecessary. Therefore, time-series trajectory data of each vehicle were recorded using avideo camera. One observation extracted from a video contains the information on theposition of a target motorcycle and other influential motorcycles at a given time. The next
observation for the same target vehicle was made after 0.5 s to capture changes in speed
and direction of these vehicles. Because the chapter covers only situations of thecongested motorcycle-only traffic, observations with non-congested situations and inwhich cars and bicycles were present were excluded from the video clips.
3.5.1 Survey location
Ho Chi Minh City has a high population of motorcycles, thus a good location to
conduct the survey. Two road segments on Phan Dang Luu Street and Cong Hoa Street
were selected for data collection. The first road segment is near an intersection and is 8.4
m wide. This segment has only one lane in the observed direction with motorcycles
running at an average speed of 20 km/h. The second road segment has 3 lanes in eachdirection, each lane being 3.65 m wide. The segment is about 100 m from the nearest
intersection. Motorcycles run at an average speed of 30 km/h and are allowed to use anylane that is available.
A video recorder was set up on a high building near the study location. Vehicle
movements on a 40-m-long road segment in the study direction (Figure 3.5) were
captured on video camera at 30 frames/s. The survey was conducted in the period of49

December 30–31, 2010, from 6:00 am to 8:00 am and 3:30 pm to 5:30 pm, to record
movements of motorcycles during peak hours. Each site was surveyed on two differentdays and 4 h worth of video clips were obtained from each site.

50

(a) Phan Dang Luu Street (Width=8.4 m, Length=40 m)

51

(b) Cong Hoa Street (Width=10.95 m, Length=40 m)
Figure 3.5 Two survey locations in Ho Chi Minh City.

52

In this study, a SONY PD170 camera with LCD monitor was employed toobserve the traffic flow. The original resolution of video was resized so as to display thevideo clips on any normal monitor. As a result, image video files with a resolution of1280 x 720 pixels were made to track the trajectories of vehicles. The resolutions of thevideo image related to the real sizes of two survey locations are listed in Table 3.1. Under
ideal situations, the error of tracking data is assumed to range in one pixel resolution.
Previous researches (Ahmed, 1999; Hidas, 2005; Lee et al., 2008) used the acceptable
pixel resolution which ranges from around 50 mm to 1300 mm. Therefore, the method of
tracking data in this study can provide data sets with high accuracy.

Table 3.1 Resolution of the video image at two locations
Pixel resolution
Phan Dang Luu Street Cong Hoa Street
Longitudinal (mm/pixel)
37.8
100.5
Lateral (mm/pixel)
42.3
34.3

3.5.2 Data extraction
Speed Estimation from Video Data (SEV) computer software was used to convert
video screen coordinates into roadway coordinates. This software was developed by
Minh et al. (2006). Input was in the video file format and the output was in Excel fileformat containing the trajectory data of traffic. A trajectory data set (X-axis and Y-axis
coordinates) for one vehicle was extracted by clicking on the positions of that vehicle inthe monitor at 0.5-s intervals, this being the average reaction time of a motorcyclist
according to Minh et al. (2006).
In this research, the SEV is used to track the trajectory of a subject vehicle andsurrounding vehicles. Clicking the mouse on the positions of their head is identified as53

one observation. The next observation of the same subject vehicle is collected after 0.5
sec. The study collected 7 to 10 observations for each subject vehicle.
As a result, 828 observations of 144 motorcycles in Phan Dang Luu Street and579 observations of 152 motorcycles in Cong Hoa Street were used to estimate theparameters of the proposed model. Although more motorcycles could have been
considered, it is unlikely that a larger sample would have made a difference to the results,
based on the many observations conducted.
3.5.3 Data description
The study presents the properties of safety space using two survey data sets. The
speed of motorcycles, the longitudinal distance and the lateral distance between subject
motorcycles and most influential motorcycles, and the relationships between them aredemonstrated.
Figure 3.6 shows the histograms of the speed at two road segments on Phan Dang
Luu Street and Cong Hoa Street. The two road segments have different road conditions,making the average speed of each segment different from each other. The road segment
on Phan Dang Luu Street is near an intersection and has only one lane in the observed
direction; thus, the average speed is around 20km/h. The road segment on Cong Hoa
Street has 3 lanes in each direction and is about 100 m farther from the intersection.
Hence, the average speed on this road segment is around 30 km/h higher than Phan Dang
Luu.
Figure 3.7 showed the scatter plots of the longitudinal distance against the lateral
distance and how these scatter plots change according to the speed. One point in the
figure will represent a relative position of the most influential motorcycle with respect tothe subject motorcycle in one observation. Therefore, the number of points is equal to thesample size.
54

(a) Phan Dang Luu Street(b) Cong Hoa Street
Figure 3.6 Histogram of the speed at two locations

55

(a) Phan Dang Luu Street

56

(b) Cong Hoa Street
Figure 3.7 Scatter plots of longitudinal distance against lateral distance57

The subject motorcycle is placed on the origin of the two-dimensional coordinate system.
From the results of the scatter plots, many assumptions on the safety space are verified asfollowings:
1) The scatter points demonstrate safety spaces surrounding the origin of thecoordinate system in which the subject motorcycle is placed. It can be concluded that the
motorcycle driver always keeps the safety space when running to avoid a possible
accident.
2) The data shows that safety spaces have the shape of an approximate halfellipse. Therefore, there is the relationship between longitudinal distance and lateral
distance and this relationship can be expressed by the equation of the half ellipse.
3) It was found that the safety space varies according to the speed. As the speed ofa subject motorcycle becomes higher or lower, the safety space is larger or smaller. The
longitudinal distance is likely proportional to the speed. However, the lateral distanceseems to be constant with the speed. These results provided evidences for the hypothesison the length of the semi-major axis and semi-minor axis of the ellipsoid safety space(see Section 3.2 and Figure 3.3).
4) By comparing the safety space between 2 different locations at the same speed
intervals: 6 ~ 8 m/s and 8 ~ 10 m/s, it shows that the safety space is likely not to dependon the road conditions such as number of lanes, and distance from the intersection (nearor far). This finding is consistent with the assumption made in calculating the safety
space.
5) The scatter patterns illustrate that the safety space varies across individuals
with different relaxation times. However, the difference in relaxation times amongindividuals is not considered in this research. The future research should pay attention tothis limitation.

58

3.6 PARAMETER CALIBRATION
The proposed non-lane-based model based on the concept of safety space wascalibrated by the regression analysis method. This model is formulated in Equation (3.5).
Suppose that the erroraD (t  TD )is normally distributed and observation data are independent.

­
§
2
§ §
··
·
y2
¸ B ¸ ¸  H if x t 0°  v& ¨ A exp¨  ¨ x
DE ¨¨ ¨ W v 2 W d 2 ¸
¸¸
°°
D
y
¹
© © D D
¹¹
©
(3.5)
®
§
2
·
§
·
§
·
°
y
¨
¨ ¨
¸ B¸¸  H
if  2d x d x d 0°  v&DE ¨ A exp¨  ¨
2 ¸
¸¸
W

d
D
y
¹
© ©
¹¹
©
¯°

To simplify the calculation of the nonlinear function, a few parameters are
assumed to be constant (see Table 3.2). The reaction time T of a motorcycle is taken to beequal to the mean value of the reaction time distribution, i.e., 0.5 s (Minh et al., 2006).
The lateral distance of the threshold safety space was measured to be 1.8 m from fielddata for two vehicles riding side by side. The physical size of a motorcycle is taken as theaverage size in reality.

Table 3.2 Given parameters for the motorcycle-only flow
Parameter
Value
0.5 s
Reaction time T
Lateral distance W
1.8 m
Vehicle size dx, dy length = 1.9 m, width = 0.8 m

SPSS software was used to derive the other parameters by solving the nonlinear
regression problem (see Table 3.3). All the parameters were calibrated at the statisticalsignificance level of 1%. The signs of the parameters A, B, and τ are positive because the59magnitude of the safety space level must have a positive value. The relaxation time τ at
the two different locations observed was almost the same: 0.5 s. As relaxation time isassumed to be the time required for the steering movement to change direction in
combination with the braking movement to change speed, in order to avoid a possible
collision, it should not differ between the two locations. This stable estimation result of
relaxation time strongly supports the reliability of the proposed concept of safety space.
Furthermore, interestingly, the estimated relaxation time is exactly equal to the reaction
time of 0.5 s. This means that drivers maintain their threshold safety space with a lateral
distance of 1.8 m and a longitudinal distance of the product of speed and reaction time.
The differences in the values of parameters A and B between the two locations show thatdrivers on Cong Hoa Street have a higher rate of acceleration than those on Phan Dang
Luu Street. Cong Hoa Street has three lanes and an average speed of 30 km/h, higher thanthe 20 km/h in Phan Dang Luu Street. A higher average speed implies a greater rate ofacceleration.

Table 3.3 Derived parameters for the motorcycle-only flow
Location
Parameter
A
B
W (s)

Phan Dang Luu Street
Estimate
Std. Error
t-value
4.031
0.874
4.61
0.470
0.122
3.85
0.501
0.054
9.28

Cong Hoa Street
Estimate
Std. Error
t-value
6.954
1.385
5.02
0.510
0.138
3.70
0.496
0.058
8.55

3.7 MODEL VALIDATIONThe estimated results were compared to field data to validate the model. The
study used statistical measures to calculate the value of errors. Root-mean-square (RMS)60

error, the measure of differences between estimated values and the field values, is asfollows:

RMS error =2
1
Vi E  Vi F¦
N i 1, N

(3.6)

where
= estimated value of speed at the ith observation= field value of speed at the ith observationN= number of observations

To measure the relative error, RMS percent error is derived as§ Vi E  Vi F ·1¸
RMS percent error =¦¨
N i 1, N ¨© Vi F ¸¹

2

(3.7)

The mean error and mean percent error are other quantitative measures expressed asfollows:

Mean error =1
Vi E  Vi F¦
N i 1, N

Mean percent error =§ Vi E  Vi F ·1¸¦¨
N i 1, N ¨© Vi F ¸¹

(3.8)

(3.9)

Positive and negative error values imply that the estimated value is over-predicted andunder-predicted, respectively.

61

These errors were calculated for the speed of motorcycles (see Table 3.4). RMS
error and RMS percent error of the speed are very small. Speed in Phan Dang Luu Street
is over-predicted because the mean error is positive. The mean speed error in Cong Hoa
Street is also positive. These indicators show that the proposed model well replicates theactual speed. To validate the zigzag movements of motorcycles, the observed swerving
maneuvers to the left or right from the current position were compared with the estimatedswerving maneuvers based on all the observations. The results in Table 3.4 show that
60.5% and 62.2% of the observed maneuvers in the two locations, respectively, could be
reproduced by the proposed model.
A new sample of trajectory data on the same Cong Hoa Street, but in the otherdirection, was extracted to confirm the validation of the proposed model. Parameters A
and B vary according to road conditions such as number of lanes, distances fromintersections, and limited speed, so the new data from the same street should exclude
those effects. A total of 994 observations for 120 motorcycles were taken from video
clips. The study used the estimated parameters of Cong Hoa Street to predict the speed of
motorcycles. The statistical analysis of the model showed stable predictions for the 2different samples.

62

Table 3.4 Statistical measures for the speed and the ratio of swerving maneuvers for the
motorcycle-only flow

Statistical
Measurement
RMS error (m/s)
RMS percent error
Mean error (m/s)
Mean percent error
Ratio of swerving
modeled correctly (%)

Phan Dang Luu
StreetValue
Cong Hoa Street

0.486
0.090
0.002
0.006

0.581
0.065
0.030
0.006

Cong Hoa Street(in anotherdirection)
0.636
0.069
0.035
0.006

60.5

62.2

63.2

3.8 SUMMARY
The chapter presented the concept of safety space developed for describing thenon-lane-based movement of the motorcycle. Safety space was introduced to describe thechanges of acceleration or deceleration behaviors in response to the changes of safetylevel of the safety space whose boundary is determined by the influence of othermotorcycles. For example, if an influential vehicle moves closer to or farther away from asubject vehicle, the safety space becomes smaller or larger; as a result, the perceived levelof safety decreases or increases and a subject vehicle decelerate or accelerate its speed.
The chapter also described the process of data collection for calibrating the
motorcycle-following model. The survey was conducted on December 30 – 31, 2010 in
Ho Chi Minh City, from 6:00 am to 8:00 am and 3:30 pm to 5:30 pm to observe traffic in
the peak hours. Two road segments were selected for survey locations. Vehicle
movements on 40 m long road segment in one direction were captured in videotape at thepace of 30 frames per second. Observation data on the positions of vehicles (X-axis andY-axis coordinate) were extracted by using SEV software. The discrete observations for atarget motorcycle and other influencing motorcycles were recorded after 0.5 sec. There63

are 4 to 8 observations for one motorcycle. In summation, 826 observations of 144
motorcycles at the Cong Hoa Street and 579 observations of 152 motorcycles at the Phan
Dang Luu Street were used for calibration.
In the calibration result, all the parameters were calibrated at the significancelevel of 1%. The average relaxation time τ at two different locations was approximately
equal to 0.5s. This stable estimation result of relaxation time strongly supported thereliability of the proposed concept.
In the model validation, the observed speed was predicted by the proposed modelwith a small RMS error and RMS percent error of speed. The proposed model could
correctly describe around 61% of swerving behaviors to the left or right. Another sampleof trajectory data on the same Cong Hoa Street, but in the other direction, was extracted
to confirm the validation of the model. Statistical measures for the speed showed stablepredictions for the two different samples.

64Chapter 4 THE TRAFFIC SIMULATOR
4.1 INTRODUCTION
In this chapter, a simulator is developed to simulate non-lane-based movements ofmotorcycles in the motorcycle traffic flow. The non-lane-based movements are
reproduced and the differences from the lane-based movements are verified.
The chapter starts with introductions of traffic simulation technique. Next, an
open source software package was chosen to develop a simulator based on the research
purposes. A detailed description on the simulator is presented including the mainfeatures, input models and calculation process. The chapter ends with the verification ofthis simulator.
4.2 TRAFFIC SIMULATION TECHNIQUE
Traffic engineering and transportation planning use simulation models ininvestigating traffic flow characteristics. These models are grouped into three types basedon the scale level of detail in description of traffic vehicles: microscopic, mesoscopic andmacroscopic.
Microscopic models track positions of each vehicle every second. The simulation
uses random number to generate vehicles from a deterministic rule, and then vehicles
select their speed based on the proposed moving rule described by differential equations
or other numerical methods. Macroscopic models assume traffic flows as fluid streams.
Traffic density, traffic volume and speed over time are simulated based on rules of fluid
streams. Hence, the former models tackle traffic on the micro-scale level of each vehicle
whereas the latter models pay attention to the macro-scale level of flow.
Mesoscopic models describe the traffic flow on the middle level of detail. Thesemodels assume that the road is divided into many cells of given size that can either be

65empty or occupied by other vehicles. Vehicles will go in one cell and move to anothercell based on the proposed rules of moving when going along a road.
Since this research focuses on issues of traffic accident caused by motorcycle
non-lane-based movements, it is appropriate to use the microscopic simulation models to
describe motorcycle driving behaviors at the level of individual vehicles and to simulate
how their movements affect the accident potential.
4.2.1 Agent-based microscopic simulation models
Microscopic simulation models are used to investigate the movements ofindividual vehicles in the traffic flow. Existing models proposed acceptable assumptionsof driving behaviors expressed by differential equations or other numerical methods.
Speed and direction of vehicles for moving ahead are decided based on the proposed
driving behaviors. Hence, microscopic models are capable to track positions of eachvehicle every second.
The agent-based modeling technique is popularly used for microscopic simulation
models of each vehicle’s driving behaviors. The term “agent” refers to an artificial life
agent (Franklin and Graesser, 1997). Agents act to meet the desired purpose bythemselves. They respond to other agents and the environment based on deterministic
rules. The agents have their characteristics, memory and even ability of learning fromexperiences. Therefore, after an agent is assigned these rules of driving behaviors, it iscapable to act like human in the traffic flow. This agent-based modeling technique is a
powerful tool to analyze characteristics of traffic flow by considering interactions andbehaviors of individual vehicles (Lee, 2008). Table 4.1 shows a list of agent-basedmodels based on developing history, tackled problems and corresponding software
packages.

66

Table 4.1 Agent-based models for the microscopic traffic simulation
Reference
Nagel

Tackled problem

Softwareand Flow – density diagram and shock wave.

TRANSIMS

Schreckenberg(1992)
Bazzan et al. Not-completely(1999)

considerationofrational

decision

mentalstatesmaking:likethe ITSUMO

emotions,

preferences, intentions.
El Hadouaj et Lane-changing
al. (2000)
Nagel

behavior

withconsiderationof ARCHISIM

forecasting duration of interaction.
and Large-scale of ten million travelers by implementing MATSim

Raney (2003)

the strategy generation and day-to-day agent-basedlearning.

Hidas(2002, Lane-changing behavior with cooperation of reducing ARTEMiS

2005)

speed and deceleration.

Palmianoet Heterogeneous traffic with midblock jeepney stops.

JSTOPSIMal. (2004)
Marchaland Location

Nagel (2007)

choiceofsecondaryactivities

with MATSim

exchanges of information through social network
connected by agents.

Lee

et

al. Heterogeneous

traffic

withmulti-vehicular BikeSim(2008)

interaction.

Rieser (2010)

Mode choice and schedule-based transit.

67

MATSim4.2.2 Tools for building traffic simulator
There are a large number of software packages which are available online forbuilding traffic simulator. Each traffic simulator has its features, different purposes ofusage and the accuracy of output results. Hence, this study will review traffic simulation
packages so as to choose the most suitable one for the research purpose. Somerequirements for software packages are presented below:
1) Open source
There are available open source simulation packages. Users can use thesesoftware free of charge. They can study and modify the source code for the research
purpose without any restrictions. However, only a few software products allow users tomodify or add a part of the source through providing tools to interact with main source.
2) Operating system
Many free software packages work under Linux operating system, and may not be
convenient if users run their computer on Microsoft Windows. Some errors could occur
when converting pictures and simulation movie clips from Linux to Windows. However,Linux and Mac OS X become more popular now and would be a good choice for
operating system.
3) Programming language
The popular programming languages are Java, Visual Basic and C.
4) Graphic presentation
This is an important factor for the users to see visual results of traffic simulation.
When running the simulation, the monitor shows movements of vehicles on the road andwhat traffic phenomenon could happen in real time. Therefore, graphic presentation is agood way to examine the verification of the simulator.

68

A number of open source software packages that meet the requirements ofbuilding a traffic simulator for this research are introduced in Table 4.2. This researchchose the open source software originally developed by Helbing et al. (2000) to build thesimulator for the motorcycle traffic. The main reason of the choice is that this researchattempts to compare performances between the social force model developed by Helbing
and the proposed concept of safety space (see Appendix A).

Table 4.2 Open source software packages
Software package or

Featuresname of author
SUMO

A microscopic traffic simulation deals with large-scale
network, route choice, vehicular communication.

Treiber (2009)

The software consists of two models: acceleration and lanechanging.

MATSim

A transport simulation toolkit provides a large scale network,
demand-modeling and traffic flow simulation.

MITSIMA microscopic simulation handles car-following model, lanechanging, traffic signal responding logic and route choicedecision based on real time route guidance information.

Helbing et al. (2000)

A simulation for pedestrian movements.

SWARM

Software toolkit offers a platform for agent-based modeling.

REPAST

A toolkit provides a simulation platform for agent-basedmodeling.

69

4.3 THE SIMULATOR
The research developed a microscopic simulator to analyze the characteristics ofthe non-lane-based traffic flow. The simulator used open source which was first
introduced for pedestrian simulation by Helbing et al. (1998). The research adopted open
source pedestrian simulation because of its modification flexibility and similar features ofdesign for non-lane-based movement modeling. The simulation program was written in
the C language and run under the Linux operating system. In the first section, the overalldesign of the simulator is presented. Then, components on each step of design process are
explained in the next section.
4.3.1 Overall design
The overall design consists of the input data and a loop-over process ofacceleration calculation and simulation outputs at every simulation time step, illustrated
in Figure 4.1.
The simulator can input data of network information, such as the length and widthof a road segment, origin-destination points, time-series of traffic rate on a road segment,
the estimated values of parameters of the threshold safety space, and the free speed of
motorcycles. Then, vehicles are generated at the original points.
The calculation process combines two different models (1) a free acceleration
model for describing the behavior of increasing speed to achieve free speed when no
influential motorcycles are running in front of a subject motorcycle and (2) the proposed
non-lane-based model for describing the behaviors of acceleration or deceleration wheninfluential motorcycles appear. After calculating acceleration, the system updates speeds
and determines the next movements of vehicles.
When vehicles arrive at destination points, they are removed from the roadsegment. The output of the program can show x, y coordinate value, speed, and70

acceleration of all the vehicles on a road over time in the form of text data and cancalculate traffic volume and density of the traffic flow.
The simulator updates calculation progress and output at 0.01 sec time intervals
and repeats them until meeting restraint conditions such as maximum simulation time,
maximum number of iterations or maximum number of vehicles.
Start
Load input data•••

A road segment length and width
Origin – destination points
Calibration parameters: safety space, free speed

Generate vehicles at origin

YES

Calculate acceleration• Based on motorcyclefollowing modelNO

Is there any influential
vehicle surrounding a
subject?

Calculate acceleration• Based on free acceleration
model

Update speed and position

YES

Remove vehicle froma road segment

Vehicle arrives at
destination?

NO

Simulation output•••

Vehicles positions in the real time
Traffic data : volume, density, speed
Graphical display: road segment, vehicle movements

UpdateNO

Terminate
simulation?

•••

real time = real time + time step
iteration = iteration + 1
number of vehicle = number of vehicle + 1

YES
Stop

Figure 4.1 Flow chart of the traffic simulation model

4.3.2 Components
This section presents the main components of the simulator in details.
The network and Original – Destination points

71

The simulator represents the network at the road segment level, based on the
research purpose. Here a straight road segment of 200 m length and 5.4 m width withuniform geometric characteristics such as the width of section and number of lanes is
considered. All the vehicles are inserted at origin points, ran on the road segment andremoved at destination points. When vehicles run at a free acceleration, they speed up in
the direction of the road. When vehicles meet obstacles, they will decrease speed andswerve left or right. However, they cannot go out of the road segment from both sides
because pushing forces along road side will be activated when vehicles approach.
The road segment is divided into square blocks with the width R= 0.5 m for each.
One block contains one vehicle inside it when the center of vehicle goes in the area of theblock. Hence the width of the block is set to be small enough to contain only one vehicle
at any point of time. When a vehicle moves out of the block i, the ID number of thevehicle will be deleted from the block i and inserted to the new one i+1. When a vehicle
wants to scan the surroundings to detect the influential vehicles, each block in thescanning area will inform whether a vehicle stays in or out of the block.
Original points and destinations points are set at two ends of the road segments.
One original – destination pair is placed on the same lane, especially when considering
car-following model simulation, as shown in Figure 4.2.

72

Figure 4.2 Screenshot of the simulator
Vehicle generation
The vehicles are generated randomly inside original points. The randomness
makes the initial relative positions between vehicles more realistic and produces thescattered plots of the traffic output data. In addition, vehicles are also generated
increasingly over the simulation time in the beginning duration, 800 sec, so as to achieve
the maximum traffic rate. Then, traffic rate is drawn from a normal distribution in which
the mean decreases with the simulation time (see Equation 4.1). When the queue of
waiting vehicles move backward and approach original points, vehicle generation is
stopped. This mechanism could simulate the traffic changing from a free flow to acongested flow (Lee et al., 2008).

Traffic rate (veh/sec)­Time
if Time d 800sec
°
°1000
®
§ 800
·
° Normal¨,0.252 ¸ if Time ! 800sec°© Time
¹
¯

73

(4.1)

Signal control
A signal is set at the end of the road segment. It is activated from the 801th sec of
the simulation time. The signal cycle of 60 sec has three displays: red, yellow (2 sec) andgreen. The length of the red light increases by 1 sec after every 120 sec of the simulation
progress. Hence, the simulation needs 2 hours to capture all the changes of red light that
affects the changes of traffic density.
Simulation time
The time to run a simulation is set to be 8000 sec.
Simulation output
The output results from the simulator are grouped into two types of data as
follows:
1) Disaggregate data: includes coordinates in the x-axis and the y-axis, speed andacceleration of each vehicle on a road segment in real time. The simulator provides not
only these data, but also graphical display of a road segment and movements of all
vehicles on the segment.
2) Aggregate data: includes mean speed, traffic volume and density of the traffic
flow on a road segment in real time. In order to achieve aggregate data, the traffic flow
on a 100-m-long target segment right behind the traffic signal is collected. The number oftraffic going through the downstream of the target segment is measured as the traffic
volume. The difference between the number of traffic at the upstream and thedownstream is measured as the density. The average speed of four test vehicles which runover 100 m on the target segment is calculated as the mean speed. When the traffic is afree flow, aggregate data is collected at every 30 sec of the simulation time. However,when it is a congested flow, collection time varies from 30 sec to 8 minutes depending on
the time needed for a test vehicle to finish running on the target segment.

74Model specifications
The models in the simulator determine the acceleration rate for each vehicle undera certain situation. In this simulator, two different models are combined: a freeacceleration model and the proposed motorcycle-following model. The rules for choosing
which model to use are as follows:
1) The road segment is divided into many blocks. For each subject vehicle, thesimulator scans the blocks which are occupied by the pre-determined safety space so as to
examine whether any influential vehicle exists inside the safety space or not. The
boundary of the pre-determined safety space is assumed to be far enough for a subject
motorcycle to perceive that it is not affected by influential motorcycles, i.e., it feels free
to accelerate its speed. For the simplicity of calculation, the boundary is supposed to be arectangle with the length and the width denoted byandas shown in

Width

(m)

Equation (4.2).

Pre-determined safety space = Length

(m)

(4.2)

2) When no influential motorcycles are inside the pre-determined safety space ofa subject motorcycle, the free acceleration model is selected to calculate traffic
acceleration rate as follows:a Dx , freev max  vDx
T freea Dy, free

0

75

(4.3)

where,are the free acceleration of a driverin the x-axis and the y-axis of a road, respectively andis the current speed on the x-axis.

maximum speed which the driverwishes to run and its direction is parallel to the x-

axis of a road.

is theis the time needed for changing from the current speed to the

maximum speed.
3) Otherwise, when influential motorcycles appear in the pre-determined safety
space of vehicle, motorcycle-following model is chosen to calculate the traffic

acceleration rate. If there is only one influential vehicle, then acceleration rate isdetermined as below:
­
2
§
§ §
··
·
y2
¸ B ¸ ¸ if x t 0°  v& ¨ A exp¨  ¨ x
DE ¨¨ ¨ W D vD 2 WD  d y 2 ¸
¸¸
°°
¹
© ©
¹¹
©
®
2
§
·
§ §
·
·
°
y
¨
¨ ¨
¸ B¸¸
if  2d x d x d 0°  v&DE ¨ A exp¨  ¨
2 ¸
¸¸
W

d
D
y
°¯
©
¹
©
¹¹
©

aD , following

where ⃗

⃗

⃗

(4.4)

denotes relative speed vector; parameter A represents themagnitude of the safety level; parameter B represents the effect of stretching out thesafety level value;safety space;is the current speed ;is the relaxation time on the x-axis of theis the lateral distance between two motorcycles on the y-axis of thesafety space; x and y indicate the current relative position of the influential vehicle with asubject vehicle on the x-axis and the y-axis;

anddenote the physical size of a

motorcycle on each axis. The direction of the acceleration vector ⃗whichshows the direction of motion and it is related to the gradient direction of the safety spaceas given by Equation (3.3).

76

If there are more than one influential vehicle and the acceleration of subject
vehiclecorresponding to the influential vehicle i is denoted by ⃗ , then acceleration

rate is determined as below:&&&&
max ^ aD 1 , aD 2 ,..., aDi ,..., aDN `

(4.5)

i

‖ ⃗ ‖ is given as the magnitude of the acceleration of vehicle

in response to the

influential vehicle i.
Emergency regime
This regime is applied in the situation when a vehicle takes an emergency brake to
avoid a collision with a preceding vehicle. The conventional regime proposed for the car(Yang and Koutsopoulos, 1996) assumed that if a following vehicle
smaller than a pre-determined threshold distancehas a headway, then its acceleration is

given as follows:aD ,emergency

where

2
­
­
½
v v

°min ®aD 1  D D 1 , aD ¾ if vD ! vD 12x®
¯¿°min a , a 
if vD d vD 1
D 1 D¯^`

denotes the acceleration of the preceding car

deceleration rate, i.e., the acceleration when applying a break;

,
,

(4.6)

is the normal
are speeds ofthe following car and the preceding car, respectively; x is the distance between two
consecutive cars. Equation (4.6) was applied for the one-dimensional movement of thecar. In this research, the equation is accepted to extend to two-dimensional motorcycle
movement as follows:77

Case 1: when a subject motorcycle follows a preceding motorcycle ()
If a motorcycle

follows another motorcyclewith the longitudinal

distance x smaller than a pre-determined longitudinal threshold distance,then a subject motorcycle applies an emergency brake to avoid an accident. The braking
accelerationof the motorcycleon the x-axis is similar to theacceleration of the car. For simplicity, a subject motorcycle is supposed to not haveenough time for swerving, i.e., accelerationon the y-axis is zero, as

expressed in Equation (4.7).

where

aDx ,emergency

2
­
­°
½°
vx  vx°min ®aDx 1  D D 1 , aD, x ¾ if vDx ! vDx 1
2x
®
°̄
°¿
°
x
, x
if vDx d vDx 1¯min aD 1 , aD

aDy ,emergency

0

^

(4.7)

`

is the normal deceleration rate on the x-axis. It is assumed that the speed

on the y-axis is not changing during the braking process but suddenly becomes zero when
its speedon the x-axis is zero. The assumption is acceptable because the speed on

the y-axis is very smaller than the speed on the x-axis; therefore, the movement on the yaxis has an insignificant effect on the rear-end collision between two motorcycles.
Case 2: when two motorcycles run alongside (If a subject motorcycle

running beside another motorcycle

lateral distance y smaller than a pre-determined lateral threshold distance| |)has the,the motorcycle is supposed to swerve farther away from an influential motorcycle to
avoid an accident. It means that it only changes the acceleration78

on the y-axis while keeping the same speed on the x-axis, i.e.,

as given in

Equation (4.8).

aDx ,emergency

0aDy ,emergency

2
­
­° y
½°
vDy  vDy 1° min ®aD 1 
, aD, y ¾ if y (vDy 1  vDy ) d 0, y t 0
2y
°
°̄
°¿
°
2
y
y
­°
½°
°
v v
® max ®aDy 1  D D 1 , aD, y ¾ if y (vDy 1  vDy ) d 0, y d 0
2y
°
°̄
°¿
°
y
, y
if y (vDy 1  vDy ) ! 0, y ! 0° min aD 1 , aD°¯max aDy 1 , aD, y
if y (vDy 1  vDy ) ! 0, y  0

^
^

where

(4.8)

`
`

is the normal deceleration rate on the y-axis. The equation is an extended

version of Equation (4.7) considering the case in which a motorcycle could perform the
backward running. The condition of

(

)

or

(

)

means

that two vehicles approach each other or move father away, respectively. The conditionoforshows that the influential motorcycle is on the right or left side of

the subject motorcycle. When an influential motorcycle approaches a subject vehicle on
the right side, then the acceleration

becomes negative and the subject motorcycle

will use the minimum value among emergency braking acceleration)(

to escape a possible accident or keep the acceleration of the preceding

motorcycle
the accelerationor the normal accelerationon the y-axis. On the contrary, whenbecomes positive, it will use the minimum value.

Stopping regime before traffic signal
A motorcycle is assumed to respond to signal control when the distance to thetraffic signal is less than the stopping distance79

on the x-axis given by:­° v x 2 min ½°
max ® D , x , Lsignal ¾°̄ 2aD°¿

Lsignal

(

where

)

is the distance for a motorcycle running with speed

decrease the speed at the deceleration
equation.

(4.9)

to

on the x-axis to a stop based on the motion

is a lower boundary of the distance.

When a motorcycle detects a traffic signal from a stopping distance, itwould decide to keep running or decrease the speed for a stop right before the signal.
While the signal is green or yellow, a driver would pass the signal if the moving time tothe signal is shorter than the remaining yellow time. Otherwise, a drive starts applying a
brake with the deceleration as follows:xaD ,signal
yaD ,signal

 vD2
2x
 vDy
( x vDx )where x is the distance from the current position of a motorcycle
stop line andrequired for a motorcycle(4.10)

with speed

to theare the decelerations on the x-axis and the y-axis
to stop safely before a traffic signal.

The deceleration in the stopping regime before traffic signal could be applied forthe lead motorcycles approaching the signal lights. For the following motorcycles, they
not only have to stop before the stop line, but also decelerate to avoid a collision with theleaders. Therefore, their deceleration will take the minimum value among a normal
following decelerationin Equation (4.4), a deceleration rate in the80emergency regime,

in Equation (4.7), (4.8) and a deceleration in the

stopping regime before traffic signal
aDx
aDy

in Equation (4.10) as follows:

^
min^a

min aDx ,emergency , aDx ,signal , aDx , followingyD ,emergency, aDy ,signal , aDy , following``(4.11)

When a traffic signal becomes green, the first leading vehicles accelerate freely
from the stop line according to Equation (4.3) and the queuing vehicles will follow theleaders to increase their speed according to Equation (4.4).
4.4 VERIFICATIONThis section presents the verification of the simulator. This simulator represents
the non-lane-based movements including oblique following and swerving movement.
Then, the differences between these lane-based movement and non-lane-based movement
are verified using the simulation results of the fundamental diagrams.
4.4.1 Reproduction of non-lane-based movements
A simulation was performed to test the original movements of motorcycles. The
oblique following behavior and swerving movement in a congested traffic situation werereproduced. The simulation conditions included a 200-m-long and 5.4-m-wide roadsegment. Traffic flow which is drawn from a normal distribution as given by Equation(4.1) changes from 0 to 9000 vehicles per hour. The free speed was set to be 28.8 km/h.
The estimated parameters of the model for the case of Phan Dang Luu Street and theother parameters were used for simulation as shown in Table 4.3.
Figure 4.3 shows the time-space diagram of the trajectories extracted fromsimulation progress at congested traffic flow rate of around 3200 veh/h. The traffic signal
is installed at a 180-m position on the 200-m-long road segment. The data on the traffic81flow behind the traffic signal is collected in a period time of 100 sec when the length of
the red light time is 15 sec.

82

Table 4.3 Parameters for simulations
Road size (length, width, in m)
Traffic flow (veh/h)Free speed(km/h)
A
B
Relaxation time W (s)Reaction time T (s)Lateral distance W (m)Vehicle size (meter length, meter width)
Safety space for free acceleration(meter length, meter width)
Time needed for changing from the current speed to the
maximum speed(s)Threshold distances in the emergency regime ( meter
length, meter width)
Lower boundary of stopping distance before traffic
signal(m)

83(200.0, 5.4)
From 0 to 9000
28.8
6.954
0.510
0.5
0.5
1.8
(1.9, 0.8)
(2 +3.8, 2.6)
1.5
(0.5 +3.8, 1.0)
20

180

Longitudinal distance (m)

160

140

120

100

80

60
100

110

120

130

140

150

160

Time (s)Figure 4.3 Time-space diagram of the trajectories
84

170

180

190

200

From the trajectories in Figure 4.3, oblique following and swerving movement are
confirmed.
Oblique Following
The simulation reproduced oblique following, which is a very typical motorcycle
non-lane-based movement in congested traffic. A motorcycle rider prefers to follow
another vehicle at an oblique angle so as to achieve a larger safety space relative to the
influential vehicle in front.
The oblique following behavior of a motorcycle is shown in the time-space
trajectories as illustrated in Figure 4.4. Each point in the figure represents a position of
the most influential motorcycle or the subject motorcycle in every 0.5 sec. Many
motorcycles are observed to keep very small headways in the long time while following
another along the road segment before approaching the traffic signal.

Lateral distance (m)The most influential vehicle

The subject vehicle

1.5

1
0.5
0
100

110

120

130

140

150

Longitudinal distance (m)Figure 4.4 Time-space trajectories of the oblique following

85

160

Swerving Movement
The swerving movement of a motorcycle was also observed by simulation. Thisbehavior shows the sudden swerving in response to changes in the lead vehicle’s speed.
The simulation results showed that motorcycles swerve in response to avoid collision asshown in Figure 4.5.
Swerving behaviors can be observed when motorcycles approach the signal. The
first motorcycles detecting the red light will decelerate their speed to a stop. Then many
following motorcycles also decrease their speed to avoid colliding with the leaders,revealing shock waves in the motorcycle traffic flow. Some other following motorcycles
are observed to swerve left or right and consequently overtake their leader in order tomove ahead. The trajectories of the swerving motorcycles are chaotic, and cross that of
the leading motorcycles as illustrated in Figure 4.3.

Lateral distance (m)2.5

The most influential vehicle

The subject vehicle

2

1.5

1
110

120

130

140

150

160

170

Longitudinal distance (m)Figure 4.5 Time-space trajectories of the swerving movement

86

180

4.4.2 Differences from lane-based movements
Very few studies have compared the lane-based movement with the non-lanebased movement because it is difficult to find a general equation that can cover both.
Interestingly, the concept of safety space could also be applied to describe the lane-based
movement, such as the car-following model. The difference between these two
movements is verified using the simulation results of fundamental diagrams.
Consistency with the Car-Following Equation
It can be demonstrated that the car-following model is just a special case of the
non-lane-based model expressed by Equation (4.12) and (4.13).

&aD­§ § x2
·
·
§
·
yv y
y2
¸ B ¸ &1 ¨ xvx ¸ if x t 0° A exp¨  ¨

2
2
2
2
¸
¨
¸
¨ ¨ W D vD
¸
v
°
W

d
W
v
W

d
D
y
D
y
°
¹
¹
© ©
¹ DE © D D(4.12)
®
2
§ §
· 1
·
yv
y
°
y
¨ ¨
¸ B¸ &
if  2d x d x d 0
2 ¸° A exp¨  ¨¸ vDE WD  d y 2
W

d
D
y
°
¹
© ©
¹
¯

&
aD
&
aD

­  VE
if aD d 0°
°  VE®  VE°
if aD ! 0
°  VE¯(4.13)

Assuming that in the car-following model, cars follow their leaders withoutchanging their lane, Equation (4.12) can be reduced to a one-dimensional movement asfollows:aD (t  TD )§ § x2 ·
· x
vDE
¸
¸
A exp¨  ¨¨
B
&
2
2
¸
¨
¸W v
© © W D vD ¹
¹ D D vDE

87

(4.14)

Here, the appearance of the relative speed

in Equation (4.14)

shows the basic equation for the car-following model. Equation (4.14) becomes anonlinear car-following model representing the effect of the distance between the leader
and the follower.
Comparison of the Fundamental Diagrams
Equations (4.12), (4.13) and (4.14) for non-lane-based and lane-based movements
of motorcycles, respectively, were applied using the parameters estimated for Phan Dang
Luu Street to predict the fundamental diagrams of traffic flow. For lane-based
movements, the original road segment of 5.4 m in width was divided into three virtual
lanes, each 1.8 m wide. It is assumed that motorcycles run on these virtual lanes. A
sensitivity analysis was conducted with three values for reaction time, namely, 0.3 sec,
0.5 sec and 0.7 sec to confirm the stability of the simulation results.
The results are shown in Figure 4.6. Because the free speed and reaction time are
the same for all motorcycles, the dispersion of the output data is small. Motorcycles run
at the free speed of around 28.8 km/h in the non-congested situation and then slow down
to 1.0 km/h in response to congestion.
For all the cases of different reaction times, two basic differences were foundbetween these movements. Firstly, lane-based traffic flow shows a better performance,i.e., higher speed, traffic flow, and density. This is logical since lane-based movement
excludes the influences of movements in the lateral direction, such as swerving left or
right. Secondly, non-lane-based behaviors lead to a greater decrease in traffic volume
under the congested conditions. This is clear because non-lane-based motorcycles need alarger width for the safety space than lane-based motorcycles in a fixed lane width.
Therefore, lane-based movement shows a better efficiency of operation. Furthermore, as

88the traffic flow improves, the required reaction time reduces. This means that riders withshorter reaction time will contribute less to traffic congestion than riders with longer
reaction time.

89

Non-lane-based

Speed(km/h)

Lane-based

30
25
20
15
10
5
0
0

2000

4000

6000

8000

10000

Flow
(veh/h)Non-lane-basedFlow(veh/h)Lane-based

10000
8000
6000
4000
2000
0
0

500

1000

1500

2000

Density(veh/km)Non-lane-based

Speed(km/h)

Lane-based

30
25
20
15
10
5
0
0

500

1000

(a)

90

1500

2000

Density(veh/km)Non-lane-based

Speed(km/h)

Lane-based

30
25
20
15
10
5
0
0

2000

4000

6000

8000

10000

Flow
(veh/h)Non-lane-basedFlow(veh/h)Lane-based

10000
8000
6000
4000
2000
0
0

500

1000

1500

2000

Density(veh/km)Non-lane-based

Speed(km/h)

Lane-based

30
25
20
15
10
5
0
0

500

1000

(b)

91

1500

2000

Density(veh/km)Non-lane-based

Speed(km/h)

Lane-based

30
25
20
15
10
5
0
0

2000

4000

6000

8000

10000

Flow
(veh/h)Non-lane-basedFlow(veh/h)Lane-based

10000
8000
6000
4000
2000

Density

0
0

500

1000

1500

2000 (veh/km)

Non-lane-based

Speed(km/h)

Lane-based

30
25
20
15

10
5
0

0

500

1000

1500

2000

Density(veh/km)(c)
Figure 4.6 Fundamental diagrams: (a) reaction time = 0.3 s, (b) reaction time = 0.5 s, and(c) reaction time = 0.7 s.

92

4.5 SUMMARY
The chapter introduced the agent-based technique for traffic simulation. An open
source software package was selected to develop a simulator based on the research
purposes. The computer simulation reproduced two basic types of non-lane-based
movements: oblique following and swerving. A comparison of the fundamental diagrams
between the non-lane-based movement and the lane-based movement was carried out.
The findings indicated that the lane-based traffic flow shows a better
performance, i.e., higher speed, traffic flow, and density than the non-lane-based. In
addition, non-lane-based behavior decreases traffic volume to a greater degree than lanebased behavior does under congested traffic condition. At last, riders with shorter
reaction time contribute less to traffic congestion than riders with longer reaction time.

93Chapter 5 SAFETY SPACE FOR CAR AND MOTORCYCLE IN THE
MIXED TRAFFIC FLOW
5.1 INTRODUCTION
This chapter focuses on the characteristics of the mixed traffic flow; a flow which
is very common in Asian developing countries. In the mixed traffic flow, cars run on lanebased on the lane-based movement and motorcycles could run on the same lane and moveto the lane of cars based on the non-lane-based movement. When cars and motorcycles
share the same lane, interactions between cars and motorcycles happen. For example,
when the density becomes high, high-speed motorcycles prefer to move to the outer lane
often used by cars to enjoy larger clearances on this lane. Then cars have to slow down so
as to keep a safe distance to avoid accident with the motorcycles. These interactions
between cars and motorcycles that affect speed-flow relationship of the mixed flow wereverified in many literatures. Kov and Yai (2010) indicated that mean speed of the traffic
flow decreases tremendously when the number of cars increases. Other researchers
estimated PCU (Passenger Car Unit) values for motorcycle (Lee et al., 2010) or MEU(Motorcycle Equivalent Unit) value (Y et al., 2010) with considerations on the
differences of sizes between cars and motorcycles.
The study aims to investigate the characteristics of the mixed traffic flow that
affect traffic safety. When running behind another vehicle, drivers must keep a distance
far enough to avoid an accident. If a driver underestimates the safety distance, a collision
may happen. The distance is likely dependent on the type of the vehicle. Therefore, theresearch problems are stated as: (1) how long the car and the motorcycle keep their safety
distances with surrounding vehicles, (2) how the safety distances differ when the vehicle
ahead is a car or a motorcycle.

94This chapter introduces an application of the concept of safety space to describe
the movements of cars and motorcycles in the mixed traffic flow. Then, by using survey
data of the mixed traffic flow collected on the same location as the one in Chapter 3,
parameter estimation is conducted. From the estimated parameters, safety spaces of car
and motorcycle are calculated, and these results are discussed. The chapter ends with ashort summary.
5.2 A MODEL FOR THE MIXED TRAFFIC FLOW
The interactions between car and motorcycle in the mixed flow are observed
when one vehicle (car or motorcycle) controls its speed to respond to the change in speedof an influential vehicle (car or motorcycle) ahead or on its side. It is assumed that a
subject vehicle responds to only one influential vehicle at a time. The influential vehicle
is determined by Equation 3.4. Generally, there are four cases of interactions; case 1: thesubject vehicle is a motorcycle, the influential vehicle is a car, case 2: the subject vehicle
is a car, the influential vehicle is a motorcycle, case 3: both the subject vehicle and theinfluential vehicle are motorcycles, case 4: both the subject vehicle and the influential
vehicle are cars. In this research, case 3 was already considered in the chapter 3. Case 4 is
excluded due to a lack of survey data, and due to the fact that this scenario is alreadyinvestigated in many conventional literatures. Hence, case 1 and case 2 are analyzed inthis chapter. Based on the concept of safety space, this research constructs safety spaces
for car and motorcycle to describe the movements of each type of vehicles in two
different cases of interaction.
Case 1 the subject vehicle is a motorcycle, the influential vehicle is a car
The safety space for a subject motorcycle is assumed to be determined by the
combination of a half ellipsoidal boundary and two parallel lines, similar to the safety
space in Chapter 3. Here, the safety space of a subject motorcycle crosses the center of95the car’s rear (see Figure 5.1). The distance (x,y) between two vehicles is measured fromthe center of the front side of motorcycle

to the rear side of car

.

Y

d Cx

d Cy

W M v MD

WM

X

d My
d Mx

 d Mx  d Cx

( x, y )Figure 5.1 Safety spaces for a motorcycle when an influential vehicle is a car

The threshold safety space is defined as the minimum level safety space that
could still be considered safe. The safety distance on the semi-major axis denoted by, whereis the average relaxation time of motorcycles andof a subject motorcycle. The safety distance on the semi-minor axis is given by, whereis the lateral distance between a motorcycle and a

car when two vehicles run side by side.
and

and

motorcycle,

is the speed

anddenote the size of the motorcycle

denote the size of the car. Hence, the acceleration of a subject
affected by an influential car can be expressed by Equation 3.2, andthis equation becomes:

96a MD (t  T )

­
§
§ §
··
·
x2
y2
¸ B ¸ ¸ if x t 0°  v& ¨ AM exp¨  ¨M22MDCE ¨¨ ¨ W M vMD¸¸°
WM  0.5d My  0.5d Cy ¸¹
°
© ©
¹¹
©
®
2
§
·
§
·
§
·
°
y
¨
¨ ¨
¸ B ¸ ¸ if  d  d d x d 0
M ¸
Mx
Cx
°  v&MDCE ¨ AM exp¨  ¨
2 ¸
¸
W

0
.
5
d

0
.
5
d
M
My
Cy
°
¹
© ©
¹¹
©
¯

(5.1)

where AM and BM are acceleration parameters of a motorcycle; T is average reaction time,
0.5 s; t is real time; x and y are distances between two vehicles in the x-axis and the yaxis; ⃗denotes the relative speed vector between the motorcycle

and the car.

Case 2 the subject vehicle is a car, the influential vehicle is a motorcycle
The safety space of a car has a different shape from that of a motorcycle. As cars
only run on lane, its safety space is assumed to be a rectangle which consists of two sides
parallel to each other, one side crossing the center of the car’s front and another sidecrossing the center of the influential motorcycle’s rear. Observations of the situation inwhich cars and motorcycles run on the same lane have showed that cars also can swerve
left or right in the same lane when approaching motorcycles. In the survey location, eachlane of the road is around 3.6 m wide and the average width of the car is measured ataround 1.6 m. Therefore, cars have a side clearance of 1 m wide on both sides and they
can turn left or right within this clearance. Based on the observations, the safety space ofcars consists of a rectangle in the middle and a quarter of the ellipse on each side as
illustrated in Figure 5.2. The distance (x,y) between two vehicles is measured from thecenter of the front side of the motorcycle

to the rear side of the car.

The threshold safety space for the car is defined in the similar way to case 1. The
safety distance on the semi-major axis is denoted byrelaxation time of cars and, whereis the speed of a subject car

the semi-major axis is given byis the average. The safety distance in, whereis the lateral

distance or the side clearance when two vehicles run side by side. Therefore, the97acceleration of a subject car,affected by an influential motorcycle can be based on

Equation 3.2, and this equation becomes:aCD (t  T )

­
2
§
§ §
··
·
y2
¸ BC ¸ ¸ if y ! 0.5d Cy , x t 0°  v& ¨ AC exp¨  ¨ x
22
CDME ¨¨ ¨ W C vCD¸¸°WC  0.5d My  0.5d Cy ¸¹
© ©
¹¹
©
°
2
§
·
§
·
°
§
·
x
°
¸ BC ¸ ¸ if y d 0.5d Cy , x t 0®  v&CDME ¨¨ AC exp¨¨  ¨¨
2 ¸
¸¸
W
v
°
© © C CD ¹
¹¹
©
°
2
§
§ §
··
·
y
°  & ¨ A exp¨  ¨¸ BC ¸ ¸ if  0.5d Mx  0.5d Cx  x  0
v
C
2
C
D
M
E
°
¨
¨ ¨ WC  0.5d My  0.5d Cy ¸
¸¸
°
¹
© ©
¹¹
©
¯

(5.2)

where AC and BC are acceleration parameters of the car, and ⃗speed vector between the car

and the motorcycle

denotes the relative

.

Y

d Mx

d My

WC

W C v CD

X

d Cy
d Cx

( x, y ) d Mx  d Cx

Figure 5.2 Safety spaces for a car when an influential vehicle is a motorcycle

985.3 PARAMETER CALIBRATIONThe study used the data collected on Cong Hoa Street in calibrating the model.
The methodology of collecting data for the mixed flow is similar to the one for the
motorcycle-only flow in Chapter 3. Observations for the mixed flow capturing cars andmotorcycles were recorded every 0.5 sec. Observations during uncongested conditions
and observations with bicycles, buses and trucks were excluded from data sample. In case
1, one observation records one subject motorcycle, one influential car and otherinfluential motorcycles surrounding the subject. In the case 2, one observation includes
one subject car and other influential motorcycles. For each subject vehicle, there are 7 ~10 observations. As a result, 631 observations for 108 subject motorcycles were used toestimate the parameters in the case 1, and 615 observations for 82 subject cars were used
to estimate the parameters in the case 2.
The proposed equations of calculating acceleration were calibrated by regression
analysis method. In the case 1, the subject vehicle is a motorcycle and the influential
vehicle could either be a car or a motorcycle. If the influential vehicle is a car,acceleration is formulated as shown in Equation (5.1). If the influential vehicle is a
motorcycle, acceleration is formulated based on Equation (3.2). Therefore, parameterswhich were estimated in Equation 3.2 are used as given parameters for calibrating
parameters in case 1. Moreover, to simplify the calculation of the nonlinear function,
several parameters are assumed to be constant. Reaction time T is 0.5 sec across all thedrivers.

is the lateral distance, 1.8 m, measured from the field data when two

vehicles run side by side.

anddenote the size of the motorcycle which is 1.9

m long and 0.8 m wide.

anddenote the size of the car measured to be 4.8 m

long and 1.6 m wide (see Table 5.1).

99

Table 5.1 Given parameters for case 1: the subject vehicle is a motorcycle, the influential
vehicle is a car
Parameter
Value
0.5 s
Reaction time T
Lateral distance WM
1.8 m
Motorcycle size dMx, dMy length = 1.9 m, width = 0.8 m
Car size dCx, dCy
length = 4.8 m, width = 1.6 m
A (case 3)
6.954
B (case 3)
0.510
W (s) (case 3)
0.496

In the case 2, the model is formulated as shown in Equation (5.2). Several
parameters are assumed to be similar to case 1. The lateral distance WC of the car ishypothesized to be equal to the side clearance of 1 m (see Table 5.2). The reason for thisis that the width of each road lane is around 3.6 m wide and the average width of the car
is around 1.6 m; thus, cars enjoy a side clearance of 1 m wide on both sides.

Table 5.2 Given parameters for case 2: the subject vehicle is a car, the influential vehicle
is a motorcycle
Parameter
Value
0.5 s
Reaction time T
Lateral distance WC
1.0 m
Motorcycle size dMx, dMy length = 1.9 m, width = 0.8 m
Car size dCx, dCy
length = 4.8 m, width = 1.6 m

SPSS software was used to derive the other parameters by solving the nonlinear
regression problem (Table 5.3). All the parameters had a statistical significance level of
1% except for parameter BC whose t-value is 1.42. The relaxation time of motorcycle is0.457 s, smaller than the relaxation time estimated in Chapter 3 which is nearly 0.5 s.
This means that motorcycles keep a smaller safety space when moving near a car than100

when moving near another motorcycle. It makes sense because cars seldom change theirdirections, and seldom suddenly change their speed, compared with motorcycles. The
relaxation time of the car is 1.529 s, longer than the one of the motorcycle. This is clear
because field observations on the mixed traffic flow showed that the car keeps a longer
headway than the motorcycle.

Table 5.3 Derived parameters of acceleration for the motorcycle and the car in the mixed
flow
Case 2 (Car)
Case 1 (Motorcycle)
Parameter Estimate Std. Error t-value Parameter Estimate Std. Error t-valueAM
10.127
2.995
3.38
AC
2.616
0.307
8.52
BM
0.402
0.129
3.11
BC
10.932
7.689
1.42
0.457
0.059
7.77
1.529
0.256
5.97
(s)
(s)

Errors for the speed of motorcycles and cars in two cases were calculated (seeTable 5.4). Speed RMS error and RMS percent error are very small. The mean speed
error and percent error is nearly 0. These indicators show that the proposed model well
replicate the actual speed. Table 5.4 shows that 67.5% and 63.2 % of the observed
maneuvers for the motorcycle and car, respectively, could be reproduced by the proposedmodel.

101

Table 5.4 Statistical measures for the speed and the ratio of swerving maneuvers of the
motorcycle and the car in the mixed traffic flow
Statistical
Measurement
RMS error (m/s)
RMS percent error
Mean error (m/s)
Mean percent error
Ratio of swerving
modeled correctly (%)

Value
Case 1(Motorcycle)
0.674
0.108
-0.0290.003
66.4

Case 2
(Car)
0.539
0.064
0.041
0.008
63.2

5.4 DISCUSSIONS ON SAFETY SPACES OF THE MOTORCYCLE AND THE CARThis section will provide discussions on the threshold safety space andacceleration for the motorcycle and the car based on the resulting parameters estimated inthree cases: case 1, 2 and 3.
5.4.1 Threshold safety space for motorcycle and car
As the average speed of a subject vehicle is assumed to be 7.0 m/s, the thresholdsafety space of the car and the motorcycle in three cases are illustrated in Figure 5.3. Bycomparing case 3 to case 1, it was found that motorcycles keep a smaller safety space infront when moving near a car than when moving near another motorcycle. Motorcycles
feel safer when running behind cars because cars usually run on lane and do not change
direction very often. This could be a big risk for collision between cars and motorcycles
because the headway between them was measured to be only 0.457 s, which is shorter
than the reaction time, 0.5 s. This finding could explain the statistic results of Hung andNguyen (2008). They reported in a paper that in 2008 in Hanoi, the number of collisionper 10,000 vehicles between car and motorcycle accounted for 48% while the number ofcollision between motorcycle and motorcycle accounts for 29%.

102

From the results of case 1 and case 2, while cars keep a very long headway of
10m, motorcycle run behind the car at around 3 m. This explains the phenomenon bywhich motorcycles prefer to move to the lane of cars to enjoy the clearance of 10 m. The
more motorcycles switch to the car-lane, the more cars decrease speed to keep the safe
distance. As a result, the speed of the car becomes lower than that of the motorcycle inthe congested situations (Kov and Yai, 2010).

103

Safety spaceY

Threshold safety space

2.6 m
X

3.5 m

3.8 m

Case 3: Both a subject vehicle and an influential vehicle are motorcycles

Y

3.0 m
X

3.2 m

6.7 m

Case 1: A subject vehicle is the motorcycle, an influential vehicle is the car

Y

2.2 m
X

1.6 m
10.7 m

6.7 m

Case 2: A subject vehicle is the car, an influential vehicle is the motorcycle
Figure 5.3 Threshold safety space for the motorcycle and the car in the mixed traffic flow104

5.4.2 Comparison of acceleration between motorcycle and car
This research compares the difference in acceleration between the cases ofmotorcycle to motorcycle interaction (case 3) and motorcycle to car interaction (case 1).
Suppose that a subject motorcycle is approaching its influential vehicle (car or
motorcycle) ahead, at an initial position of 5 m longitudinal distance and 0.5 m lateral
distance, in the speed of 7.0 m/s and relative speed of -1.5 m/s. There, the influential
vehicle ahead does not change its speed, the subject motorcycle has to decrease its speed
and change its direction of movement. Based on these assumptions, the accelerations withrespect to distances in both case 1 and case 3 were computed. Figure 5.4 (a) indicated thata subject motorcycle starts applying a brake later when the influential vehicle is a carthan when the influential vehicle is another motorcycle. Therefore, its acceleration isslower when it is farther and becomes suddenly faster when it is nearer to avoid apossible accident with the car. When the relative speed of two vehicles is zero at a
distance of around 1.3 m, a subject motorcycle begins to increase its speed to follow thehead vehicle. Figure 5.4 (b) confirms the swerving of the motorcycle when changing its
direction to avoid an accident. When two vehicles run side by side at the longitudinal
distance of 0 m, the two vehicles keep the lateral distance of around 1.8 m long enough to
avoid a side collision. In summary, motorcycles are likely to decelerate its speed in thelater time when running behind cars and hence they need a harder brake to escape therear-end accident with cars.
There are difficulties when comparing acceleration of the motorcycle in case 1 tothe car in case 2 under the same situations because, apparently, cars keep headways ofaround 3 times longer than motorcycles do. With this observation, this research further
examines the shape of the car acceleration in case 2.

105

It is assumed that a car is approaching its influential motorcycle ahead on onedimensional coordinate system at an initial position of 30 m with the speed of 7.0 m/s andrelative speed of - 4.0 m/s. If the influential motorcycle ahead does not change its speed,
the subject car has to decrease its speed. The acceleration results are illustrated in Figure
5.4 (c). It was found that cars start braking from a very long distance of over 30 m. The
deceleration increases slowly until the relative speed between the car and the motorcycle
ahead of it is zero. Then, when the speed of a car is slower than that of the motorcycle,
the car will increase its speed to follow the leader. After the speed of the car is higher
than that of the motorcycle, the car will again brake to decrease its speed. This process isrepeated over time while the distance between them is smaller. In conclusion, cars arefound to respond to motorcycles ahead at a farther headway than motorcycles do because
cars cannot change their movement direction in the same manner as motorcycles can.

106

0.40

Longitudinal distance (m)Acceleration (m/s2)

0.20
0.00
-0.20

0

1

2

3

4

5

-0.40
-0.60
-0.80
-1.00
Case 3 Interaction between motorcycle and motorcycle
Case 1 Interaction between motorcycle and car

(a)
0

1

2

3

4

5

0.00

Longitudinal distance (m)Lateral distance (m)

-0.50
-1.00
-1.50
-2.00
-2.50
Case 3 Interaction between motorcycle and motorcycle
Case 1 Interation between motorcycle and car

(b)
1.0
0.8

Acceleration (m/s2)

0.6
0.4

0.2
0.0
-0.2

0

5

10

15

20

25

30

-0.4
-0.6
-0.8

Longitudinal distance (m)-1.0Case 3 Interaction between car and motorcycle(c)Figure 5.4 Relationships between acceleration and distance in 3 cases of interaction1075.5 SUMMARY
To investigate the characteristics of the mixed traffic flow related to issues oftraffic safety, this research introduces an application of safety space to describe
movements of motorcycles and cars under congested traffic conditions. Safety spaces forthe car and the motorcycle are examined by considering their interactions in two cases:
case (1) the subject vehicle is a motorcycle, the influential vehicle is a car, case (2) the
subject vehicle is a car, the influential vehicle is a motorcycle. For each case, acceleration
parameters were estimated using field data collected on Cong Hoa Street, Ho Chi Minh
City. Almost all the parameters were significant at the significance level of 0.01.
This research also quantified threshold safety space for the car and the
motorcycle. By comparing acceleration in three cases of interaction, this research could
explain the differences between driving characteristics of two types of vehicles. First,
motorcycles are likely to decelerate its speed in a later time when running behind cars
hence they need a harder brake to escape a possible rear-end accident with cars.
Secondly, cars are found to respond to motorcycles ahead at a farther headway thanmotorcycles because cars cannot change their direction of movement in the same manneras motorcycles.

108

Chapter 6 MOTORCYLE SAFETY ASSESSMENT IN VIETNAM
6.1 INTRODUCTION
In Vietnam, motorcycle traffic safety is difficult to assess due to the lack ofaccident data as well as effective estimation models for the motorcycle. Hence, theapproaches to describe driving behaviors based on microscopic models are the important
tools to address this problem. Results from microscopic simulations are expected to bevery useful in understanding the characteristics of driving safety for the motorcycle
traffic flow in developing countries.
In the second section, the chapter presents new features of the safety space model
to assess the traffic conflict for motorcycle by considering factors such as accelerationand deceleration, and conditions of choosing a lead vehicle to accelerate. In the third
section, the model calibration for parameters estimation is summarized. As a model
application in the fourth section, a computer simulation is applied to evaluate traffic
conflict for motorcycle by calculating the probability of sudden braking when the densityof the motorcycle flow is altered. The last section summarizes the content of this chapter.
6.2 A MODEL FOR MOTORCYCLE TRAFFIC SAFETY ASSESSMENT
A model is developed to assess motorcycle traffic safety based on the concept ofsafety space. The safety space approach has a good potential in the analysis of traffic
safety. Many factors related to accident potential evaluation, are considered in theapproach.
6.2.1 Acceleration and deceleration
A rear-end collision happens when a preceding vehicle brakes suddenly and avehicle following crashes into it. A side-swipe collision is caused when a preceding
motorcycle swerves left or right suddenly and is hit on the side by a following

109motorcycle. In order to consider two types of collision, the safety space is determined by
two parallel lines connected to a half ellipsoidal boundary (see Figure 3.2). Equation (3.2)
of acceleration is rewritten after taking the derivative, as follows:

aD

where

­
§ § x2
·
·
§
·
yv y
y2
¸ B ¸ v 1 ¨ xvx ¸ if x t 0° A exp¨  ¨

αβ
2
2
2
2
¸
¨ τ v
¸
¨ ¨ τ α vα
¸
°
W

d
W

d
α
y
α
y
°
¹
© α α
¹
© ©
¹
(6.1)
®
2
§ §
·
·
§
·
yv
y
°

1
y
¸ B¸ v¨¸ if  2d d x  0
A exp¨  ¨αβx°¨ W d 2 ¸¨ W d 2 ¸
¨
¸
α
y
α
y
°
©
¹
©
¹
©
¹
¯

and

are relative speeds between a subject motorcycle and an influential

motorcycle in the axis x and y, respectively.
To verify the difference of numerical values between acceleration and braking,the study distinguishes acceleration and deceleration by replacing the original parameters(A,B) in equation (6.1) with two new parameter sets (Aacc,Bacc) and (Adec,Bdec).
yvy
xvx
When the acceleration is positive, i.e.,t 0 , then22
τ α vαWα  d yaD­§ § x2
·
·
§
·
yv y
y2
¸ B ¸ v 1 ¨ xvx ¸ if x t 0° Aacc exp¨  ¨
accαβ¨ τ v 2 W d 2 ¸¨ ¨ τ α vα 2 Wα  d y 2 ¸
¸
°
α
y
°
¹
© α α
¹
© ©
¹
®
§ §
·
·
§
·
yv y
y2
°
¨¨
¸ B ¸ v 1 ¨
¸ if  2d d x  0
A
exp
acc
x
°
¨ W  d 2 ¸ acc ¸ αβ ¨ W  d 2 ¸
¨
y
y
°
¹
© α
¹
© © α
¹
¯

(6.2a)

When the acceleration is negative, i.e.,

110

xvx
τ α vα2yvyWα  d y2 0 , then­§ § x2
·
·
§
·
yv y
y2
¸ B ¸ v 1 ¨ xvx ¸ if x t 0° Abcc exp¨  ¨

bcc
αβ
2
2
2
2
¸
¨ τ v
¸
¨ ¨ τ α vα
¸
°
W

d
W

d
α
y
α
y
°
¹
© α α
¹
© ©
¹
®
§ §
·
·
§
·
yv y
y2
°
¨¨
¸ B ¸ v 1 ¨
¸ if  2d d x  0
A
exp
bcc
bcc
αβ
x
°
¨ W d 2 ¸¨ W d 2 ¸
¨
¸
α
y
α
y
°
©
¹
©
¹
©
¹
¯

aD

(6.2b)

Equation (6.2a) and (6.2b) show that the acceleration will be zero when two
motorcycles come near each other, i.e., the distance between two motorcycles is zero.
This result is reasonable when a subject vehicle reacts to only one influential vehicle
during the journey, which is the same as in the case of car-following model. However,under congested situation, a motorcycle has to respond to many motorcycles, hence, amotorcycle is assumed to achieve maximum deceleration when nearing anothermotorcycle. The formulation of variable x and y at the maximum deceleration is easily
derived from equation (6.1) by taking the derivative of this function with respects tovariables of x and y as follows:( x, y )

where

(6.3)

is a value at which the derivative of the acceleration with respect to x when

, is zero;
when

­§
·
Bdec
y2
¸ if x  x , x t 0°¨ x0 d x  W D vD

,
y
0
2
¨
¸
2
°©
WD  d y¹®
Bdec ·°§¨¸ if y  y0 ,  2d x d x  0°¨ x, y0 r WD  d y
¸
2
¹
¯©

is a value at which derivative of the acceleration with respect to y
, is zero.

111

6.2.2 Conditions of choosing a lead vehicle to accelerate
A subject motorcycle needs to choose a lead motorcycle so as to accelerate its
speed and follow the leader. The conditions of choosing a leader are as follows:
Critical following angle φ0
A motorcycle feels safe and comfortable to accelerate and follow a leader
travelling ahead from it with an angle φ, which is smaller than the critical following angle
φ0 (See Figure 6.1). The critical following angle is related to maximum swerving angle
when a vehicle turns left or right to follow its leader.

2 : not a leader

Subject

φ0
φ1

Figure 6.1 The critical following angle of the motorcycle

Following route width RWα
A subject motorcycle will accelerate and follow any vehicle ahead of it if there
are no other vehicles on the following route. Consider vehicle 4 in Figure 6.2, the subject
vehicle could not follow it because vehicles 2 and 3 are inside the virtual “following
route”. The width RWα of the following route decides whether a vehicle runs on the routeor not. The route width is used when calibrating the parameters of the proposed model
because calibration data were discrete based on trajectory observations in every 0.5 s inchoosing a leader among many preceding vehicles after every 0.5 s.

112

1

Subject

3
2

RWD

4 : not a leader: Route width of subject vehicle α

Figure 6.2 The following route for the motorcycle to follow a leader

6.3 MODEL CALIBRATION
We used the same data sets in Chapter 3 for calibrating the model. Discreteobservations for a target motorcycle and other influential motorcycles were recorded
every 0.5 sec. There are 6 to 12 observations for the subject motorcycle. Observations inuncongested conditions and observations with cars and bicycles were excluded from data
sample. As a result, 826 observations for 144 motorcycles in Phan Dang Luu Street and579 observations for 152 motorcycles in Cong Hoa Street were used to estimate theparameters of the proposed model.
6.3.1 Parameter calibration
The proposed non-lane-based model based on the concept of safety space wascalibrated by the regression analysis method. This model is formulated in Equation (6.3).
To simplify the calculation of the nonlinear function, all drivers were assumed to havethe same reaction time T and several parameters were assumed to be constant (see Table
6.1). The reaction time of a motorcycle is taken to be equal to the mean value of thereaction time distribution, i.e., 0.5 s (Minh et al., 2006). The lateral distance of thethreshold safety space was measured from the field to be 1.8 m for two vehicles riding
side by side. Average size of the real motorcycles in the field is used for the parameter
113

values for vehicle size. Critical following angle is set to be 300 and the width of following
route is 2.0 m to achieve small errors of the estimation result.

Table 6.1 Given parameters when distinguishing acceleration and deceleration
Parameter

Value

Reaction time T (s)0.5Lateral distance W (m)1.8

Vehicle size dx (m), dy (m) length = 1.9, width = 0.8
Critical following angle(0)30Following route width (m)2.0SPSS software was used to derive the other parameters by solving the nonlinear
regression problem (Table 6.2). All the parameters have statistical significance level of
1% except for parameters

on Cong Hoa Street which t-value is 1.22. The signs of

the parameters A, B, andare positive because the magnitude of the safety space musthave positive values. The relaxation times

at the two different locations observed were0.57 s and 0.68 s. As relaxation time is taken as the time required for the combination of
the steering movement (to change direction) and the braking movement (to change speed)in order to avoid a possible collision, it does not differ largely for different locations.
These values of relaxation time are higher than the one, 0.5s estimated in Chapter 3
because when distinguishing acceleration and deceleration, motorcycles tend to increase
speeds to follow the further leaders, and as a result, the threshold space becomes larger
than the one in Chapter 3. The differences in the values of parameters A and B between
the two locations show that drivers on Phan Dang Luu Street have a smaller rate ofacceleration than those on Cong Hoa Street. Cong Hoa Street has three lanes and vehicles

114

travelling have an average speed of 30 km/h, which is higher than the 20 km/h in Phan
Dang Luu Street. A higher average speed implies a greater rate of acceleration.

Table 6.2 Estimated parameters when distinguishing acceleration and deceleration
Parameter
Aacc
Bacc
Adec
Bdec
W (s)

Phan Dang Luu Street
Cong Hoa Street
Estimate Std. Error t-value Estimate Std. Error t-value
2.147
0.476
4.51
4.850
1.000
4.85
3.046
1.242
2.45
3.005
2.461
1.22
11.9763.608
3.32
20.752
6.049
3.43
0.142
0.039
3.64
0.131
0.034
3.85
0.573
0.052
11.02
0.678
0.065
10.43

6.3.2 Model validation
These errors were calculated for the speed of motorcycles (see Table 6.3). RMS
error and RMS percent error of speed are very small. These indicators show that the
proposed model well replicates the actual speed. To validate the zigzag movements ofmotorcycles, the observed swerving maneuvers to the left or right from the current
position were compared with the estimated swerving maneuvers based on all theobservations. The results in Table 6.3 show that 63.0% and 63.7% of the observed
maneuvers in the two locations, respectively, could be reproduced by the proposedmodel. The rates of acceleration were also compared in the same way. 59.8% and 57.9%of the observed behaviors can be modeled correctly.

115

Table 6.3 Statistical measures of speed, ratio of swerving and acceleration modeled
correctly when distinguishing acceleration and deceleration
Parameter
RMS error (m/s)
RMS percent error
Mean error (m/s)
Mean percent error
Ratio of swerving modeled correctly (%)
Ratio of acceleration modeled correctly (%)

Phan Dang Luu
Street
0.481
0.091
0.026
0.010

Cong Hoa
Street
0.576
0.064
0.041
0.007

63.0
59.8

63.7
57.9

6.4 AN APPLICATION TO TRAFFIC SAFETY ASSESSMENT
In this section, traffic conflict situations in road segments are categorized by typesof maneuver. A measure for determining these conflict situations using microscopic
simulation is introduced. Then, a microscopic simulation is applied to calculate the safetylevel using the proposed traffic conflict measure. Lastly, the results on traffic safetyassessment are discussed.
6.4.1 Conflict situations at a road segment
Situations with many conflicts have a higher probability of accidents. This
research classified conflict situations at a road segment under congested conditions into
three basic types:
Type 1: a preceding vehicle applies a brake suddenly (rear-end collision).
Type 2: a preceding vehicle swerves left or right suddenly (side-swipe collision).
Type 3: two side by side vehicles speed up to follow a leader at the same time(side-swipe collision).

1166.4.2 Safety index: Deceleration Rate
Safety index is used for measuring the frequency and severity of conflicts such as
Gap Time, Time to Collision, Deceleration Rate. Here deceleration rate (DR) is adopted
to be a safety index for the motorcycle. DR is the value of deceleration taken by the
subject vehicle when it applies a brake to avoid a possible collision with other influential
vehicles. DR indicates an accident possibility and severity which was linked to crashangle and crash speed. If DRs exceed a given critical value, “sudden braking” is assumed
to happen. Because deceleration rates are available directly in the simulation model at
each time step, the probability of “sudden braking” can be calculated easily from thesimulation result.
6.4.3 Scenario settings for computer simulation
The simulator developed in Chapter 4 is employed to calculate the safety level
and acceleration of motorcycles.

100 m
5.4 m

Figure 6.3 Non-lane-based road segment for simulation

The simulation conditions included a 100-m-long and 5.4-m-wide road segment(Figure 6.3). All the vehicles are assumed to be identical. The estimated parameters of themodel for the case of Phan Dang Luu Street from Table 6.2 and the other parameters
shown in Table 6.1 were used. The free speed was set as 25 km/h, the maximum speed
taken from the data sample. Table 6.4 summarizes the basic settings of the scenario.

117

Table 6.4 Simulation parameters
Road size (length, width, in m)(100.0, 5.4)
Free speed (km/h)
25.0
Aacc, Bacc
(2.147,3.046)
Adec, Bdec
(11.976,0.142)
Relaxation time τ (s)0.573
Reaction time T (s)0.5oSwerving angle ( )30Route width (m)2.0Lateral distance W (m)1.8
Vehicle size (meter length, meter width)(1.9, 0.8)

6.4.4 Effects of flow density on traffic conflict
The simulation is performed for two purposes: (1) to test whether different typesof collision in a congested traffic situation can be reproduced or not, and (2) to verify
effects of flow density on the probability of “sudden braking” which increases accident
potential.
For the first purpose, 3 types of collision were confirmed when two vehicles
overlap each other. When a vehicle brakes suddenly and its reaction time is not shortenough to avoid a collision, the overlap will happen. Because overlapping vehicles still
keep their maximum deceleration during the overlap time, they will separate from eachother after a short time.
For the second purpose, it was found that higher flow density led to a greater
increase in probability of “sudden braking” in 2 cases of the given critical deceleration
rates, -0.4 m/s2 and -0.6 m/s2 as illustrated in Figure 6.4. This is clear, because safetylevel decreases quickly as motorcycles run near each other. Under congested condition,
when a motorcycle increase speed to turn left or right to follow its leader, an alongsidetravelling motorcycle perceives its safety space becomes smaller thus pushes a brake to118

escape a side-swipe collision. As a result, a vehicle behind the alongside travelling
vehicle also applies a brake to avoid a rear-end accident.
Although the probability of sudden braking cannot estimate the number ofaccidents, the increase in probability of sudden braking at high level flow density could
reflect the increase in probability of accident rates (Gettman and Head, 2003; FHWA,
1985; Kaub, 2002). Further research to investigate the relationship between sudden
braking counts and the number of traffic accidents should be taken into consideration in
the future.

2.5

Probability ofsudden braking(%)

2

Deceleration < -0.4 m/s2
Deceleration < -0.6 m/s2

1.5

1

0.5

Density(veh/m)
0
0

0.1

0.2

0.3

0.4

0.5

0.6

Figure 6.4 Effects of flow density on probability of sudden braking

119

0.7

6.5 SUMMARY
This study proposed new features of the motorcycle-following model to assess the
traffic conflict of the motorcycle. First, the difference of numerical values between
acceleration and braking was considered by introducing two new parameter sets foracceleration and decelerate. Second, the conditions considered in choosing a leader were
described, such as the critical following angle and the following route width.
Parameters of deceleration and acceleration are estimated. The observed speed
can be predicted by the proposed model with small RMS error. The proposed model cancorrectly reproduced more than 63% of swerving behaviors, to the left or right, andaround 58% of acceleration behaviors.
Conflict situations and an index of deceleration rate for the safety assessment
were discussed. A computer simulation was developed to assess the traffic conflict by
calculating deceleration rates at each time step when the density of the motorcycle flow
was changed. Simulation results confirmed 3 types of collision. The findings highlighted
that higher flow density led to a greater increase in probability of traffic accident.

120Chapter 7 CONCLUSIONS AND FUTURE WORKThis chapter begins with the conclusions corresponding to the research objectives
in chapter 1. Then, the recommendations on future work are presented at the end of thechapter.
7.1 CONCLUSIONS
1) To investigate the characteristics of non-lane-based movements of motorcycles
by considering driving behaviors in the congested conditions.
The basic difference between the car and the motorcycle is related to the lanebased movement of the former and the non-lane-based movement of the latter. In
comparison with the car, the motorcycle on the road possesses a smaller size and a better
ability of swerving to the left or right easily due to its two wheels. The observed driving
behaviors related to the non-lane-based movements were categorized by traffic situation
and road geometry. This research focuses only on the behaviors at the road segment
under congested situations such as alongside travelling, oblique following and swerving
movement. In this study, these behaviors are described by the motorcycle-following
model.
The literature reviews focused on conventional car-following models, the mixed
traffic flow models, and the pedestrian movement models. It is concluded that thedifficulties of developing a model to describe the non-lane-based movement comes fromthe assumptions of the relationship between the longitudinal movement and the lateral
movement. For the motorcycle, the more freedom it gets, the more attention it pays tosafety. Therefore, safety factors such as reaction time, safety distance, and speed
difference related to the description of collision avoidance behavior should be taken into
account.

1212) To propose a concept of safety space to describe these behaviors, i.e., dynamic
movements of motorcycles in traffic made up only of motorcycles.
The study presented the concept of safety space developed for describing the nonlane-based movement of the motorcycle. Safety space was introduced to describe thechanges in acceleration or deceleration in response to the changes of safety level of thesafety space, whose boundary is determined by the influence of other motorcycles. The
proposed concept can deal with the limitations of the previous models
The survey was conducted on 30th - 31th December 2010 in Ho Chi Minh City,
from 3:30 pm to 5:30 pm to observe traffic in the peak hours. Two road segments wereselected for survey locations. Vehicle movements on 40 m long road segment in one
direction were captured in videotape at the pace of 30 frames per second. Observation
data on the positions of vehicles (X-axis and Y-axis coordinate) was extracted by using
SEV software.
In the calibration result, all the parameters were calibrated at a significance levelof 1%. The average relaxation time τ at two different locations was nearly equal toreaction, i.e. 0.5s. This stable estimation result strongly supports the reliability of the
proposed concept.
In the model validation, the speed of the motorcycle was predicted by the
proposed model with a small RMS error and RMS percent error of speed. The proposedmodel could correctly describe around 61% of swerving behaviors to the left or right.
Another sample of trajectory data on the same Cong Hoa Street, but in the otherdirection, was extracted to confirm the validation of the model. Statistical analysis
showed stable predictions for the two different samples.
3) To develop a microscopic traffic simulator based on the concept of safety space
to verify the zigzag movements of the motorcycle.

122

A simulator was developed based on the proposed motorcycle-following model.
The computer simulation reproduced the two basic types of non-lane-based movements:
oblique following and swerving movement under congested situations.
A comparison of the fundamental diagrams between the non-lane-based
movement and the lane-based movement was carried out. The findings indicate that thelane-based traffic flow shows a better performance, i.e., higher speed, traffic flow, anddensity then the non-lane-based.
4) To investigate the characteristics of the mixed traffic flow that affect traffic
safety.
This research introduced an application of safety space to describe movements ofmotorcycles and cars in the mixed traffic flow under congested traffic conditions. Safety
spaces for the car and the motorcycle are examined by considering the interactions
between cars and motorcycles in two cases of interactions: case (1) the subject vehicle isa motorcycle, the influential vehicle is a car; case (2) the subject vehicle is a car, theinfluential vehicle is a motorcycle. For each case, acceleration parameters were estimatedusing field data collected on Cong Hoa Street, Ho Chi Minh City. Almost all theparameters were significant at statistical significance level of 1%.
This research also quantified threshold safety spaces for the car and the
motorcycle. By comparing acceleration in cases of interaction, this research could explain
the differences between driving characteristics of car and motorcycle. Firstly,
motorcycles are likely to decelerate its speed in a much later time than when runningbehind other motorcycles and hence they need a harder brake to escape the rear-end
accident with cars. Secondly, cars are found to respond to motorcycles ahead at a farther
headway than motorcycles because cars cannot change moving directions in the similar
as motorcycles.

1235) To assess the motorcycle traffic conflict brought by the non-lane-based
movements
This study proposes new features of the motorcycle-following model to assess the
motorcycle traffic conflict. First, the difference of numerical values between acceleration
and braking was clarified. Second, the conditions in choosing a leader were described;
namely, the critical following angle and the following route width.
Conflict situations and an index of deceleration rate for the safety assessment
were discussed. A computer simulation was developed to assess the traffic conflict by
calculating deceleration rates at each time step when the density of the motorcycle flow isassumed to be changed. The findings highlighted that higher flow density led to a greater
increase in probability of traffic accident.
7.2 FUTURE WORK
The proposed model has many limitations. Recommendations on future
researches are discussed as below:
1) It appeared that different drivers react to different types of stimuli. The
research assumed that the drivers respond to only the most influential vehicle in theirmotorcycle-following movements. It is acceptable in the congested situation. However,other drivers also consider the second and third influential vehicles. The differences
make sense for a flow of vehicles driving in non-dense traffic when they do not need tofollow a leader but try to overtake the leaders or filtering through lateral clearances
between two other vehicles. In the mixed flow, a motorcycle driver driving behind atruck may feel difficult to consider more leaders. Hence, the influence of parameter
heterogeneity in model specifications on the driver behaviors of different drivers should
be considered carefully in specific situations.

1242) The reaction time in the model calibration was assumed to be constant for all
the motorcycle. In the real world, the reaction time varies across different motorcycles.
To understand the impact of heterogeneity in the randomness of reaction time fordifferent drivers on the stability of simulation results, a new calibration method should be
proposed.
3) Validation for evaluating motorcycle traffic conflict should be implemented.
For example, data on traffic conflict and traffic density at a survey location could becollected. The hypothesis on the relationship between the number of traffic conflictcounts and traffic density can be tested by comparing the observed data to the simulated
data.
4) The model was not designed to cover other behaviors of individual motorcycle
drivers. The driving behaviors under uncongested situations such as free-speed travelling,
overtaking and filtering; or at the intersections such as free deceleration, obliquefollowing, left or right turning could be developed in future research.
5) Other human factors affect driving behaviors. For example, sleepiness andfatigue caused by long hours or working time of day could increase crash risk. Moreover,aggressive attitudes and driving experiences have effects on traffic accidents. How thesehuman factors affect driving behavior and traffic accident are interesting issues.

125

Appendix A
This research attempts to apply social force approach to motorcycles. Helbing etal., 1995, 1998, 2001) used this approach to describe the movement of pedestrian (. Insocial force approach, the driving behaviors are taken as social forces that influence theinteractions and movements of a driver. A social force is different with a physical force
because it comes from the mind of a driver and shows the effect of a psychologicalbehavior on the movement. Social forces can be put into an equation of motion todescribe changes in movements of a driver.
A.1 SOCIAL FORCE MODEL FOR THE MOTORCYCLE
Social forces for the motorcycle are discussed below.
1. Acceleration force
A motorcycle driver
direction ⃗ ( ‖ ⃗ ‖prefers to run with desired speed

in a desired) oriented toward the destination. If the motorcycle runs on mid-block, its direction of movement is parallel to the direction of the road. If the motorcycle
turns right/left at the intersections, it performs two directions of movement toward thedestinations: first is toward the right/left lane of its current road, and second, toward theright/left lane of the next cross-road. A driver will change from actual speed ⃗ todesired speed⃗ within a certain time(relaxation time) given no obstacle infront. This behavior of changing speed can be described by the acceleration forces ⃗shown below.

&
FDA

1

WD

& &
vD0 eD  vD

126

(A.1)

2. Repulsive force of other driver
A subject motorcycle

keeps a “safety space” from other vehicle

to avoid acollision. When a motorcycle approaches another, it reduces its speed. The closer they
are, the lower the motorcycle’s speed become. Consequently, the effect of reduction in
speed can be explained by the repulsive force ⃗driveron the subject

and is given by&
FDER

where ⃗

of other driver⃗&
VDE (b(rDE ))(A.2)⃗ is distance vector between motorcycle

and motorcycle.

is assumed to be equipotential lines shown in Figure A.1. These lines have the form of anellipse with semi-minor axis b. Repulsive function( ) is monotonically a decreasing

function of b. Based on these assumption, one safety space around a motorcycle driver
can be drawn by a closed curve of ellipse. When other vehicle comes closer to a target
vehicle, the semi-minor axis of the ellipse becomes smaller, and as a result, repulsive
force gets bigger.

b

E

D

&
&
&
(vE  vD )'t
rDE

&R
FDE

VDER (b)Figure A.1 Equipotential lines of repulsive force

127Field observations showed that the subject motorcycle estimates the movement ofother motorcycles in advance within time step(i.e. the moving estimation time).

Therefore, it is reasonable to assume that the distance between two focus points of anellipse is equal to ( ⃗⃗ ). This means that the semi-minor b axis of the ellipse isperpendicular to direction of the relative speed vector between two drivers. This isbecause, based on the property of ellipses, the sum of the distances from any motorcycleon the elliptical curve to the two focal points is constant

& &
& &
&
&
rD  rE  rD  rE  (v E  vD )'t

&
§1 &
·
2 b  ¨ v E  vD 't ¸
©2
¹

2

2

const

(A.3)

, semi-minor b can be derived from (A.3) as below:

b

1
2

2
2
& &
& &
& &
& &
rD  rE  rD  rE  (vE  vD )'t  vE  vD 't(A.4)

3. Repulsive force of border
A motorcycle

keeps a distance from border B (median strip, guardrail) to avoid

hitting it. If the motorcycle runs close to the guardrail, it reduces the speed and changes
the direction to move away from it. This effect can be explained by repulsive force ⃗of the border as below:&
FDB&
UDB rDB(A.5)

Equation (A.5) has the same formulation as Equation (A.2). Therefore, theassumptions of repulsive force of other driver can be applied in repulsive force of border.

128‖ ⃗ ‖=‖ ⃗⃗ ‖ indicate the distance from location of motorcycle to border B which isnearest to the motorcycle.

is assumed to be the repulsive function which ismonotonically decreasing in distance ‖ ⃗ ‖ .
4. Angle of sightMotorcycle drivers can only see objects in their angle of sight (Figure A.2). If
objects are out of its angle of sight, the motorcycle cannot see them. Therefore, repulsive
force holds for situations within the angle of sight; and, it has a weaker influence c (0< c < 1) for situations happening behind the driver.

φ

&
rDE
&
e

α
φ

β

Figure A.2 Angle of sight for motorcycle

The weight factor is introduced here to capture this affect:w

where ⃗ ⃗‖ ⃗ ‖ ‖ ⃗‖means that if motorcycle& & &­1 if rDE e t rDE cosM®
¯c otherwise

(⃗

⃗)

‖⃗ ‖

(⃗

is in the angle of sight, i.e.

factor is equal to 1. If motorcycle(A.6)⃗) . Therefore, Equation (A.6)(⃗⃗), the weightis out of the angle sight, weight factor become c.

The weight factor is used to modify Equation (A.2) for calculating repulse force of othervehicle as follows:
129

&
FDER

&
wVDE (b(rDE ))(A.7)

After describing behaviors of motorcycles by equations of social forces, equationof motion for a motorcycle can now be derived. Equation of motion is defined as the totalof social forces which is equal to the change of actual speed ⃗ within a certain time dt :

&
dvD
dt

&
&
&
FDA  ¦ FDER  ¦ FDB  fluctuations
E

(A.8)

B

Fluctuations term in the Equation (A.8) captures other behaviors that cannot be measured.
This can be assumed to be normally distributed.
A.2 PARAMETER CALIBRATIONThis study calibrated the parameters using two different data sets of motorcycle
trajectory collected at two road segments in Ho Chi Minh City (see Section 3.5). The
parameters of desired speed and moving estimation time for calibration are illustrated inTable A.1 because these parameters have strong correlations with other estimation
parameters of acceleration. A sensitivity analysis was conducted, with two values formoving estimation time, 1.0 s and 2.0 s, and two values for desired speeds, the observed
maximum speed and another lower value, so as to confirm the stability of the simulation
results.

130

Table A.1 Given parameters for motorcycles in the social force modelParameters
Desired speed v0(m/s)
Moving estimation
time
(s)

Phan Dang Luu Street
Case
Case
Case
Case
1
2
3
4

Cong Hoa Street
Case
Case
Case
Case
1
2
3
4

11

11

8

8

13

13

10

10

2

1

2

1

2

1

2

1

Because of lack of data, repulsive force of border cannot be calibrated this time.
Repulsive forces of other motorcycle are assumed to decrease exponentially as shown
below:

VDE

where

,

,

V 0 (b  b 0 ) V

are estimated parameters of repulsive force. Relaxation time

(A.9)

in theacceleration force formula is the time which a vehicle needs to reach the desired velocity.
For simplicity, it is assumed to be constant for all motorcycles. Hence, all the parameters
needed to estimate the proposed model are summarized as below:
Parameters
00Repulsive force ( V , b , V )Relaxation time W

The computer software SPSS was used to estimate these parameters by solving the nonlinear regression problem. Due to the difficulties in attaining convergent solutions, all theestimated parameters were constrained to be greater than the value of 0.01. These
constraints are appropriate for social force equations because estimated values ofparameters should be positive. Therefore, sequential quadratic programming is applied131

under these constraints to minimize errors in running the acceleration equation. The
resulting parameter values are shown in Table A.2. All the parameters are estimated with
low t-value when t-test is employed.

Table A.2 Parameter estimates for motorcycles in the social force model
Phan Dang Luu Street
Case 1Case 2
Case 3
Case 4
Parameters
Mean Std. tMean Std. tMean Std. tMean Std.
tError value
Error value
Error value
Error value
0.059 0.271 0.22
0.098
0.986
0.10
0.010
0.679
0.01
0.085
0.712
0.1
V0
0
0.010 1.649 0.01
0.010
2.155
0.00
0.010
9.584
0.00
0.010
3.091
0.0
b
2.592
277.31

6.380
326.8

Case 1
Parameters
Mean
Std.
Error
0.184
0.779
V0
0
0.010
1.476
b
2.563
2.0E+5

4.407
1.9E+8

0.41
0.85

4.679
309.9913.164362.05

0.36
0.86

7.778
637.02112.031735.7

0.07
0.37

2.546
76.6987.811
28.714

0.3
2.7

Phan Dang Luu Street
Case 2
Case 3tMean
Std. tMean
Std.
value
Error value
Error

Case 4
tMean
Std.
value
Error

tvalue

0.24
0.01
0.58
0.00

0.11
0.00
0.41
0.00

0.11
0.00
0.42
0.00

0.184
0.010
2.563
1.9E+5

0.769
1.460
4.364
1.8E+8

0.24
0.01
0.59
0.00

0.291
0.010
3.226
1.7E+5

2.606
2.663
7.904
1.3E+8

0.291
0.010
3.226
1.6E+5

2.560
2.616
7.757
1.2E+8The statistical errors are calculated for the speed of motorcycle using two data setscollected on different locations, and using two different models, i.e. the proposed modeland the social force model (see Table A.3). The RMS error and RMS percent error of
speed in the proposed model are much smaller than those of the social force model. For
the swerving movement to the left or right, the proposed model shows better values forthe ratio between the estimated values and the observed values. These results imply thatthe proposed model could perform better estimations than the social force model.

132

The social force model provided many interesting ideas to address issues on how
to capture the interactions between vehicles using the equation of motion and the effects
of density on changes in driving behaviors. This research referred to the ideas of thesocial force model to develop the concept of safety space.

Table A.3 Statistical measures for the speed of motorcycles in the social force model
The proposed model
Statistical
Measurement
RMS error (m/s)
RMS percent error
Mean error (m/s)
Mean percent error
Ratio of swerving
modeled correctly (%)

Phan Dang
Luu Street
0.485
0.090
-0.0020.006

Cong Hoa
Street
0.581
0.065
0.021
0.005

61.4

64.1

133

The social force model(Case 1)
Phan Dang
Cong Hoa
Luu Street
Street
0.503
0.604
0.093
0.241
-0.010-0.698
0.005
0.011
50.5

47.2

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