効果的な交通安全対策立案のための信号交差点安全性
定量評価シミュレーション手法の開発― 平成 22 年度（本報告）タカタ財団助成研究論文 ―ISSN 2185-8950

研究代表者

中村 英樹

研究実施メンバー

研究代表者

名古屋大学大学院工学研究科教授

中村 英樹

研究協力者

名古屋大学大学院工学研究科助教

浅野 美帆

研究協力者

首都大学東京都市環境科学
研究科教授

研究協力者

秋田大学工学資源学部准教授

研究支援者

名古屋大学大学院工学研究科研究員

大口 敬
浜岡 秀勝

ALHAJYASEEN Wael K. M.
研究支援者

名古屋大学大学院工学研究科研究員
WOLFERMANN Axel

Table of Contents
1 Introduction ................................................................................................................................... 1
1.1 Background .............................................................................................................................. 1
1.2 Project overview ...................................................................................................................... 1
1.3 Safety at signalized intersections ............................................................................................. 2
1.4 Outline ..................................................................................................................................... 3
2 Methodology of Basic Models....................................................................................................... 4
2.1 Overview .................................................................................................................................. 4
2.2 Path of vehicles ........................................................................................................................ 5
2.3 Speed profile of vehicles .......................................................................................................... 6
2.3.1 Overview .......................................................................................................................... 6
2.3.2 Derivation of mathematical model ................................................................................... 6
2.3.3 Empirical modeling .......................................................................................................... 7
2.3.4 Connection between path and speed profile ................................................................... 10
2.4 Stop-go decision at the onset of yellow ................................................................................. 10
2.5 Drivers acceptance to gaps between pedestrians ................................................................... 11
3 Angle Collisions between Right-turning and Cross Traffic .................................................... 15
3.1 Overview ................................................................................................................................ 15
3.2 Stop-go behavior at the onset of yellow................................................................................. 15
3.3 Path of right-turning vehicles................................................................................................. 16
3.4 Speed profile of right-turning vehicles .................................................................................. 17
3.5 Start-up behavior of through traffic ....................................................................................... 22
3.6 Safety Indices ......................................................................................................................... 23
4 Left-turning Vehicle Conflicts with Pedestrians ...................................................................... 27
4.1 Overview ................................................................................................................................ 27
4.2 Pedestrian behavior analysis .................................................................................................. 27
4.2.1 Methodology................................................................................................................... 27
4.2.2 Data collection and processing ....................................................................................... 29
4.2.3 Analysis of pedestrian speeds ......................................................................................... 31i

4.2.4 Pedestrian speed modeling ............................................................................................. 34
4.3 Gap acceptance models .......................................................................................................... 36
4.4 Path of left-turning traffic ...................................................................................................... 37
4.5 Speed profiles of left-turning traffic ...................................................................................... 38
4.5.1 Maneuver parts ............................................................................................................... 38
4.5.2 Empirically derived model parameters ........................................................................... 40
4.6 Safety Indices ......................................................................................................................... 47
5 Simulation Development ............................................................................................................. 49
5.1 Introduction............................................................................................................................ 49
5.1.1 Outline and objectives .................................................................................................... 49
5.1.2 Requirements and capabilities ........................................................................................ 49
5.1.3 Simulation framework .................................................................................................... 51
5.1.4 Input and output .............................................................................................................. 51
5.2 Realization ............................................................................................................................. 52
5.2.1 Simulation software basics ............................................................................................. 52
5.2.2 User interaction .............................................................................................................. 53
5.2.3 Network elements ........................................................................................................... 54
5.2.4 Traffic flow elements...................................................................................................... 56
5.2.5 Signal control elements .................................................................................................. 58
5.3 Model integration ................................................................................................................... 59
5.3.1 Overview ........................................................................................................................ 59
5.3.2 Traffic generation and link flow ..................................................................................... 60
5.3.3 Reaction to traffic signals ............................................................................................... 62
5.3.4 Gap acceptance models .................................................................................................. 63
5.3.5 Entering acceleration rate of entering vehicles ............................................................... 63
5.3.6 Paths of turning vehicles in the intersection ................................................................... 63
5.3.7 Speed of vehicles ............................................................................................................ 64
6 Simulation Validation and Case Study...................................................................................... 69
6.1 Overview ................................................................................................................................ 69
6.2 Car following model .............................................................................................................. 71ii

6.2.1 Introduction .................................................................................................................... 71
6.2.2 Calibration methodology ................................................................................................ 71
6.2.3 Verification ..................................................................................................................... 72
6.3 Conflicts between clearing right-turning traffic with starting through traffic ....................... 74
6.4 Conflicts between left-turning traffic with pedestrians.......................................................... 78
6.5 Sensitivity analysis ................................................................................................................ 81
7 Conclusions and Outlook ............................................................................................................ 85
7.1 Conclusions............................................................................................................................ 85
7.2 Outlook .................................................................................................................................. 85
References ....................................................................................................................................... 88iii

1 Introduction
1.1 Background
Signalized intersections are the most critical elements in any transportation network. Their
operations considerably affect the performance of the whole road system. Road users of different
types in different masses, from different directions and moving at different speeds have to use thesame space, resulting in a large number of potential conflicts. Whereas intersections constitute avery small part of the entire transportation network, more than 50% of all motor vehicle accidents
occur at intersections. In some European countries, percentages of up to 70% of the total accident
number are reported (Kuciemba and Cirillo 1992).
Various operational policies and design layouts have been implemented at signalized intersections
all over the world based on the cultural customs, prevailing traffic characteristics and available
technologies locally. For instance, signal control has long been the most important operational
strategy for traffic on urban streets. Control methods and control systems (hardware and software)differ case by case, as do the objectives. It is no doubt that different operational policies or design
layouts possesses benefits as well as drawbacks in terms of reliability and efficiency. However, areliable tool which can quantitatively evaluate traffic quality and safety is not available yet.
This project aims at developing a microscopic simulation model for the safety evaluation of
signalized intersections. This simulation will allow practitioners to evaluate the effects of various
improvements in the geometric layouts and operations of signalized intersections on the overall
safety performance. For instance, through this microscopic simulation, it would be possible topredict the impacts of adding channelization or adjusting the positions of crosswalks or intersection
corner radii. And it can further be applied to modify the signal timings such as all-red intervals.
However in order to develop such a simulation model, user behavior must be reasonably reflected.

1.2 Project overview
Figure 1.1 shows the main tasks to be accomplished by this project within the two-years period.
This Figure is the same one included in the first project report submitted last year (Report 1, R 1).
Several tasks have been completed during the first year such as pedestrian and vehicle datacollection by video survey (Tasks 1 & 2) and accident records analyses to identify the mostfrequent accident types (Task 5). Some tasks could not be completed during the first year such as
user behavior analysis and modeling (Tasks 4 & 5). The tasks related to the microscopic simulation
model development and the safety evaluation indices (Tasks 8, 9 &10) have been addressed during
the second year.
1(1) Selection of the surveyed intersections
調査対象交差点の選定(2) Video survey
ビデオ観測調査・走行実験(3) Vehicle behavior data collection/analysis
車両挙動データの収集/分析(6) Pedestrian behavior data collection / analysis
歩行者挙動データの収集/分析(4) Modeling vehicle behavior
車両挙動モデルの構築(7) Modeling of pedestrian behavior
歩行者挙動モデルの構築(5) Analysis of the relationship between
accidents and vehicle manuever
車両挙動と事故発生との関連分析

Finished tasks in the1st year
Shared tasks in the 1st
and the 2nd year
Tasks of the 2nd year(8) Study on Safety Performance Indices
安全性能評価手法の検討(9) Development and validation of simulation model
シミュレーションモデルの開発と検証(10) Case study
交差点事故対策のケーススタディ

Figure 1.1 Overall tasks of the project

1.3 Safety at signalized intersections
The safety evaluation of signalized intersections is one of the most challenging topics. An accident
analysis identified the most prominent type of accidents at urban signalized intersections in Japan.
There are mainly five types of conflicts as shown in Figure 2.2. As shown in the first year reportangle collisions and left-turning vehicles with pedestrian/cyclist collisions are among the mostfrequent collisions at signalized intersections. Furthermore, although signalized intersections areoperated in a way to give pedestrians a prioritized right of way, more than one-third of the total
traffic accident fatalities are pedestrians (Japan National Police Agency, 2010). Thus, in this project,
two types of collisions are chosen for the safety evaluation of signalized intersections. Conflicts
between left-turning vehicles and pedestrians/cyclists (Figure 1.2d)) and angle collisions between
clearing right-turning vehicles and starting crossing through traffic (Figure 1.2b)), are the subject

2

a)Rear-end collisionsd)b)Angle collisions (1)Between clearing rightturners and starting throughcross traffic

Left turning vehicles withpedestrians/cyclists collisionse)c)Angle Collisions (2)Between starting rightturners and clearing opposite
through traffic

Right turning vehicles withpedestrians and cyclists collisions

Figure 1.2 Types of collisions to be considered
conflicts in the modeling and safety evaluation in this project. For the safety evaluation, newindices will be used for each type of conflicts as will be explained in Sections 3.6 and 4.6.

1.4 Outline
This report explains firstly the methodology of the basic models used in the modeling of different
conflict types (vehicle path, vehicle speed profile, stop-go decision at the onset of yellow,
acceptance of gaps in pedestrian streams). Chapters 3 and 4 expand upon the details of the models
used for conflicts of right-turning and left-turning traffic. In Chapter 5 the simulation softwaredeveloped to apply the models and evaluate the safety of signalized intersections is introduced. The
validation of the simulation tool and a case study are explained in Chapter 6. The report closes withconclusions and an outlook to further research (Chapter 7).

3

2 Methodology of Basic Models
2.1 Overview
All maneuvers analyzed in this project require four basic underlying models to describe the driver
behavior (Figure 2.1). Car following and lane changing behavior follows the same principles atintersections and on links. For this, existing models can be used. The models as described here
assume free flowing cars. Car following and lane changing behavior is, hence, not further discussed.

Car following andlane changing• Car following behavior• Lane changing behavior

Trajectories

Reaction to signal• Path• Speed• Start-up behaviour• Stop-go decision at
onset of yellow

Reaction to othertravellers• Reaction to crossing
vehicles• Reaction to pedestrians

Figure 2.1 Basic models underlying turning maneuvers at signalized intersections
The path and speed of vehicles are described in two separate trajectory models. The connection is
ensured by the empirical modeling of the input parameters. The trajectory models are explained in
Sections 3.3 and 4.4.
The reaction to traffic signals is divided into two aspects: the signal change from red to green(start-up behavior) and the signal change from green to red (stop-go decision). The models havebeen developed and calibrated for through traffic (start-up, cf. Section 3.5) and right turning traffic(stop-go, cf. Section 2.3.4 and 3.2). Thus, the models focus on specific aspects of these two
movements. However, they prove the validity of the approach and represent a basis forgeneralization.

4

The reaction of turning vehicles to other travelers is developed for the reaction of left-turning
traffic to crossing pedestrians (cf. Section 2.5, 4.3 and 4.5). To realistically model this maneuver
the behavior of the pedestrians is analyzed (Section 4.2).

2.2 Path of vehicles
One of the important aspects in analyzing driver behavior, which is a vital element in the safety
performance of signalized intersections, is vehicle trajectories. Several existing studies found that
there are significant variations in trajectories of turning vehicles dependent on intersection
geometry and operational policies. It is rational to assume that such variations might result increating specific unfavorable conditions which might lead to collisions. In reality, road users
behave by anticipating other users’ behavior in order to avoid any collisions with them. Broadly
varying road user behavior and trajectories may lead to misunderstanding of other users’ decisions
which might result in safety problems. Therefore, it is quite important to consider not only averagevehicle maneuvers but also their variation which is affected by the geometric layout of intersections
and the interaction with pedestrians.
Modeling individual vehicle trajectories was completed in the first year of the project by applying
the Euler-spiral-based approximation methodology. The basic idea is that vehicle trajectories canbe represented by modeling the change in the curvature. Thus three types of segments are used;straight lines, circular curves and Euler spiral curves as shown in Figure 2.2. The parameters which
represent the three segments are modeled as a function of the geometric characteristics of theintersection, vehicle type and speed. The general forms of the developed empirical models areshown by Equations (2.1) to (2.3).
D HN_ OUT

vexit
ク ロソ イド 2
交差角

D HN_ OUTA2

D HN_ INθ

vexit ク ロ ソ イ ド 2

円弧

ク ロソ イド 1

A2
円弧

歩車道境界線から の距離

Rmin

IP点
交差角

θ

Rmin

A1

隅角部半径

D HN_ IN

IP点

ク ロソ イド 1

Rc

A1

直線
直線
中央分離帯 (M edian hard-nose)

右折IP点から 中央分離帯ま での距離： D HN

venter左折
ventera) Trajectory of right-turning vehiclesb) Trajectory of left-turning vehicles
Figure 2.2 Modeling the trajectory of turning traffic5(2.1)(2.2)(2.3)
Where A1 and A2 are entering and exit clothoid parameters (m), respectively; Rmin is the radius of thecircular curve (m) and α, β, γ are model parameters. For detailed information about the assumptions
behind this trajectory model, refer to the first year report of the project (R 1).

2.3 Speed profile of vehicles
2.3.1 Overview
Section 2.2 described the modeling of the path of turning vehicles. Here the model to represent
their speed is introduced. Based on empirical data a mathematical model was chosen that
accurately reproduces speed and acceleration behavior of turning vehicles (Subsection 2.3.2). The
speed profiles are influenced by the intersection geometry and the approach speeds of the vehicles
among others. This influence was empirically modeled as described in Subsection 2.3.3.
2.3.2 Derivation of mathematical model
To accurately model the speed of turning vehicles at signalized intersections, empirically gatheredtrajectory data has been analyzed. The speed profile of free flowing cars follows a typical shape asshown in Figure 2.3a. From the entering speed venter the drivers decelerate to the minimum speed
vmin and accelerate again to the exiting speed vexit. The acceleration at the beginning and ending of
the maneuver (aenter/aexit) is commonly assumed to be zero.
The acceleration does not have to be symmetric to the deceleration. The speed profile can beseparated into two parts with the time tmin when the minimum speed is reached as the division point.
If this speed profile is described by a function that not only fits well to the speed data itself, butalso reflects the acceleration behavior as the derivative of the speed, sufficiently accurate outcomescan be expected. A polynomial of third degree for the speed as a function of the time fulfills thisrequirement as shown by Equation (2.4).
(2.4)
The congruency of the shapes of observed and model speed profile is highlighted in Figure 2.3a.
The acceleration profile is in this way a polynomial of second degree. Figure 2.3b shows theacceleration for the speed profiles from Figure 2.3a and the model acceleration profile.
6

3

50

2

Acceleration (m/sec²)

Speed (km/h)

60

40
30
20
10

1
0
0

2

4

6

8

10

12

14

16

-1

-2

0

2

4

6

8

10

12

14

16

-3

Time (sec)a) Speed profilesb) Acceleration profiles

2.5

60

2
1
0.5

0
2

4

6

8

10

12

14

16

Speed (km/h)

Jerk (m/sec³)

1.5-0.5 0Inflow

3

Outflow

50

2

40

1

30

0

20

-1

Speed

-1

10

-1.5

-2
-2.5

Time (sec)

Acceleration

tmin

0
0.0

Time (sec)c) Jerk profiles

2.0

4.0

6.0

texit
8.0

10.0

-2

Jerk

Acceleration (m/sec²) / Jerk (m/sec³)

0

-3
12.0

14.0

16.0

Time (sec)d) Modeled speed, acceleration and jerk profiles

Figure 2.3 Speed profiles of free flowing turning vehicles
Figure 2.3c illustrates that while the jerk as the derivative of the acceleration varies markedly due
to its sensitivity to speed changes and the limited precision of the data acquisition, the general trend
is still represented by the chosen function for the speed.
The principle shape of the speed function and its first and second derivative are illustrated in Figure
2.3d. This general speed profile for turning traffic not influenced by signals, other vehicles, orpedestrians is called ideal speed profile. It is divided into the inflow of the curve and the outflow of
the curve, with the minimum speed as the division between the two regions. This general shape canbe used for both left-turning and right-turning vehicles.
2.3.3 Empirical modeling
Most of the coefficients of the speed function are determined by constraints (speed v andacceleration a at the beginning and the ending of the maneuver). The remaining coefficients andunknowns reflect the difference in driver behavior due to individual characteristics and due to7intersection properties. These unknowns are modeled as random variables with intersection
properties as influencing factors. Figure 2.4 highlights the constraints of the two parts of the ideal
speed profile (inflow and outflow), and the eight coefficients used in the speed function (four foreach part).

Speedvi  c1, k ti3  c2, k ti2  c3, k ti  c4, kaenterventerai  3c1, k ti2  2c2, k ti  c3, kvexit

i : enter, min, exit

c1,in , c2,in ,aexit

k : in, out
c1,out , c2 ,out ,c3,in , c4,in

c3,out , c4 ,out

Ideal profile(inflow)

amin

Ideal profile(outflow)

vmin

texit

t min

Time

Figure 2.4 Constraints of the ideal speed profile
The characteristic parameters for the individually chosen random distributions (x) are modeled as alinear combination of the influencing factors (Xi) as shown in Equation (2.5). The overall process is
illustrated in Figure 2.5.
(2.5)
Trajectory data from signalized intersections (cf. R 1) has been used to calibrate the speed profiles.
The raw data first had to be processed. The data was separated into the inflow and outflow partwith the minimum speed marking the boundary. Least square fitting was used to derive thecoefficients and unknowns of the speed function which has been described in Subsection 2.3.2.
Outliers have been determined by individual visual inspection of the profiles as illustrated in Figure
2.6 (black and dark red respectively represent the observed speed and acceleration; the light colors
show the best fit for inflow and outflow).
The thus derived coefficients can be used to statistically analyze the influence of different factors
on the shape of the speed profile. Three of the four coefficients c1 to c4 are dependent on constraints(speed and acceleration at the beginning and ending of the profile parts). The remaining coefficientand characteristic points of the speed profile (position along the vehicle path, minimum speed)incorporate the influences by intersection geometry and driver characteristics. The following
factors have been analyzed for correlation with the speed function characteristics:
8

•

approach speed venter•

exiting speed vexit•

intersection angle•

curb radius Rc•

distance of the hard nose to the trajectory tangent intersection HN•lateral distance of the vehicle in the exit from the curb

Raw speed
data

Fitting ofspeedfunctionsto inflow andoutflow ofeach trajectory

Identificationof outliers

Modeling offunctionparameters

Figure 2.5 Illustration of overall speed profile modeling process

The speed profiles used in the simulation are, thus, dependent on the empirically modeled
parameters and constraints as highlighted in Figure 2.7.
Due to sample limitations, the results of the empirically modeling can only be seen as preliminary.
However, it already reflects well the impact of different intersection layouts, speed levels, etc. as
will be demonstrated in a case study (Chapter 6). The details of the empirical models are derived

20

2

18

1.5

16

1

Speed (m/sec)

14

12

0.5

10

0

8

-0.5

6
Speed
Speed (fit out)
Acc (fit in)

4
2

-1

Speed (fit in)Acceleration
Acc (fit out)

Acceleration (m/sec²)

separately for the right-turning (Section 3.4) and left-turning (Section 4.5) vehicles.

-1.5

0

-2
0

2

4

6

8

Time (sec)

10

12

14

16

Figure 2.6 Visual comparison of fitted and observed speed and acceleration profiles (Outlier)9Constraints
aenter , venter
aexit ,vexit

Curb radiusIntersection
angle

c1,in
c1,outvmin
xmin

N(m,s )G(α, β)Entering
speed
lateraldistance at
exit

Hard nose
distance

Figure 2.7 Illustration of speed function calibration
2.3.4 Connection between path and speed profile
The speed profile is related to the intersection indirectly by relating it to the path of the vehicle.
The distance between the beginning of the turning path of the vehicle as described in Section 2.2
and the position where the vehicle reaches its minimum speed is empirically modeled as a random
distribution. In this way the path, the speed profile and the intersection geometry are connected toeach other (Figure 2.8).

2.4 Stop-go decision at the onset of yellow
When drivers approach an intersection and they observed the signal change from green to yellow,
they need to make a decision either to stop or to go through the intersection. Drivers’ stop-go
decision is a function of several parameters such as time to stop line at the onset of yellow, all-red
interval, vehicle speed and vehicle type. In this study, the probability that a vehicle will stop is
modeled using a Logit model as shown in Equation (2.6).

(2.6)

Where Pstop is the probability to stop at the onset of yellow and Vstop is stopping utility function. For
detailed information about model assumptions and estimation refer to the first year report of the
project.

10

projected vehicle path
Straight

Clothoid (in)Radialcurve

Clothoid (out)distance covered by path model
speed

distance covered by speed profile model

minimum speed
vmin
distance
position of minimum speed
along vehicle path x min

Figure 2.8 Illustration of position of minimum speed with reference to vehicle path

2.5 Drivers acceptance to gaps between pedestrians
Gap is the time difference between two subjects arriving at the same position. In the vehiclepedestrian conflicts, the available gaps between pedestrians for drivers are defined as the timedifference between two pedestrians arriving at the conflict point. These gaps are opportunities fordrivers to cross. If no suitable gap is available when the vehicle will reach the crosswalk, the driver
has to adjust the speed, if necessary to a full stop. The driver will then have to wait until an
acceptable gap appears or until all pedestrians have cleared the crosswalk. Therefore, whether
available gaps will be accepted or rejected is significantly affected by driver behavior. The
occurrence of gaps depends on the characteristics of pedestrian movements.
For the purpose of this research, a gap is defined as the time difference between two successive
pedestrians passing the conflict point while a lag is defined as the time needed for one pedestrian toreach the conflict point. Pedestrian movements can have their origin at either the near side or thefar side of the crosswalk with reference to conflicting vehicles. Near-side pedestrians are those whostart crossing from the side of the vehicular traffic that is exiting the intersection while far-sidepedestrians are those who start crossing from the side of the incoming vehicular traffic as shown in
Figure 2.9. Considering the vehicle size, the gap is the time difference between the first pedestriancrossing the far edge of the vehicle trajectory and the second pedestrian crossing the near edge of11

Far-side

Near-side
Far-side

Near-side

Vout

Far-side

Far-side

Near-side

Near-side

Far-sideDistance from the vehicle
to the conflict point

Near-side

Distance from the pedestrian
to the conflict pointa) The definition of near-side and far-side pedestrian origin-destination
Vehicle starts
to stop Vehicle cross theconflict point

Time

0

Rejected gap

Accepted gap

Time

0

b) Gap/lag definition
Figure 2.9 Pedestrian origin-destination and gap/lag definition considering vehicle size

the vehicle trajectory. The lag is the time between the pedestrian crossing the near edge of thevehicle trajectory and the vehicle arriving at the conflict point as shown in Figure 2.9.
Gaps and lags are calculated when the turning vehicle arrives at the near border of the crosswalk.
The gaps between pedestrians who crossed the conflict point before the vehicle reaches the
crosswalk are defined as the “unavailable gaps” and they are not considered in this research. The
gaps/lags which are used by drivers are called “accepted gaps/lags”, while other gaps/lags which
are available but not utilized by drivers are called “rejected gaps/lagｓ”.
12Near-side

Type A
Lags of pedestrians from thenear-side of the crosswalk.

Type D
GAps between two pedestrians approachingfrom the far-side of the crosswalk.

Far-side

Type B
Lags of pedestrians from theFar-side of the crosswalk.

Type E
Gaps betweEn a pedestrian approaching from thenear-side of the crosswalk and another one
approaching from the far-side of the crosswalk.

Type CGaPs between two pedestrians
approaching from the near-sideof the crosswalk.

Figure 2.10 Assumed types of gaps/lags
Generally, lags/gaps are classified into five different types depending on the pedestrians’ directionof movement as shown in Figure 2.10.
Type A: lags of pedestrians approaching from the near side of the crosswalk;Type B: lags of pedestrians approaching from the far side of the crosswalk.
Type C: gaps between two pedestrians approaching from the near side of the crosswalk;Type D: gaps between two pedestrians approaching from the far side of the crosswalk;Type E: gaps between a pedestrian approaching from the near side of the crosswalk and anotherone approaching from the far side of the crosswalk.
In order to estimate the gap/lag acceptance probability distribution for each type of the defined
gaps/lags, empirical data is necessary. After collecting the required data, gaps/lags are categorized
into several classes. The gap/lag acceptance probability for class i is calculated according toequation (2.7).
P(x)i No. Accept ed gaps/la gs(in category i)
Total No. of obserev ed gaps/la gs(2.7)

A Cumulative Weibull Distribution is used to fit the observed gap/lag acceptance probability
distributions. The Weibull Distribution is a widely used function to represent the breakdown
probability おｎ highways and expressways. It is also widely used to represent various gap
acceptance conditions between different travelers in the transportation network. Equation (2.8)

13presents the Cumulative Weibull Distribution function with two parameters; the shape parameter α
and the scale parameter β.

P( x )  1  e

 x
 
 



(2.8)

Where P(x) is the acceptance probability of gap/lag x; α and β are Weibull Distribution parameters.

14

3 Angle Collisions between Right-turning and Cross Traffic
3.1 Overview
To represent angle collisions, the behavior of clearing right-turning vehicles and conflicting
through traffic need to be well represented inside the simulation environment. The required models
to represent angle collisions are summarized in Figure 3.1b). They are divided into models
representing the behavior of the clearing right-turning vehicles (stop-go decision and trajectory)
and models representing the behavior of the entering through traffic in the cross street (start-up
behavior). All of these models have already been developed during the first year of the project,
except the speed profile model as part of the trajectory modeling which will be presented in detail
here.
Space

Maneuver of Clearing
Right-turning vehicles

Intergreen Time IG

Y

AR

Start-up Behavior of FirstEntering Through vehicles

R
Stop-go Decision Model at
the Onset of Yellow
Start Response Time Model
(SRT)

PET
Conflict point

Turning Path Model

Time

Entering Acceleration Model

Late Exit Time (LET)

Speed Profile Model

Represent the conflict between clearing right-turning
vehicles and entering cross through vehicles

Start Response Time (SRT)a) Conflict between clearing right-turning
vehicles and entering through vehiclesb) Necessary models

Figure 3.1 Required models to represent the conflict between clearing right-turning vehicles andentering through traffic

3.2 Stop-go behavior at the onset of yellow
As explained in Section 2.3, the probability of drivers to decide to stop when approaching theintersection at the onset of the yellow signal is modeled by using a Logit Model (Equation (2.6)).
The stopping utility function is assumed to have a linear form with independent variables as shownin Table 3.1. By using Equation (2.6) and Table 3.1, the stopping probability can be estimated andthen the stop-go decision can be assigned randomly. For detailed information about theassumptions behind this stop-go decision model、 refer to the first year report of the project.

15

Table 3.1 Right-turning vehicle stop-go model parameter estimation
Estimate (t-value)
単純 4 現示制御
Permissive followed by
exclusive right-turning
phase

矢印制御
Exclusive rightturning phase only

Travel time to the stop line at the onset ofyellow (sec)

0.71 (7.33)

0.88 (6.29)

Follower dummy (Follower = 1, Otherwise= 0))-1.12 (-2.00)-1.37 (-2.57)

Constant-2.25 (-3.56)-3.25 (-4.44)

0.362

0.366

的中率 (%)
Hit ratio %

80.7

79.6

Sample size

238

167

Explanatory variable

3.3 Path of right-turning vehicles
As explained in Section 2.1, the path of turning traffic is modeled by a combination of straight,
circular and Euler spiral curves. The estimated models for the curve segments which are shown inEquations (2.1), (2.2) and (2.3) are listed in Table 3.2 and Table 3.3. It was assumed that theentering spiral curve parameter A1 and the exit spiral curve parameter A2 are dependent on theminimum speed along the turning maneuver. This minimum speed is modeled for both parts of the
trajectory estimation: path and speed.
Table 3.2 Results of estimated Euler spiral parameters for right-turning vehicles

Explanatory variables
Const.
Minimum speed Vmin(km/h)
Distance from IP point to DHN_IN
hard nose (m)*DHN_OUT
Modified R2
Sample SizeParameter of entering Euler spiralcurve A1(m)Parameters (t-values)-8.65(-3.33)
0.294 (4.48)
0.172 (6.90)－
0.663

Parameter of exit Euler
spiral curve A2 (m)Parameters (t-values)
3.63 (1.64)
0.287 (3.05)－
0.241 (4.84)
0.424

151

* Refer to Figure 2.2.

Thus Vmin is modeled assuming Normal Distribution. For detailed information refer to the first year
report of the project.

16

Table 3.3 Results of estimated minimum radius and minimum speed for right-turning vehicles

time

AverageStandard
deviation

Explanatory variables
Const.
Intersection angle (deg)Distance from IP point DHN_IN
to hard nose (m) *DHN_OUT
Minimum between DHN_IN and
DHN_OUT
Minimum speed Vmin(km/h)
Const.
Intersection angle (deg)Minimum speed Vmin(km/h)
Sample Size

Radii of circular
curve Rmin (m)Parameters (t-values)
0.0621 (3.80)-

Minimum speed Vmin
(km/h)
Parameters (t-values)
4.49 (2.62)
0.0717 (5.57)
0.00920 (4.52)
0.105 (3.17)

0.159 (4.35)-

0.438 (7.63)
0.130 (17.4)

0.380 (13.13)
0.124 (2.69)
1.71 (4.57)
151* Refer to Figure 2.2.

3.4 Speed profile of right-turning vehicles
The basic principles of the speed of vehicles when turning at a signalized intersection have been
explained in Section 2.3. The particularities of right-turning speed profiles are incorporated into themodel by empirical analysis of the speed function coefficients and constraints. Table 3.4 shows theconstraints for the speed equation (2.4) with the acceleration as the first derivative and their four
unknowns for both the inflow and outflow part of the ideal speed profile (cf. Figure 2.4). Thissystem of linear equations is underdetermined. The coefficient c1 (inflow and outflow) and theminimum speed vmin are empirically modeled.
Table 3.4 Constraints and modeled parameters for ideal speed profile
Parameters

inflow

outflowv (in)

ventervmin

v (out)(vmin)vexit

a (in)

aenter0a (out)0aexit

t (out)(tmin)(texit - tmin)

Degree of freedom/constraints

5/3

5/4

vmin, c1,in

c1,outModeled parameter

In addition to vmin, c1,in and c1,out the position of the speed profile with reference to the path of thevehicle xmin is empirically modeled (cf. Subsection 2.3.4). The observed behavior of vehicles
reveals that these parameters are related to certain intersection characteristics, namely the
17

0.14

FittedObserved

Relative frequency (-)

0.12
0.1
0.08
0.06
0.04
0.02
0

0.01 0.03 0.05 0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23 0.25 0.27 0.29

Coefficient c1 (m/sec⁴ )a) c1 for inflow

Relative frequency (-)

0.24
0.22

Fitted0.2

Observed

0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
-0.19

-0.17

-0.15

-0.13

-0.11

-0.09

-0.07

-0.05

-0.03

-0.01

Coefficient c1 (m/sec⁴ )b) c1 for outflow
Figure 3.2 Modeled and fitted c1 coefficients or the inflow and outflow of right-turning vehicles
intersection angle and the position of the hard nose (cf. Figure 2.2). Correlation charts with thedifferent influencing factors are shown on the following pages. The linear trend is shown with themean plus/minus the standard deviation indicated by dashed lines.
The parameters are modeled as randomly distributed values. For the coefficients characterizing therandom distribution, a linear combination of the most important influencing factors has been used.
The coefficients are given in a table for each speed profile parameter.
Coefficients c1,in (inflow) and c1,out (outflow)
The coefficient c1 is a jounce parameter (first derivative of the acceleration). It determines theshape of the speed profile. For the inflow it is positive, for the outflow it is negative. The
distribution shows a distinct positive skew. Therefore, a Gamma Distribution was chosen to
represent the data as shown in Figure 3.2.

18

While for the outflow no significant influencing factors on the shape and scale of the Gamma
Distribution could be determined, a correlation between the coefficient of the inflow andintersection angle and entering speed can be discerned (Table 3.5).

Table 3.5 Models of c1,in and c1,out coefficients for right-turning vehicles
Gamma
Distribution

ConstIntersection angle(degrees)Entering speed (m/sec)
ConstIntersection angle(degrees)Entering speed (m/sec)
Log Likelihood
Sample Size

α

β

c1,in

c1,outαβEstimate (Sig.)
9.412827 (0.000)

αβ
Estimate (Sig.)
2.089874 (0.000)-0.0759988 (0.000)--0.0548171 (0.000).0231397 (0.000)

0.0007814 (0.000)-

0.0015876 (0.006)

-

87

66

Parameters

Minimum speed
The distribution of minimum speeds of right-turning vehicles is symmetric as shown in Figure 3.3
thus a Normal Distribution is used to fit the minimum speed distribution. However, this distribution
is affected by different parameters, for instance intersection angle, entering speeds and vehicle type.
Since sufficient data to analyze the effect of heavy vehicles is not available, the analysis is limited
to approaching speed and intersection angle. Figure 3.4 indicates a linear correlation between theminimum speed and the entering speed and the intersection angle. The two dashed lines stand forthe area around the mean with The final model for minimum speed is presented in Table 3.6.

10

100%

Frequency
Cumulative %

9
8

80%

Frequency (-)

7
6

60%

5
4

40%

3

2

20%

1

13.8

13.2

12

12.6

11.4

10.8

10.2

9

9.6

8.4

7.8

7.2

6

6.6

5.4

4.8

4.2

3

3.6

2.4

1.8

1.2

0

0%

0.6

0

Minimum speed (m/sec)

Figure 3.3 The distribution of observed minimum speeds vmin for right-turning vehicles

19

14

10
8

m s

6

m s

12

Minimum speed (m/sec)

12

Minimum speed (m/sec)

14

m s

4

2

10

8
6

m s

4
2

0

0
6

8

10

12

14

16

18

20

22

50

60

70

80

90

100

110

120

Intersection angle (degrees)Entering speed (m/sec)a) Entering speed and Minimum speedb) Intersection angle and Minimum speed

Figure 3.4 Correlation between entering speed, intersection angle and minimum speed for rightturning traffic

Table 3.6 Minimum speed vmin and position of minimum speed xmin models for right-turning
vehiclesGamma
Distribution

Parameters

μ

Const
Intersection angle (degrees)Entering speed (m/sec)
Distance from IP point toentering hard nose DHN_IN (m)

σ

Const
Intersection angle (degrees)Entering speed (m/sec)
Distance from IP point toentering hard nose DHN_IN (m)Log likelihood
Sample Sizevmin
N
Estimate (Sig.)
2.650751 (0.002)
0.0289023 (0.000)
0.1879437 (0.000)

xmin
N
Estimate (Sig.)
7.34586 (0.222).0775984 (0.236)
0.5006655 (0.113)-

0.2883846 (0.006)

1.404181 (0.002)-.0053573 (0.311)--0.0350408 (0.394)-0.5276275 (0.029)--

0.110498 (0.059)-118.95941
87-288.69583
87

Position of minimum speed xmin on the vehicle path
The position of the minimum speed xmin is defined as the distance from the beginning of the turning
path of the vehicle (first clothoid) of the vehicle path in the intersection to the point where theminimum speed vmin occurs (cf. Subsection 2.3.4). As shown in Figure 3.5 xmin follows a symmetric
distribution; therefore, it is modeled as a Normal Distribution. The final model for xmin is presented
in Table 3.6.
20

9

100%

Frequency

8

90%

Cumulative %
80%

7

70%

Frequency (-)

6

60%
5
50%
4
40%
3

30%

2

20%

55

53

51

49

47

45

43

41

39

37

35

33

31

29

27

25

23

21

19

17

15

13

0%

9

10%

0

11

1

Position of minimum speed xmin (m)Figure 3.5 The distribution of observed xmin (position of minimum speed) for right-turners

60

50

Position of minimum speed xmin (m )Position of minimum speed xmin (m)

60

m s

40
30
20

m s

10
0

m s

50
40
30
20

m s

10

0
40

60

80

100

120

0

5

Angle (deg)

10

15

20

25

Entering speed (m/s)a) Intersection angle and xminb) Entering speed venter and xmin

Position of minimum speed x min (m)

80
70
60

m s

50
40
30

m s

20
10
0
0

10

20

30

40

50

Distance from IP point to hard nose DHN_OUT (m)c) Distance from IP point to hard nose DHN_OUT and xmin
Figure 3.6 Correlation between several parameters and position of minimum speed xmin for rightturning vehicles
21

3.5 Start-up behavior of through traffic
At intersections with the common lag-lag phasing plan (単純 4 現示制御), it was observed that theclearing behavior of right-turning traffic affects the start-up behavior of the following cross throughtraffic. Thus, the start-up response time (SRT) of the through traffic is modeled assuming a Weibull
Distribution. As shown in Equation (3.1), the Weibull Distribution has three distribution
parameters, shape α, scale β, and location γ. Each of them was estimated by influencing factors
such as intersection geometry, signal control, and traffic conditions. More specifically, explanatory
variables include the distance between the opposite stop-lines, set-back of the stop-line, theentering distance (xSe), late exit time (xLET), length of the all-red time (xAR), signal phasing plan(dummy variable:the permitted-and-protected right-turn phasing plan or the dual-lagging protectedonly right-turn phasing plan), and vehicle type (dummy variable, xheavy: passenger car or heavy
vehicle). Based on statistical tests, the basic structure of the final models is described throughEquations (3.1)~(3.4), and the estimated coefficients are presented in Table 3.7.
 t    1t (
) exp(  (
) )
 


(3.1)

  a0  aheavyxheavy(3.2)

  b0  bSe xSe  bAR x AR  bprotected only x protected only

(3.3)

  c0  cLET xLET

(3.4)

f (t ) 

Where, a0, b0, and c0 are constants; aheavy, bAR, bprotected-only, and cLET are coefficients. The empiricallyestimated constants and coefficients are listed in Table 3.7. For detailed information about theestimated start-up response time SRT model refer to the first year report of the project.
After determining the SRT, it is necessary to estimate the acceleration of the entering throughvehicle until it reaches the conflict point. An empirical analysis was conducted to understand the
distribution of this acceleration. Finally, as it was reported in the first year report, the entering
acceleration is modeled assuming a Normal Distribution. The mean and standard deviation aremodeled as a function of explanatory variables as shown in Table 3.8. The SRTs were divided into
two populations by taking 0.7s as the threshold value. Both populations are described by Normal
Distributions as shown in Table 3.8. The results suggest that hurry-start vehicles adjust theiracceleration rates based on the onset time of green, while the other vehicles adjust theiracceleration rates according to late exit time LET of the clearing vehicles. For detailed informationrefer to the first year report of the project.
22

Table 3.7 Estimated coefficients of the SRT model
VariablesαβγDummy variable of vehicle type, aheavy(1: heavy vehicle; 0: otherwise)
Constant a0
Entering distance bSe [m]Dummy variable of signal phasing plan, bprotected-only(1: the dual-lagging protected-only g right-turn phasing
plan; 0: otherwise)
Constant b0
Late exit time, xexit [s]Constant c0
ρ2
Sample size

Coefficientst values

-3.40

-2.95

11.8
-0.0106

7.33
-5.49

0.274

3.30

13.9
-0.0597
11.8

7.65
-5.47
6.56
0.56
1189

Table 3.8 Estimated parameters of the acceleration model for the entering though vehicles

μSRT<0.7s

σμSRT≥0.7sσParameters of Normal Distribution
Start-up response time, SRT [s]Constant
Start-up response time, SRT [s]Constant
Sample size
Late exit time, LET [s]Constant
Late exit time, LET [s]Constant
Sample size

Coefficients
0.246
1.63
－
0.374
217
-0.0369
1.92-0.0123
0.436
879

t values
13.8
55.3
－
20.5
-5.79
106.0
-2.27
34.7

3.6 Safety IndicesAfter modeling the clearing behavior of right-turning traffic and the starting behavior of crossing
through traffic, the conflict between these two traffic movements can be evaluated and assessed.
Various safety indices can be used to quantify these conflicts such as post encroachment time(PET) or time to collision (TTC). In this study, a unique index is proposed for the safetyassessment of angle collision between right-turning and cross traffic. The proposed index is called
Angle Collisions Index ACI. This index is based on combining two dimensions, the frequency andthe potential severity of vehicle-vehicle conflicts.
In past research, the frequency or rate of reported accidents is commonly used for the evaluation of
the safety at intersections. When applying such methods, comprehensive historical accident data isnecessary comprising at least several years. Therefore, this accident analysis is suitable for long23

term a posteriori assessments. Different alternative intersection layouts or signal timing plans
cannot be assessed a priori.
In those cases, the traffic conflict technique (TCT) is applicable in which time indices, e.g. post
encroachment time (PET), suggested by Allen, et al. (1978) are usually the measures for safety or
risk. However, most of them are initially proposed for estimating safety when gap-acceptance or
merging maneuver occur during the green intervals. Very few of them have been widely accepted
as a safety measure for signal change intervals (intergreen intervals), due to the complicated traffic
flow during this interval. For instance, Tang and Nakamura (2008) proposed the PET as a measurefor safety performance during intergreen intervals. A PET correspondent to a change of phases isthen defined as the elapsed time from when the last clearing vehicle in the previous phase passes
the conflict point till when the first entering vehicle released in the subsequent phase arrives there.
In this study, PET is used to estimate the number of conflicts. Conflicts are defined as
encroachments between two vehicles with a PET of less than t sec.
However, the PET alone cannot assess the safety of angle collisions, for example the impulse of thevehicles involved in the conflict is not considered, although it is a very important factor in
determining the severity of a potential accident. Therefore the proposed Angle Collision Index isdefined as in Equation (3.5) to incorporate both the frequency and the potential severity of conflicts.

(3.5)
Δke is the change in the total kinetic energy before and after the collision. The term

is used toweight the conflicts depending on the value of PET. As the PET becomes shorter, the likeliness of theconflict becomes higher.

To estimate the change in kinetic energy Δke, the following assumptions are made:•The vehicles undergo a perfectly inelastic collision.

•

The two vehicles move with the same speed together after the collision.

•

The friction between the vehicles and the road can be neglected.

•

The loss in Energy reflects how much energy is released if the collision occurs.

•

The system is isolated, where the momentum will be conserved.

Figure 3.7 illustrates the assumed kinetic energy concept after a collision. Since the collisionenvironment is assumed as being isolated, the momentum is conserved along both reference axes asshown inFigure 3.7c). Thus Equations (3.6) and (3.7) can be derived. By solving these equations, the change
in kinetic energy Δke can be estimated as shown in Equation (3.8).
24

u2

v

Clearing right-turning vehicle

2

Conflict Area

1


u1

Entering through vehicle

Conflict Areaa) Angle collisions between right-turningand cross traffic

u2
2

1

b) Assumed collision mechanismv
m2u2 sin  2(m1  m2 )v sin 
m1u1 cos 1

m1u1 sin 1

u1

m2u2 cos  2(m1  m2 )v cos 

Conflict Areac) Momentum analysis along reference axis
Where u1 is speed of the clearing right-turning vehicle (m/sec), u2 is the speed of the entering throughvehicle (m/sec), v is speed of clearing right-turning vehicle and entering though vehicle after collision(m/sec), θ1 is the angle between clearing right-turning vehicle and the positive x-axis at the conflictpoint (degrees), θ2 is the angle between entering through vehicle and the positive x-axis at theconflict point (degrees), α is the angle between the collided vehicles and the positive x-axis after
collision (degrees), m1 is the mass of the clearing right-turning vehicle (kg) and m2 is the mass of theentering through vehicle (kg).

Figure 3.7 The estimation of energy loss Δke due to angle collisions
(3.6)
(3.7)
(3.8)
This index will be used as the output of the simulation model for the safety assessment of angle
collisions at signalized intersections.
To demonstrate the sensitivity of PCI to PET and conflicting vehicles speed, Figure 3.8 ispresented. It assumes a conflict angle of 90 degrees between the two conflicting movement, and aweight of 1500kg for each vehicle with equal speeds. It is rational to see that as PET increases thevalue of ACI decreases. If PET becomes higher than 5 seconds, the value of ACI becomes
negligible. Furthermore at a constant PET, when the speeds of the conflicting vehicles increase,25

ACI increases as shown in Figure 3.8. This is quite rational since it reflects that the severity of aconflict increases as the speed of any of the conflicting vehicles increases.
70000

Speed of conflicting vehicles is10 m/sec

60000

Speed of conflicting vehicles is11 m/sec

ACI (-)

50000

Speed of conflicting vehicles is12 m/sec
Speed of conflicting vehicles is13 m/sec

40000

Speed of conflicting vehicles is14 m/sec

30000

Speed of conflicting vehicles is15 m/sec

20000

Assuming: 90 degrees Conflict Angel and the weightof each conflicting vehicle is 1500 kg (Passenger car)

10000
0
1

1.5

2

2.5

3

3.5

4

4.5

5

PET (sec)

Figure 3.8 The sensitivity of ACI to PET and the speed of conflicting vehicles

26

4 Left-turning Vehicle Conflicts with Pedestrians
4.1 Overview
Left-turning vehicles are modeled based on four separate models as shown in Figure 4.1. Firstly the
behavior of the pedestrians on the crosswalk is analyzed (Section 4.2). Secondly the path of theturning vehicles is modeled (Section 4.4). The vehicles can only pass the crosswalk when sufficient
gaps in the pedestrian stream are available. The assessment of the gaps is described in the gap
acceptance model (Section 4.3). In addition to the intersection geometry and the driver
characteristics, the gap acceptance influences the speed of the vehicles. The speed profile of theturning vehicles is analyzed in Section 4.5. The basic principles of the mentioned models have been
described in Chapter 2. Based on these models, conflicts of left-turning vehicles with pedestrians
can be assessed by using reasonable safety indices which is discussed in Section 4.6.

4.2 Pedestrian behavior analysis
4.2.1 Methodology
Many factors such as visibility, geometric layout of the intersection, driver behavior while turningand pedestrian behavior influence conflicts between pedestrians and left-turning vehicles. Most of
the existing studies which try to analyze the mechanism of such collisions concentrate on driver
behavior assuming that it is the most critical factor in determining pedestrian-vehicle collisions.
Road users try to anticipate other users’ behavior in order to avoid any collisions with them.
Widely varying road user behavior and trajectories may lead to misunderstanding of other users’
decisions which might result in safety problems. Therefore, it is quite important to consider not
only vehicles’ maneuver but also pedestrians’ maneuver and its variation which are affected by the

Maneuver of Left-turning
vehiclesPedestrian Behaviour

Gap Acceptance Model
Pedestrian Origin-Destination
Model
Turning Path Model
Pedestrian Speed Model
Speed Profile Model

Represent the conflict between left-turning vehicles andcrossing pedestrians

Figure 4.1 Required models to represent the conflict between left-turners and pedestrians
27

geometric layout of intersections, signal timing, and the existence of turning vehicles.
A preliminary macroscopic analysis on pedestrian speed considering the existence of turning
vehicles was not successful in finding any significant relationship. Therefore, a microscopic
approach is necessary to tackle pedestrian reaction to turning vehicles. Due to the limited time andthe complexity of pedestrian maneuver, this study focuses on the effect of pedestrian signal timing
and crosswalk geometry upon pedestrian speed at crosswalks as a first step.
In this study, two different spot speeds and two different travel speeds are defined and estimatedfor each observed pedestrian. Figure 4.2 illustrates the estimated speeds which are defined asfollows:-

Entering speed (vin): The spot speed at the entering edge of the crosswalk (m/sec).

-

Exit speed (vout): The spot speed at the exit edge of the crosswalk (m/sec).

-

First half travel speed (v1): The travel speed in the first half of the crosswalk (m/sec).

-

Second half travel speed (v2): The travel speed in the second half of the crosswalk (m/sec).

Figure 4.2 shows how to estimate travel speeds (v1 and v2). Pedestrian origin-destination is definedas pedestrian movement direction which is divided into two categories; near-side or far-side. Oneof the reasons behind dividing pedestrians into far-side and near-side is to macroscopically analyze
the effect of turning vehicles on pedestrian speed. When comparing v1 and v2, it is important toremember that the first half of the crosswalk for near-side pedestrians is the second half for far-sidepedestrians. In the analysis, pedestrians are also classified into two categories; pedestrians who facePhasing plan at observed
intersections

Far-side

f1
Position (x3 ,y3 )Timing t3
Exit spot speed vout

Travel speed of the second halfof the crosswalk v2v2 

Position (x2 ,y2 )Timing t2( x3  x2 ) 2  ( y3  y2 ) 2
t3  t 2

Travel speed of the first halfof the crosswalk v1

v1 
Position (x1 ,y1 )Timing t1
Entering spot speed vin( x2  x1 ) 2  ( y2  y1 ) 2
t 2  t1

f2

f3

f4

Near-side

Figure 4.2 Definition of pedestrian spot speeds and travel speeds
28

R1

G1

G3

G2

5 sec

R2

PFG

L/2vp
PG

Where: L is crosswalk length (m), vp is average pedestrian speed (assumed 1m/sec), PG is pedestrian
green (sec), PFG is pedestrian flash green (sec), R1 signal interval just before the start of pedestrian
green, and R2 is signal interval just after the end of pedestrian flash green.

Figure 4.3 Dividing pedestrian signal timing into several intervals
Table 4.1 Surveyed site characteristics

Intersection
nameCrosswalkposition

Dimensions
w(m)×L(m)Survey hours

ImaikeSuemori-Dori2
Nishi-Osu

East Leg
South Leg
North Leg

9m×20m
7m×18m
5m×36m

13:00-15:00
09:00-12:30
09:00-12:30

Pedestrian green
time PG (sec)

Cycle
Length(sec)

PG G1 G2

G3

Pedestrian
flashing green
time PFG (sec)

140
140
160

35
47
38

5
5
5

25
38
20

8
8
10

5
4
13

a turning vehicle while crossing (“with”) and who did not face a turning vehicle (“without”).
Pedestrian signal timing is divided into six intervals; R1, G1, G2, G3, PFG and R2 as shown in
Figure 4.3. G1 is defined as 5 s long, assuming that this time in average is enough for the waiting
pedestrians to discharge at the edge of the crosswalk. The second interval G2 is defined based on
the time needed for one pedestrian to cross a half of the crosswalk by assuming a speed of 1 m/sec.
In this way G2 is independent of a pedestrian platoon crossing at the same time. The remaining
pedestrian green time is defined as G3. Pedestrians who start crossing before the beginning ofpedestrian green PG are classified as crossing during R1 while those who start crossing after theend of pedestrian flash green PFG are classified as crossing during R2. R1 is defined as being 10 s,
the remaining pedestrian red time is R2.
v1, v2 and vout for each pedestrian are categorized depending on the entering time to the crosswalk.
For example, if a pedestrian entered the crosswalk in G1, then v1, v2 and vout for that pedestrian will
be classified as crossing during G1.
4.2.2 Data collection and processing
In order to analyze the pedestrian speed at crosswalks, video data was collected at three signalized
crosswalks. Table 4.1 presents the observation dates, the geometric and signal timing
characteristics of the study sites. All these sites are located in Nagoya City, Japan. The observed
crosswalks have significantly different geometric and operational characteristics such as crosswalk
29

Table 4.2 Observed number of pedestrians crossing in different pedestrian signal intervals

Crosswalk

Crosswalkposition

ImaikeEast Leg

SuemoriDori2South Leg

Nishi-Osu

North Leg

Crosswalk

Crosswalkposition

Average
L.T.V.
demandveh/hrDirectionnear-side
far-sidenear-side
far-sidenear-side

Observed No. of pedestrians
Total

126
312
344

far-side

R1

G1

with

without

withwithout

withwithout

62
199
49
59
172

200
43
41
4
21

1
9
0
1
4

12
4
1
0
11

4
106
5
26
82

130
27
35
2
5

141

2

4

0

73

0

Observed No. of pedestrians

ImaikeEast Leg

SuemoriDori2South Leg

Nishi-Osu

North Leg

Direction

G2

G3

PFG

R2

near-side
far-sidenear-side
far-sidenear-side

with
5
27
8
7
64

without
37
5
2
1
1

with
39
43
33
22
20

without
11
6
2
1
4

with
13
10
3
3
2

without
7
1
1
0
0

with
0
4
0
0
0

without
30
0
00

far-side

45

1

12

1

5

0

2

0

length and signal timing parameters. All the observed intersections are operated by a 4-phase plan
where a shared through-left turning phase is followed by an exclusive right turning phase as shownin Figure 4.2.
The trajectories of pedestrians are extracted from video data by using the image processing system
TrafficAnalyzer (Suzuki and Nakamura, 2006). The position of each pedestrian was extracted
every 0.5 seconds. The video coordinates were converted to global coordinates. The point where
the feet of the pedestrian are touching the ground is the reference observation point. All video
observations were done from high buildings around the intersections, thus for all video tapes, theobservation angle is large which enables tracking pedestrians without facing any obstacles.
It is important to note that all observed sites have high through traffic demand, thus most of theright turning vehicles turn in their exclusive phase which explains why most of the pedestrian
involved in conflicts are with left turning vehicles. Table 4.2 presents the observed number ofpedestrians who start crossing in various signal intervals, who face (“with”) or do not face(“without”) turning vehicles, and average left turning vehicle demand (L.T.V). According toobservations, the number of pedestrians who start crossing after the end of pedestrian flash green is

30

3.50

Entering speed vin (m/sec)

2.70

3.16

85 Pecentile
Mean( ) Sample size

3.00
2.62

2.50
2.00
1.50

1.97

1.89
1.44

1.57

1.84
1.39 1.37
1.53

1.34

1.00

1.17

1.06

1.74

1.72

1.67

1.72

1.50
1.49

1.20

2.03

1.96

1.95

1.561.36 1.39
1.48 1.27
1.40
1.37
1.33
1.22
1.06
0.94

1.50

1.58

1.62

1.33
1.09

0.50
0.00

G1 G2 G3 FG G1 G2 G3 FG G1 G2 G3 G1 G2 G3 G1 G2 G3 G1 G2 G3(134) (42) (50) (26) (133) (32) (49) (19) (40) (10) (35) (28) (8) (23) (87) (65) (24) (73) (46) (13)Near-side

Far-side

Near-side

ImaikeFar-side

Suemoridori2

Near-side

Far-side

Nishiosu

Figure 4.4 The mean and 85 percentile of entering speeds vin in different signal intervals
very small while those who start crossing before pedestrian green starts is higher, especially at
Imaike Intersection where pedestrian demand is much higher than at other sites.
4.2.3 Analysis of pedestrian speeds
There are several factors that might affect the variations in pedestrian speeds. According to the
conducted analysis, signal timing, crosswalk length and the existence of turning vehicles are themost significant factors that affect pedestrian speeds while crossing.
Figure 4.4 shows the mean and the 85 percentile of pedestrians’ entering speeds vin from the nearside and far-side of the crosswalk. It is clear that the average entering speed increases as the time ofpedestrian green proceeds. This tendency is understandable, since pedestrians who see the green
indication early before reaching the crosswalk tend to hurry up so they can cross before the signal
change. This phenomenon is affected by crosswalk length. It is found that both near-side and farside average pedestrian entering speeds during G3 at Nishiosu intersection are significantly higher(at 95% confidence level) than other sites. Due to the extremely long crosswalk at Nishiosuintersection, pedestrians hurry up when they approach the crosswalk during pedestrian green
interval trying to secure as much time as possible for the long crossing distance. This also explains
why the differences between the entering speeds in G1, G2 and G3 increase as crosswalk length

31

3.50
85Percentage
Mean( ) Sample size

Exiting speed vout (m/sec)

3.00
2.50
2.07

2.00
1.50

1.57 1.53 1.61 1.65 1.65 1.56
1.38

1.00

1.24

1.46
1.34

1.74

1.40 1.32

1.69
1.43

1.61 1.53 1.73

1.71 1.74

1.83

1.57
1.54
1.53
1.40
1.44
1.22

2.03

1.94
1.70 1.66
1.56
1.42 1.41

1.66

1.55

1.62
1.46 1.35

0.50

0.00

G1 G2 G3 FG G1 G2 G3 FG G1 G2 G3 G1 G2 G3 G1 G2 G3 G1 G2 G3(134) (42) (50) (26) (133) (32) (49) (19) (40) (10) (35) (28) (8) (23) (87) (65) (24) (73) (46) (13)Near-side

Far-side

Near-side

ImaikeFar-side

Suemoridori2

Near-side

Far-side

Nishiosu

Figure 4.5 The mean and 85 percentile of exiting speeds vout in different signal intervals
increases. Simultaneously, it is clear that the average entering speeds of near-side pedestrians arehigher than far-side pedestrians especially during G3.
Figure 4.5 shows that the mean exit speed vout of far-side pedestrians is significantly higher thanthat of near-side pedestrians which can be attributed to the effect of exiting turning vehicles. Thereis no clear difference in exiting speeds between G1 and G2. However, exiting speeds are
significantly higher in G3 compared to G1 and G2, which means that pedestrians in the second halfof signal green interval tend to exit the crosswalk faster compared to the first half of the green
interval.
It is interesting to see that the exit speed vout distribution during PFG of far-side pedestrians is
significantly higher compared to that of near-side pedestrians as shown in Figure 4.5. This can bereferred to the effect of turning vehicles since far-side pedestrians exit from the side where theymight encounter conflicts with turning traffic. This explains why far-side pedestrians hurry up
when they reach the second half of the crosswalk which is simply to clear the conflict area as fast
as possible. Meanwhile, near side pedestrians exit from the side where they don’t have conflicts
with turning traffic, thus they feel safer which make them slow down. Such behavior is very criticalsince drivers might not be able to predict such change in pedestrian speeds which might lead tomisjudgments and wrong decisions.
Figure 4.6 and Figure 4.7 show the mean and the 85 percentile of first half v1 and second half v2
travel speeds and for near-side and far-side pedestrians respectively. For near-side pedestrians,
32

Travel speed in the first half v1 (m/sec)

3.50
3.00

2.97

3.00

85 Percentage
Mean( ) Sample size

3.10

2.50

1.50

2.00
1.75
1.52 1.68
1.55
1.34
1.34 1.34

1.77
1.50

1.48

1.38

1.00

2.10

2.06

2.00

1.24

1.59 1.54
1.59
1.42
1.31

1.75

1.77 1.85
1.65

1.53

1.56

1.56

1.64

2.10
1.66

1.42 1.43

1.96
1.54

1.71
1.45 1.41

0.50
0.00

G1 G2 G3 FG G1 G2 G3 FG G1 G2 G3 G1 G2 G3 G1 G2 G3 G1 G2 G3(134) (42) (50) (26) (133) (32) (49) (19) (40) (10) (35) (28) (8) (23) (87) (65) (24) (73) (46) (13)near-side

far-sidenear-side

Imaikefar-side

Suemoridori2

near-side

far-side

Nishiosu

Figure 4.6 The mean and 85 percentile of first half travel speeds v1 in different signal intervals
there were no significant differences (95% significance level) between v1 distributions in G1 andG2. This also applies to v2 distributions. However at Suemori-Dori2 intersection, the means of v1
and v2 for near-side pedestrians in G1 and G2 are significantly different as shown in Figure 4.6 andFigure 4.7. The inconsistent results at Suemori-Dori2 intersection might be due to the insufficient
sample size. The travel speed distributions in G3 are significantly different from those in G1 andG2 at all intersections. This can be explained that pedestrians predict how long time is available
before the termination of pedestrian green interval, which makes them speed up.
Generally, it is concluded that the travel speeds of the pedestrians waiting at the beginning of green
interval (G1) from near-side and far-side are quite similar. The significant change occurs in thesecond half of pedestrian green interval (G3). This phenomenon is very important to be consideredsince most of the severe conflicts between pedestrians and turning vehicles occur during the second
half of pedestrian green in which number of crossing pedestrians becomes smaller. Moreover, bycomparing the travel speeds (v1 and v2) at Nishiosu Intersection with those at Imaike and SuemoriDori2 intersections, it is clear that travel speeds at Nishiosu intersection are significantly higher(95% significance level) as shown in Figure 4.6 and Figure 4.7, which can be referred to theextremely long crosswalk.
In Figure 4.4, Figure 4.5, Figure 4.6, and Figure 4.7, the entering, exit and travel speeds duringpedestrian flash green interval PFG are presented. The speeds during PFG are presented forpedestrians at Imaike Intersection only, since the observed number of pedestrian during PFG at the33

Travel speed in the second half v2 (m/sec)

2.50
2.00

85Pecentage
Mean( ) Sample size
1.68

1.60
1.62
1.67
1.52

1.52

1.40

1.39
1.28

1.34 1.32

1.42

1.74
1.89 1.58

1.59

1.67

1.50

1.49

1.59

1.40

1.32

2.18

2.11

2.10

1.86

1.54

1.50

2.30
2.12
1.72
1.58
1.641.55
1.42 1.41

1.56

1.63

1.52

1.65
1.45

1.00

0.50
0.00

G1 G2 G3 FG G1 G2 G3 FG G1 G2 G3 G1 G2 G3 G1 G2 G3 G1 G2 G3(134) (42) (50) (26) (133) (32) (49) (19) (40) (10) (35) (28) (8) (23) (87) (65) (24) (73) (46) (13)near-side

far-sidenear-side

Imaikefar-side

Suemoridori2

near-side

far-side

Nishiosu

Figure 4.7 The mean and 85 percentile of second half travel speeds v2 in different signal
intervals

other sites is very small. The distributions of entering speeds for far-side and near-side pedestrians
in PFG are not significantly different as shown in Figure 4.4. This somehow contradicts with theresults during G3 where near-side pedestrians have significantly higher entering speeds comparedto far-side pedestrians at all sites. Furthermore, it is concluded that the average of entering speeds
during PFG is significantly higher than that of G1, G2 and G3.
Regarding the effect of turning vehicles, the mean travel speed (v1 and v2) for far-side pedestrians
who faced (with) and did not face (without) turning vehicles are significantly different at 95%
confidence level while no significant differences can be found for near-side pedestrians. Basically,
the effect of turning vehicles on pedestrian speed is totally dependent on the circumstances when
they meet, such as vehicle speed, vehicle type, pedestrian signal timing, etc. Therefore, it isdifficult to reasonably assess the effects of turning vehicles in macroscopic analysis level.
4.2.4 Pedestrian speed modelingIn this section, models to represent the speed profile of pedestrians on crosswalks are introduced. In
this study, it is assumed the speed profile of each pedestrian is formed from the two travel speeds v1
and v2. Thus these two speeds are modeled as normally distributed and as a function of crosswalk
geometry, pedestrian demand, pedestrian origin-destination and the defined pedestrian signal
intervals G1, G2, G3 and PFG as shown in Figure 4.3.
34

Table 4.3 First half travel speed v1 models in different pedestrian signal intervals
Gamma
Distributionμσ

G1 and G2

PFG

Estimate (Sig.)

G3
v1 N
Estimate (Sig.)

1.347372 (0.000)
0.004494 (0.002)

1.113781 (0.000)
0.0221197 (0.003)

2.023283 (0.000)-0.005097 (0.000)--

0.241910 (0.000)
0.004254 (0.000)-0.0643659 (0.519)
0.023111 (0.000)

0.708038 (0.000)--0.003817 (0.000)---113.33673
698-113.6195
194-48.31568
45

Parameters

Const
Crosswalk length (m)Pedestrian demand*(ped./hr/m_width)
Const
Crosswalk length (m)Pedestrian demand*(ped./hr/m_width)
Log likelihood
Sample Size-

* Pedestrian demand per hour per meter width of the crosswalk.

Table 4.4 Second half travel speed v2 models in different pedestrian signal intervals
G1 and G2

G3
v2 N
Estimate (Sig.)

PFG

Gamma
Distribution

Parameters0.4282726 (0.000)

0.510429 (0.000)

0.727701 (0.000)

0.614326 (0.000)

μ

Const
First half travel
speed v1 (m/sec)
Crosswalk length (m)Pedestrian demand*(ped./hr/m_width)
Dummy (Far-side=1,
Near-side=0)--.048067 (0.000)-0.002302 (0.002)--

0.021047 (0.199)

0.031439 (0.462)

-

Const
First half travel
speed v1 (m/sec)
Crosswalk length (m)Dummy (Far-side=1,
Near-side=0)
Log likelihood
Sample Size

0.149236 (0.000)-0.030211 (0.476)

0.003041 (0.970)

0.113909 (0.000)

0.186845 (0.000)

0.158452 (0.001)-0.004377 (0.000)--

0.049379 (0.000)

0.08538 (0.005)-

104.07288
698-37.197825
194-48.31568
45

σ0.002715 (0.991)
0.342651 (0.000)* Pedestrian demand per hour per meter width of the crosswalk.

Table 4.3 shows the developed first half travel speed v1 models for different pedestrian signal
intervals, while Table 4.4 shows the developed second half travel speed v2 models. Travel speeds v1
and v2 during G1 and G2 are significantly affected by pedestrian demand per hour per meter widthof the crosswalk which is not the case during G3 and PFG. Furthermore, it is clear that crosswalk
length is one of the most significant parameters and it has a positive relationship with pedestrian
travel speed. During PFG, it is difficult to clarify the significance of several parameters such aspedestrian origin-destination due to the few available samples. Thus it is necessary to collect moredata to develop a reliable model.
354.3 Gap acceptance models
To be able to estimate the speed adjustments of left-turning vehicles due to pedestrians, theacceptance of gaps between crossing pedestrians by drivers needs to be modeled and quantified. In
this section, the acceptance of lags and gaps between pedestrians by left-turning drivers aredescribed. The maneuvers of left-turning traffic and pedestrians are extracted from video data byusing the image processing program TrafficAnalyzer (Suzuki and Nakamura, 2006). Refer to
Section 2.5 for an explanation of the methodology.
The characteristics of the observed sites are listed in Table 4.5. Collected data are classified
according to the defined types of lags/gaps in Figure 2.10. The cumulative Weibull Distribution isused to fit the collected lag/gap acceptance distributions as shown in Figure 4.8. Developed models
are applicable only for passenger cars, since sufficient data for heavy vehicles are not available tocalibrate the models. As shown in Figure 4.8, drivers tend to accept shorter gaps of pedestrians
arriving from the near-side (Type A) than from the far-side (Type B), thus highlighting theimportance of the pedestrians’ crossing direction on driver behavior.

Table 4.5 Number of accepted and rejected lag/gaps of each type for observed sites
Type A

Type B

Type C Type D Type E

A*

R*

A*

R*

A*

R*

A*

R*

A*

R*

1

3

4

16

4

20

3

32

8

30

北 north

1

-

10

3

-

-

-

2

-

-

西 west

2

0

5

2

-

-

-

-

-

-

-

2

-

-

2

-

2

6

4

6

東 east

3

-

5

4

-

-

-

1

-

-

北 north

13

14

13

6

13

8

11

5

12

7

西 west

15

20

10

12 12

10

12

12

8

5

1

2

2

14

-

-

1

3

-

3

東 east

9

2

20

4

-

2

6

1

5

0

南 south

-

-

4

3

-

-

-

1

-

-

西大須 Nishiosu

西 west

6

4

25

16

4

20

3

33

8

30

太閤通り Taikodori

西 west

4

20

6

12

4

6

5

2

5

7

55

67 104 92 39

66

43

98

50 88

Intersection name Approach
今池 Imaike
青山 Aoyama
川名 Kawana

末盛通 Suemoridori

広路通 Hirojidori
堀田 Horita

Total* A is accepted lag/gap while R is rejected lag/gap.

36

100%

90%

Probability of acceptance80%

Type A
Type B
Type CType D
Type E

70%

60%

50%

Lag/Gap
Type

40%

Parameter Estimate
α
β
α
β
α
β
α
β
α
β

A
30%

B
C

20%

D
10%

E

Error

2.011
3.338
2.643
4.344
3.526
4.951
4.766
7.774
4.829
7.264

0.461
0.263
0.398
0.178
0.938
0.268
0.644
0.169
0.943
0.226

11

12

Adjusted Sample size
R2

A

R

0.96

55

67

0.98

104

92

0.93

39

66

0.98

43

98

0.96

50

88

0%

0

1

2

3

4

5

6

7

8

9

10

13

14

15

16

Lag/Gap (sec)Figure 4.8 Fitted Weibull lag/gap acceptance models and their parameters

4.4 Path of left-turning traffic
As explained in Section 2.1, the path of turning traffic is modeled by a combination of straight,
circular and Euler spiral curves. The estimated models for the curve segments which are shown inEquations (2.1), (2.2) and (2.3) are listed in Table 4.6 and Table 4.7. It is assumed that the enteringspiral curve parameter A1 and the exit spiral curve parameter A2 are dependent on the minimum
speed along the turning maneuver. Thus Vmin is modeled assuming a Normal Distribution. For
detailed information refer to the first year report of the project.

37

Table 4.6 Results of estimated Euler spiral parameters for left-turning vehicles

Explanatory variables
Const.
Corner radius Rc (m)Intersection angle (degrees)
Heavy vehicle dummy (heavy vehicle:1,
passenger car: 0)
Lateral distance from shoulder to centerof exit lane (m)Minimum speed Vmin(km/h)
Modified R2

Parameter of entering Euler spiralcurve A1(m)Parameters (t-values)-1.65(-1.85)
0.334(8.73)
0.0404(3.61)－

Parameter of exit Euler
spiral curve A2 (m)Parameters (t-values)
2.33(2.83)
0.335(7.52)－
2.05(2.89)

0.461(7.70)

1.04(15.2)

0.369(9.04)
0.772

0.268(6.88)
0.774

Table 4.7 Results of estimated minimum radius and minimum speed for left-turning vehicles
Radii of circular
curve Rmin (m)Parameters (t-values)-6.46(-6.31)
0.390(12.9)
0.127(13.1)

Minimum speed Vmin
(km/h)
Parameters (t-values)
1.20(0.91)
0.212(4.20)
0.156(11.6)－-4.62(-5.32)

0.862(16.8)

0.794(9.22)-2.86(-3.77)

2.22(8.26)

Corner radius Rc (m)0.0624(3.09)－

Intersection angle (deg)0.0363(4.95)－

Lateral distance fromshoulder to center of exit
lane (m)0.118(3.89)

0.169(3.15)

Explanatory variables

AverageStandard
deviation

Const.
Corner radius Rc (m)Intersection angle (degrees)
Heavy vehicle dummy(heavy vehicle:1, passenger
car: 0)Lateral distance fromshoulder to center of exit
lane (m)Const.

4.5 Speed profiles of left-turning traffic
4.5.1 Maneuver parts
Left turning traffic commonly has to yield to crossing pedestrians. If no pedestrians are present,
the driver will follow an ideal speed profile. He might have to deviate from this profile if he has toreact to pedestrians. Neglecting car-following behavior, which is modeled separately, and thereaction to signals, which is also modeled separately, the drivers approaching the crosswalk will
have to observe pedestrians and react according to the assessment of the situation. If the driver is
not sure that he can clear the crosswalk safely, he will decelerate, if necessary to a full stop. Only

38

once he perceives a sufficient gap in the pedestrian stream he will accelerate and clear the conflictarea at the crosswalk.
To model this behavior the turning maneuver is divided into three parts as follows:•

The driver approaches the intersection and reduces the speed in order to turn safely. During
this part the driver follows the ideal speed profile. This profile is determined by intersection
geometry and driver characteristics.

•

The driver perceives pedestrians on the crosswalk and yields to them. It is assumed that thedriver reduces the speed in a way that he can come safely to a full stop in front of thecrosswalk, if necessary. This deceleration is described by a stopping profile. The time when
the driver changes from the ideal speed profile to the stopping profile with reference to thestart of the turning maneuver is called yielding time

. While the driver decelerates, hecontinues to observe the crosswalk and waits for an acceptable gap.
•

Once the driver perceives a suitable gap in the pedestrian stream on the crosswalk, heaccelerates to the desired exiting speed and, thus, clears the crosswalk. This behavior isdescribed by a clearing profile. The time when the driver decides to pass is called passing time.

This three step process is illustrated in Figure 4.9. The driver starts the approach to the intersection
at point . At point  he scans the pedestrian crosswalk for the first time and decides to yield (nosuitable gap at time A). During each time step he re-assesses the situation at the crosswalk. This reassessment is highlighted for point . Since the driver wants to safely pass as early as possible, he

Speedventer 0
vexit
1

A

Clearing profile
B

vmin
2

C

3

t yield4

Ideal profile Ideal profile(inflow)(outflow)

Reaching the crosswalk

Stopping profilet min t pass

texit

Time

Figure 4.9 Ideal speed profile, stopping profile, and clearing profile in reaction to pedestrians

39

assumes the clearing profile for the acceleration and predicts his arrival at the crosswalk to be at B.
He rejects the gap available at this time and follows the stopping profile further. At point  theassessment leads to the acceptance of the gap at C. The driver switches to the clearing profile(passing time), passes the crosswalk at C, accelerates to the desired exiting speed and finishes theturning maneuver at point .
The available gap is checked using the gap acceptance model described in Section 2.5. The driverassumes constant walking speed of the pedestrians.
Yielding time and passing time are determined by the driver reaction to pedestrians. For
simplification it is assumed that the driver reacts to pedestrians once he passed the stop line. From
this time on, the driver will scan the crosswalk and assess the gaps in the pedestrian stream.
It is not possible to adequately verify this simplified model without extensive driving experiments.
However, the speed profiles resulting from this model can be validated with empirical data. In
reality drivers will assess possible gaps in dependence of their own distance from the crosswalk.
The farther they are from the crosswalk, the more uncertainty is involved in predicting thepedestrian behavior. Due to insufficient data on the effect of this uncertainty, the model will notconsider the distance of the vehicle from the crosswalk.
4.5.2 Empirically derived model parameters
The basic principles of the speed of vehicles when turning at a signalized intersection have been
explained in Section 2.3. The particularities of left-turning speed profiles are incorporated into themodel by empirical analysis of the speed function coefficients and constraints. Table 4.8 shows theconstraints for the speed equation (2.4) with the acceleration as the first derivative and their four
unknowns (cf. Figure 2.4). This system of linear equations is underdetermined for the ideal speed
profile (inflow and outflow) and for the clearing profile. The coefficient c1 and the minimum speed
vmin are empirically modeled.
In addition to vmin, c1,in, c1,out, and c1 of the clearing profile the position of the speed profile withreference to the path of the vehicle xmin is empirically modeled (cf. Subsection 2.3.4). The observed
behavior of vehicles reveals that these parameters are related to certain intersection characteristics,
namely the intersection angle, the curb radius, the lateral distance of the vehicle in the exit, theentering speed, and the exiting speed (cf. Figure 2.2). Correlation charts with the different
influencing factors are shown on the following pages. The linear trend is shown with the mean
plus/minus the standard deviation indicated by dashed lines.

40

Table 4.8 Constraints and modeled parameters for the speed profile of left-turning vehicles
Ideal
profile(inflow)

Parameters

Ideal
profile(outflow)

Stopping
profileClearing
profilexCW+xinv (in)

ventervmin

videalvstop

v (out)(vmin)

vexit

0

vexit

a (in)

aenter0

aidealastop

a (out)

0

aexit

0

aexit

t (out)(tmin)(texit - tmin)(tstop - tin)(texit - tin)

Degree of freedom/constraints

5/3

5/4

5/5

5/4

vmin, c1,in

c1,outModeled parameter

c1

14

12

Speed (m/s)

10

8

6

4

c1,in=0.01, c1,out=-0.01, vmin=5, xenter=20
c1,in=0.01, c1,out=-0.01, vmin=4, xenter=0
c1,in=0.01, c1,out=-0.02, vmin=5, xenter=0
c1,in=0.005, c1,out=-0.01, vmin=5, xenter=0
c1,in=0.01, c1,out=-0.01, vmin=5, xenter=0

2

0
0

5

10

15

20

25

30

35

Time (s)Figure 4.10 Illustration of empirically modeled coefficients and constraints for the speed profile(left-turning)
The parameters are modeled as randomly distributed values. For the coefficients characterizing therandom distribution, a linear combination of the most important influencing factors has been used.
The coefficients are given in a table for each speed profile parameter.

41

0.14

ModeledRelative frequency (-)

0.12

Observed

0.1
0.08
0.06
0.04
0.02
0
0.01 0.03 0.05 0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23 0.25 0.27 0.29

Coefficient c1 (m/sec⁴ )a) c1,in for inflow
0.18

ModeledObserved

0.16

Relative frequency (-)

0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
-0.19

-0.17

-0.15

-0.13

-0.11

-0.09

-0.07

-0.05

-0.03

-0.01

Coefficient c1 (m/sec⁴ )b) c1,out for outflow
Figure 4.11 Modeled and fitted c1 coefficients or the inflow and outflow of left-turning vehicles

Coefficients c1,in (inflow) and c1,out (outflow)
The coefficient c1 represents a jounce (second derivative of the acceleration). It determines theshape of the speed profile. For the inflow it is positive, for the outflow it is negative. The
distribution shows a distinct positive skew. Therefore, a Gamma Distribution is chosen to represent
the data as shown in Figure 4.11.
Due to the great number of potential factors influencing the coefficient c1 of the ideal speed profile
for left-turning vehicles, a big sample size is required to study them. Figure 4.12 indicates amoderate correlation between entering speed, the lateral position of the vehicle at the exit (related
to the chosen exit lane), the intersection angle, the curb radius and the coefficient c1,in for the inflow.
In case of the outflow coefficient c1,out the exiting speed and the lateral position of the vehicle in theexit appear to be important factors as shown in Figure 4.13. The chosen models are given in Table
4.9.
42

0.35

Inflow c1 Coefficient (m/sec⁴ )Inflow c1 Coefficient (m/sec⁴ )

0.35

0.3
0.25

0.3

0.25

m s

0.2

0.2

m s

0.15

0.15
0.1

m s

0.1

0.05

0.05

m s

0

0
0

5

10

15

20

0

25

4

Entering speed (m/sec)

8

12

16

20

Lateral exit distance (m)

0.35

0.35

Inflow c1 Coefficient (m/sec⁴ )b) Lateral exit distance and c1,in Coefficient

Inflow c1 Coefficient (m/sec⁴ )a) Entering speed and c1,in Coefficient
0.3

0.3

0.25

0.25

m s

0.2

m s

0.2

0.15

0.15
0.1

m s

0.05

0.1

m s

0.05

0

0
40

80

120

0

160

4

8

12

16

20

24

Corner radius (m)Intersection angle (degrees)

0.05

Outflow c1, out Coefficient c1 (m/sec⁴ )Outflow c1, out Coefficient c1 (m/sec⁴ )c) Intersection angle and c1,in Coefficientd) Corner radius Rc and c1,in Coefficient
Figure 4.12 Correlation between several parameters and c1,in Coefficient for left-turning vehicles

m s

0

-0.05

m s

-0.1

-0.15
-0.2

-0.25
-0.3
5

10

15

20

0

m s

-0.05
-0.1

m s

-0.15
-0.2

-0.25
-0.3
0

25

Exiting speed (m/sec)

5

10

15

20

Lateral exit distance (m)a) Exiting speed and c1,out Coefficientb) Lateral exit distance and c1,out Coefficient
Figure 4.13 Correlation between exiting speed, lateral exit distance and coefficient c1,out for leftturning vehicles
43

Table 4.9 Models of c1,in and c1,out coefficients for left-turning vehicles
Gamma
Distribution

c1,in

c1,outαβEstimate (Sig.)
2.090837 (0.019)

αβEstimate (Sig.)
1.402047 (0.013)

0.2563564 (0.000)--0.0154569 (0.046)

-

-

-

-0.1678538 (0.006)

0.0633479 (0.033)--0.0224424 (0.623)

0.0573156 (0.000).0771912 (0.000)-0.001729 (0.000)--0.001088 (0.002)-

0.0021931 (0.022)---.0035521 (0.004)

336.43562
202

379.66862
188

Parameters
Const

Entering speed(m/sec)Intersection angle(degrees)
Corner radius (m)Lateral exit distance(m)
Exiting speed(m/sec)αConstEntering speed(m/sec)Corner radius Rc(degrees)
Lateral exit distance(m)
Exiting speed(m/sec)βLog likelihood
Sample Size

Minimum speed
The distribution of observed minimum speeds follows an only slightly skewed distribution asshown in Figure 4.14. A Normal Distribution still fits the data well. The minimum speed

11

100%

Frequency
Cumulative %

10

90%

9

80%

Frequency (-)

8

70%

7

60%
6
50%
5
40%
4
30%

3

20%

2

12

11.6

11.2

10.8

10

10.4

9.6

9.2

8.8

8

8.4

7.6

7.2

6.8

6

6.4

5.6

5.2

4.8

4

4.4

3.6

3.2

0%

2.8

0

2

10%

2.4

1

Minimum speed (m/sec)

Figure 4.14 The distribution of observed minimum speeds vmin for left-turning vehicles
44

14

14

Minimum speed (m/sec)

Minimum speed (m/sec)

10

8

m s

6
4

10
8

4
2

0

0

10

15

20

m s

6

2

5

m s

12

m s

12

25

0

4

14

14

12

12

m s

8

6

m s

4

12

16

20

b) Lateral exit distance and c1,in Coefficient

Minimum speed (m/sec)

Minimum speed (m/sec)a) Entering speed and c1,in Coefficient

108Lateral exit distance (m)Entering speed (m/sec)

2

m s

10

8
6

m s

4

2

0

0
0

20

40

60

80

100

120

140

0

Intersection angle (degrees)

5

10

15

20

25

Corner radius (m)c) Intersection angle and c1,in Coefficientd) Corner radius Rc and c1,in Coefficient

Figure 4.15 Correlation between several parameters and minimum speed for left-turning vehicles

potentially depends on a range of factors. Figure 4.15 indicate a correlation of entering speed,
lateral position of the vehicle in the exit, curb radius, and intersection angle with the minimum
speed. The chosen model is shown in Table 4.10.

45

Table 4.10 Minimum speed vmin and position of minimum speed xmin models for rightturning vehicles
Gamma
DistributionμσParameters
Const
Entering speed (m/sec)
Corner radius Rc (m)Intersection angle (degrees)
Lateral exit distance (m)Heavy vehicle dummy(HV:1, PC:0)
Const
Lateral exit distance (m)Corner radius Rc (m)Log likelihood
Sample Sizevmin
N
Estimate (Sig.)-0.3006497 (0.496)
0.0907563 (0.003)
0.0606657 (0.000)
0.0386817 (0.000)
0.2327502 (0.000)

xmin
N
Estimate (Sig.)
1.418104 (0.516)
0.5861338 (0.000)
0.0896472 (0.000)
0.5774585 (0.000)-.4964164 (0.107)-

0.6649318 (0.000)
0.041912 (0.019)-257.82707
202

0.1351356 (0.828)
0.3356169 (0.000)
0.1443846 (0.002-541.88456
199

Position of minimum speed on the vehicle path
The position of the minimum speed xmin is defined as the distance from the beginning of the turning
path of the vehicle (first clothoid) of the vehicle path in the intersection to the point where theminimum speed vmin occurs (cf. Subsection 2.3.4). As shown in Figure 4.16 xmin follows asymmetric distribution; therefore, it is modeled as a Normal Distribution. It is found thatintersection angle, curb radius, and lateral position of the vehicle in the exit are the most significant
influencing factors as shown in Figure 4.17. The chosen model is shown in Table 4.10.

16

14

100%

Frequency
Cumulative %

90%
80%

12

Frequency (-)

70%

10

60%

8

50%
40%

6

30%
4
20%
2

10%
0%

0
1.5
3
4.5
6
7.5
9
10.5
12
13.5
15
16.5
18
19.5
21
22.5
24
25.5
27
28.5
30
31.5
33
34.5
36
37.5
39

0

Position of minimum speed xmin (m)Figure 4.16 The distribution of observed xmin (position of minimum speed) for left-turning
vehicles46

45

Position of minimum speed xmin (m)Position of minimum speed xmin (m)

45

m s

40
35
30
25
20
15

m s

10
5
0
40

60

80

100

120

40
35
30

m s

25
20
15

m s

10

140

5
0
0

5

Intersection angle (degrees)a) Intersection angle and xmin
Position of minimum speed xmin (m)

10

15

20

25

Corner radius Rc (m)b) Corner radius and xmin

45

m s

40
35
30
25

m s

20

15
10
5
0
0

5

10

15

20

Lateral exit distance (m)c) Lateral exit distance and xmin
Figure 4.17 Correlation between several parameters and position of minimum speed xmin for leftturning vehicles

4.6 Safety Indices
Following the same discussion in Section 3.6, an index to evaluate the conflicts between pedestrianand left-turning vehicles is an essential requirement. Most of the previous studies use PET to assess
such conflicts which means that the kinetic energy of the turning vehicle is not considered.
However the speed of the vehicle and its type is an important factor in determining the severity andthe damage caused by the collision. Thus, a new index which is called as Vehicle Pedestrian Index
VPI is proposed for the assessment of conflicts between pedestrians and turning vehicles as shownin Equation (4.1).

47

(4.1)

Where m is the mass of the turning vehicle (kg), and u is the speed o the turning vehicle at theconflict point (m/s). VPI will be used as the output of the simulation model for the safetyassessment of conflicts between pedestrian and turning vehicles at signalized intersections.

48

5 Simulation Development
5.1 Introduction
5.1.1 Outline and objectives
To enable a safety assessment as described in Sections 3.6 and 4.6, a simulation environment was
programmed. This simulation software provides a simple framework to integrate the models forconflicts inside of intersections. The basic vehicle behavior follows the same principles as existing
microscopic traffic flow simulations. Traffic generation based on OD matrices, car following
behavior, different vehicle types with individual randomly distributed characteristics and simple
pre-timed signal control modules enable a basic representation of the traffic flow along links
between nodes.
The developed micro-simulation, however, focuses on the vehicle behavior inside of intersections.
In this way the simulation goes beyond existing software. So far the start-up behavior of throughtraffic, the clearing behavior of right turning traffic, the turning behavior of right and left turning
traffic, the reaction of left turning vehicles to pedestrians, and the passing behavior of pedestrians
on crosswalks has been implemented.
Objective of the simulation is the validation and demonstration of the developed models, and,furthermore, the safety assessment of different intersection layouts and signal timings.
5.1.2 Requirements and capabilities
To address the advantages of the proposed simulation model, it is useful to compare it with thecapabilities of existing simulation programs. Table 5.1 shows a comprehensive comparison
between the proposed simulation program and another three popular microscopic simulation
programs. The references of this comparison are Gettman and Head (2003), Jones, et al. (2004) and
AIMSUN 5.1 Micro-simulator User’s manual (2006).
Table 5.1 Comparison between proposed and existing simulation models
Characteristic
General characteristic
Graphical editor
Road systems
Signal timing
Traffic assignment
Behavior models
Vehicle gap
acceptance model

VISSIM

AIMSUNPARAMICS

Proposed simulation
program

Yes
Network
Actuated
Dynamic

Yes
Network
Actuated
Dynamic

Yes
Network
Actuated
Dynamic

Yes
Isolated intersection*
Pre-timed*
Fixed*

Yes

Yes

Yes

Yes

49

Lane changing model
Car following model

Yes
Yes

Yes
Yes

Yes
Yes

Reaction to yellow

By driver, by
signalYes

By driver

Reaction to green

No

No

No

Driver reaction time
Variable
acceleration/decelerati
on rateSight distance limits

No

Yes

Yes

*
Yes
By vehicle type,distance to leading
vehicle, signal,
approaching speed,
distance to stop-line
By driver, signal,
clearing vehicle.
Yes

Yes

Yes

Yes

Yes

Yes
Gap
acceptancemodelsYes
Gap
acceptancemodelsYes
Gap
acceptancemodelsVariations in turning
paths at intersections

No

No

No

Turning speeds atintersections

By turning
radius,vehicle types

UnclearMaximumturning speed
only

Yes
Gap acceptancemodels and speed
adaptations
By geometriccondition, vehicle
types, approaching
speed.
By approaching speed,
position of vehicle,
vehicle type,intersection geometry.

Yes

Yes

Yes

No

No

Yes
(for various types ofconflicts)

Yes

Yes

Yes

By type
By vehicletype

By type
By vehicletype

By type

Vehicles interact withpedestrian

Data extraction
Road users’ stateYesexportable to file
Conflictcharacteristics
Limited to(Position, timing,rear-end
speed of conflicting
conflicts only
vehicles, etc.)
Calibration and parameters
Update time steps canYes
be changed
Vehicle size
By type
By vehicle
Variable headways
type

By vehicle type

* Planned to be improved in the near future

To achieve the objectives described before, the simulation environment has to fulfill certain
requirements. The major focus is the generation of safety indices for the conflicts mentioned.
Therefore, the vehicle behavior inside of intersections has to be accurately simulated. Minimum
requirements are as follows•

Isolated intersection with defined geometry and layout (approach and exit lanes, curb radii,
hard nose positions etc.)•

Pre-timed signal control
50

•Passenger cars with defined properties (dimension, desired and limiting speeds andaccelerations etc.)•

Traffic demand between origin and destination lanes.

The intersection should reflect a typical layout, which has to be considered in the driver behavior
models. In this way, each individual vehicle follows a unique trajectory. The trajectory is
influenced by intersection characteristics, other travelers (vehicles and pedestrians), and signal
control. These minimum requirements are fulfilled in the simulation.
The software, moreover, provides a flexible framework in order to easily extent the capabilities.
The vehicle parameters, trajectories and safety relevant variables are recorded in standardized
format for subsequent processing. To visually check and easily adjust the simulation input andoutput, a graphical user interface is provided.
So far the vehicles follow the randomly assigned routes from an origin lane to a destination lane
(no lane changing behavior). The number, width and type of lanes can be freely chosen. Threevehicle types are already defined. In future versions, the software will be extended by further
models like lane changing models and models for other then the mentioned conflict types. Morecomplex signal control algorithms can be incorporated.

5.1.3 Simulation framework

The simulation software processes the movement of vehicles and pedestrians in a network. The
network is split into roadways (detailed by lanes) and intersections (detailed by layout andgeometry). The position of vehicles is further classified into functional areas. Depending on thefunctional area the vehicle currently passes, it reacts to specific network elements (traffic signals,
intersection geometry, other vehicles or pedestrians etc.). These reactions are modeled. At eachtime several models can be required to accurately describe the vehicle behavior.
The network of the current version is limited to one intersection. Not all models are implemented
yet. The simulation framework, however, is designed in a way that new models can easily be
integrated.

5.1.4 Input and output

The simulation requires detailed information on the intersection layout (crosswalk and hard nose
position, curb radius etc.) in addition to a simple network description by links and nodes only.
Origin-destination matrices have to be defined with reference to entering and exiting lanes. The

51

simulation can be calibrated by a range of vehicle properties, which can be so far defined for threedifferent vehicle types. The state variables of all vehicles are recorded. The state is defined by:
•

ID

•

Type of vehicle•

coordinates (X,Y)•

travelled distance•speed and acceleration•

parameters of the trajectory (clothoid parameters and radius)

For clearing right-turning traffic the late exit time (LET) is recorded, for entering through traffic
the starting-response time (SRT) is saved. Furthermore, the traffic signal timing is recorded.
One of the advantages of the simulation program is, that the user can track the information ofrunning vehicles in real-time. By directly clicking on vehicles which are running on the simulation
canvas, the information of the tracked vehicle is shown in a panel as shown in Figure 5.1.

Vehicle tracker
panel
Tracked vehicle

Time - speed diagram

Speedometer

Figure 5.1 Real-time tracking system

5.2 Realization
5.2.1 Simulation software basics

The software is implemented in the C# programming language. The system architecture of thesimulation program is displayed in Figure 5.2. The four main subsystems are:52•

Main Graphical User Interface, which provides an intuitive mode for interacting with theusers;•

Simulation Calculation Engine is the “brain” of the system, it contains all the analyticalmodels, algorithms and is responsible for processing information;•

Encoding/Decoding engine which is responsible for transformation of graphical input
information as well as other input data to text data and vice versa;•

Data record Engine which is responsible for recording all of the simulation information forfurther processing and analysis.

The simulation uses an updating step of 0.1 s, which is independent of the frame rate of theanimation.

Analytical
ModelsStorage
Encoding/
Decoding Engine

Input

Algorithms

Simulation calculation
EngineGraphical display

OutputData Record
EngineDatabase
Main Graphical User Interface

Users

Figure 5.2 Simulation software components

5.2.2 User interaction

Graphical User Interface (GUI)
Figure 5.3 presents the main Graphical User Interface of the simulation program. It consists of thedisplay canvas, where roadways and intersections as well as other elements are drawn and theanimated traffic is shown, a menu bar, a toolbar, and a status bar.

53

Menu bar
Curbside corner

Raised median
CrosswalkConnected roadway
ToolbarStopbarSignal lights
Pedestrians
Canvas with/without
map optional field

VehiclesStatus bar

Figure 5.3 Main Graphical User Interface of the simulation program (Screenshot)
Data storage
Data is stored in the Extensible Markup Language (XML) to provide a standardized and wellstructured format. In the simulation program, XMLEncorder and XMLDecorder Engines areprovided for loading and saving data. Thus, all graphical objects including their characteristics andother input data will be encoded into text data and stored in XML format files. When opening an
existing project, the encoded information from XML files will be decoded into graphical elements.
Vehicle and pedestrian animation
The vehicle and pedestrian animation poses high requirements on the computer. The algorithms
and calculation steps in the simulation program have been optimized to avoid judder (non-smooth
motion). The Time-Based Animation technique is used. The advantage of this technique is that it
can maximize animation compatibility across multiple processors and the simulation step is
independent of the frame rate.

5.2.3 Network elements

The program has functionalities that allow a user to quickly design an intersection and connect it toroads as well as to other elements. The major difference to existing microsimulation software is therepresentation of intersections in the network. Intersections are described in detail by their size,
curbside corners, stop-bars, crosswalks, and signal lights (Figure 5.4). The intersection elements
and other network elements are discussed in detail in the following paragraphs.

54Intersection layouts

Stop-bars

Signal lights
VehiclePedestrian

Roadways

Curbside corner

Crosswalks

No. of lanes

Angle

Width

RadiusLengthLanecharacteristic

Width of eachlaneMedianLane control

Width
LengthThrough lane
Exclusive right turnExclusive left turnThrough-left turnFigure 5.4 Geometric elements in the simulation program
Intersections
So far the simulation is limited to isolated intersections. The intersection is connected to roadways.
A corner of the intersection is defined by two roadways and connected by a circular curve withmodifiable radius.
Roads
The simulation program currently supports roadways with a straight segment, which connects froma starting point to an ending point of a roadway. Each roadway consists of a constant number oflanes (so far no lane additions or subtractions). The cross section of a roadway will be determinedby the number of lanes, the individual width of each lane, and the width of the raised median. The
user can assign a traffic flow direction for each lane (shared or exclusive lanes). Furthermore, thelength of the median can be modified, since it is an input factor for the turning models.
Stop-bar and stopping position
The user can draw a stop-bar at any position at the intersection (even inside of the intersection forright-turning vehicles that are waiting for an acceptable gap in the conflicting through traffic). The
stop bar is taken as the stopping position of waiting vehicles. The user can design individual stopbar and stopping positions for each lane of a roadway.
Traffic lights
Traffic lights display the current phase of the signal controller.

55

Crosswalk
Crosswalks are designed at intersections with a defined width. Pedestrians will be generated at bothsides of crosswalks. The near-side and far-side with reference to conflicting traffic will be
automatically determined depending on the distance of the origin position and the destination
position of the pedestrian to the conflict area.
Possible modifications
After drawing connected roadways, intersections as well as other elements with default setting
values, the user can easily modify the elements by directly dragging on the graphic interface. The
properties of elements can also be obtained or modified by right-clicking on a particular element
and selecting the required functionalities from a pop-up menu.

5.2.4 Traffic flow elements

Vehicle types and sizes
In the simulation program, so far three types of vehicles are implemented (Passenger Cars, Single
Unit Trucks and Buses) as shown in Figure 5.5. The user can design the size (length and width) andcertain driving characteristics (desired speed, maximum acceleration/deceleration) for each type of
vehicles.

Passenger Car

Single Unit Truck

Bus

Figure 5.5 Vehicle shapes in the simulation program
The desired speeds of vehicles are randomly generated based on a Normal Distribution. Whenvehicles are launched a desired speed will be assigned. The free-flow vehicles incline to reach andmaintain a desired speed when running.
Mean m and standard deviation sdepend on the vehicle type. In the simulation program the default
values of m and sare defined as shown in Table 5.2.

56

Table 5.2 Default values of parameters of desired speed distributions
Parametersms

Passenger car
45
5

Heavy vehicle
40
5

unit
km/h
km/h

The maximum acceleration rate (for a vehicle starting from zero speed) and maximum deceleration
rate are defined as in Table 5.3 based on AASHTO 2004 and FHWA-HRT-04-040.

Table 5.3 Acceleration/Deceleration characteristics of vehicles
Type of vehicle
Passenger car
Heavy vehicle

Max Acc3.05 (10ft/s2)
1.50 (5ft/s2)

Max Dec
3.6 (12ft/s2)
3.6 (12ft/s2)

Unit
m/sec2
m/sec2

Pedestrians
A simulated pedestrian has a shape as shown in Figure 5.6. Sizes of simulated pedestrians are
determined by actual scale.

Figure 5.6 Shape of a pedestrian in the simulation program
Traffic Demand
Origin-Destination (O-D) trip tables represent the demand between entry/exit-lane pairs. As shownin Figure 5.7, the origins are initial points of input lanes (marked by capital characters) of aconnected roadway and the destinations are the end points of output lanes of other connectedroadway. In the simulation program, a trip from the origin to the destination of a vehicle is assumed
to be fixed. Vehicles will be generated from the origin source and they cannot change the lane
when running toward to the destination.

57

Figure 5.7 Example of an Origin-Destination O-D trip table in the simulation program (screenshot)

5.2.5 Signal control elements

Traffic signal control follows a pre-timed four phase control most common in Japan with lagging
protected right turn. Vehicle signals follow a green-yellow-red sequence. Pedestrian lights have agreen, flashing green and red sequence. Figure 5.8 presents an example of signal groups for anintersection, while Figure 5.9 shows phase modeling of the same intersection.
Vehicles are assumed not to react to signal lights when farther than 200 m upstream of the stop-bar.
This distance provides enough time for approaching vehicles with speed lower than 70 km/h to join
a queue before the stop-bars of the intersection.

where G is green time (sec); Y is yellow time (sec); AR is all Red time (sec); PG is pedestrian
green time (sec); PF is pedestrian flashing time (sec); C is cycle length (sec).
Note: Phase 1, 3,4 and 6 are vehicle phase; Phase 2 and 5 are pedestrian phases

Figure 5.8 Example of signal groups of an intersection

58

Figure 5.9 Illustration of the implementation of the phase plan shown in Figure 5.8

5.3 Model integration

5.3.1 Overview

The simulation is focuses on two types of conflicts so far: conflicts of right turning vehicles withcross traffic, and conflicts of left-turning traffic with pedestrians. The models underlying thesimulation of these conflicts have been explained in the last sections of this report.
The right-turning and through traffic conflicts occur when the last clearing vehicle of the right turnphase clears the intersection and the first entering vehicle of go-through phase enters theintersection as shown in Figure 5.10. Behavior models of the last clearing right turning vehicle arenecessary for examining this type of conflict that include stop/go decision at the onset of yellow,
turning path and turning speed. Crucial models for the first entering go-though vehicles are startup
respond time (SRT) and entering acceleration rate. In addition to implement the simulation
program, other models like car following models are necessary.

59Right-turning and throughtraffic conflicts

Go throughvehiclesRight turning
vehiclesCar following
modelsCar following
modelsEntering
acceleration rateTurning pathmodelsStartup Responsetime (SRT)

Turning speed
models

Stop/go models

Stop/go models

Figure 5.10 Conflicts between Right turning and through traffic and necessary models
The second type of conflict is left-turning traffic conflicting with pedestrians at crosswalks asshown in Figure 5.11. For this conflict a gap acceptance model which can explain the decisionmaking procedure when left-turning vehicles approach the crosswalk is developed. Other models
that are necessary for examining this conflict are listed in Figure 5.11.

Left turning traffic andpedestrians conflicts

Left turning
vehiclesPedestrian

Car following
modelsPaths

Turning pathmodels

Crossing speed

Turning speed
modelsGap acceptancemodelsFigure 5.11 Conflicts between Left-turning traffic and pedestrian at crosswalks and necessarymodels
5.3.2 Traffic generation and link flow
Vehicle and pedestrian arrivals
Random arrivals of vehicles and pedestrians are assumed. Their headways, thus, conform to anegative exponential distribution (Gerlough and Huber, 1975) as shown in Equation (5.1).
60

f ( h  t )  e  t  hmin /  H  hmin (5.1)

where h is the headway (s); t is a time interval (s); H is the average headway (s); hmin is theminimum headway (s), hmin is 0 for pedestrian flows and 1s~1.2 s for vehicles flows.
Lane choice
So far the chosen lanes are determined by the OD matrix. When a vehicle enters the simulation, itsroute is defined by the randomly assigned origin and destination lane.
Car following behavior
The car-following model is an important sub model used in the simulation program. It shows howeach driver responds to the surrounding traffic. In this simulation program, the Intelligent-Driver
Model (IDM) (Martin Treiber 2000) is used to simulate the longitudinal dynamics. According to
the model, the acceleration or deceleration rate of a vehicle depends on its own speed, and on the
speed and relative position of the leading vehicle immediately ahead of it. The following equationshows the acceleration/deceleration rate of a vehicle at time t:  v   s *  2 dv
 a 1       dt  vo   s  

(5.2)

vv 

s*  so   vT 
2 ab 
(5.3)

where vo is the desired speed (m/sec); T is the desired safety time headway (sec); a is the maximum
acceleration rate (m/sec2); b is the maximum deceleration rate (m/sec2); s0 is minimum bumper-tobumper distance to the front vehicle (m); s is the current bumper-to-bumper distance to the frontvehicle (m) and  is an acceleration exponent which indicates how the vehicle increases speed.
Usually for enhancing startup behavior when 1; s is estimated as( x2  x1 ) 2  ( y2  y1 ) 2with P1(x1,y1) as the middle point of the head bumper of the following vehicle and P2 (x2,y2) as the
middle point of the rear bumper of the leading vehicle. For a free-flow vehicle, the acceleration rate
is given by Equation (5.4). The used default values of the car-following model parameters asshown in Table 5.4.
 v dv
 a 1    dt  vo  


61

(5.4)

Table 5.4 Default values of Car-following model parameters
Parameter
v0
T
s0
a
b


Passenger car
NormalDis (45,5)
1.0
2.0
3.05 (10 ft/sec2)
1.50 (5 ft/sec2)
4

Heavy vehicle
NormalDis (40,5)
1.2
3.0
3.6 (12 ft/sec2)
3.6 (12 ft/sec2)
4

Unit
m/sec
sec
m
m/sec2
m/sec2-5.3.3 Reaction to traffic signals

Stop/go models
When approaching the intersection at the onset of yellow, the driver has to meet a stop/go decision.
The decision of simulated vehicles is estimated based on the results of a stop/go model. If the
distance is not far enough to comfortably decelerate in time, the driver will pass. The reaction to
the signal of the following vehicles depends on the decision of the leading vehicle. Only if theleading vehicle decides to pass, the following vehicle will meet an independent decision as if itwould be the leading vehicle.
The stop/go decision model is developed for through and right turning traffic only. For left turning
vehicles, the stop/go decision depends on the minimum distance to stop at the stop-bar only.
SRT models of entering vehicles
So far, SRT models are developed for the through traffic only, for right-turning and left-turning
traffic a fixed value of SRT = 0.7 s is assumed.
For through turning traffic, the SRT is calculated five seconds before the signal changes to green,
because of the SRT distribution. Due to the model, SRT depends on the Late Exit Time (LET) of
the last clearing vehicle of right-turning traffic (cf. Section 3.5).
The last clearing vehicle of right turning traffic is predicted based on the stop/go decision at theonset of yellow. If the last clearing vehicle enters the intersection (passes the stop line) during thegreen time, the exit is not late. In this case, LET is set to zero. The SRT distribution will be
generated based on this zero LET.
In cases when the last clearing vehicle passes after the onset of yellow, LET will be predicted basedon the ideal speed and the distance to the conflict point with through traffic. Because the last62

clearing vehicle usually is not a leading vehicle, the real speed of the vehicle depends on the carfollowing model. This behavior is not yet considered in the SRT model.

5.3.4 Gap acceptance models

The gap acceptance in the pedestrian stream on the crosswalk is part of the left-turning trafficmodels (cf. Chapter 4). The gap acceptance of right-turning traffic concerning the opposing traffic
during the permitted phase has not been developed yet. In the simulation program it is assumed thatright turning vehicles reject all gaps during the permitted phase.

5.3.5 Entering acceleration rate of entering vehicles

The entering acceleration rate is the acceleration rate of the first vehicle entering the intersection
when green starts until it passes the conflict point with the cross traffic.
The entering acceleration model is developed for through traffic only. For right-turning traffic andleft-turning traffic, the acceleration rate of entering vehicles is given by Equation (5.4). According
to the acceleration rate model of through traffic, the acceleration rate of entering vehicle depends
on the SRT. Therefore, it is calculated after calculating SRT.

5.3.6 Paths of turning vehicles in the intersection

The simulation uses models for the path of right-turning and left-turning vehicles (cf. Sections 3.3
and 4.4). The path is determined before the vehicle enters the intersection. This path is taken as
fixed and does not change during the turning maneuver. Before the turning-vehicle enters theintersection, the driver determines a target lane (based on the OD route) on the downstream
roadway. The path is generated based on this exit lane. As an example, Figure 5.12 shows theturning paths of right turning and left turning vehicles when entering the intersection.
For through traffic it is assumed that vehicles use the same lane on the intersection exit withoutchanging lanes while crossing the intersection.

63

Figure 5.12 An illustration of turning paths of right and left turning vehicles (screenshot)

5.3.7 Speed of vehicles

In the simulation program, three general scenarios are classified in order to determine the speed
profile of vehicles. The scenarios are classified based on the movement direction of vehicles as gothrough, turning left and turning right vehicles. For each direction, the whole trip of vehicles fromorigin to destination is divided into three segments as shown in Figure 5.13: lane moving,
approaching intersection, crossing intersection (or entering intersection).

Lane moving

Approaching

EnteringFigure 5.13 Running segments of vehicles
Vehicles are considered as moving on lanes when the distance to the stop-bar of an intersection isgreater than 200 m. At lane moving segments, speeds of all vehicles are determined based on the64car following behavior as shown in Equations (5.2) and (5.4). During the approach they react to thetraffic signal. Vehicles are considered as crossing the intersection when they passed the stop-bar.
Through vehicles
1. Approaching intersection: In this segment, vehicles both react to the traffic signal and to thesurrounding traffic. If the vehicle crosses during green, the speed choice behavior is the samewith vehicles that are running on the lane moving segment. If the vehicles react to the yellow
or red light, the speed depends on the order of vehicles as shown in Figure 5.14. For the first
approaching vehicle (number 1) as shown in Figure 5.14, the speed choice behavior depends on
the signal timing and stop/go decision. The acceleration rate of the vehicle will be calculated asin Equation (5.5)

v2
a
2d

(5.5)

where a is the acceleration rate of the vehicle (m/sec2); v is the speed of the vehicle (m/sec)
and d is the distance to the stop-bar (m). Otherwise if the vehicle chooses to pass, theacceleration rate is calculated by Equation (5.4).
For the vehicle number i, the speed choice behavior depends on the signal timing and thedecision of the vehicle number i-1. When vehicle number i-1 chooses to stop, the vehicle
number i automatically follows the vehicle number i-1 by car following model. If the vehicle
number i-1 chooses to go, the vehicle number i will meet its own stop/go decision. If vehicle
number i chooses to stop, the acceleration rate calculated by Equation (5.5) will be applied.
Otherwise vehicle number i will follow the vehicle number i-1 as in the car following model.

Approaching


i

i-1 …

1



Figure 5.14 Through vehicles are running at the approaching segments65

2. Entering segments: For the first entering vehicle at the beginning of green; the speed of thevehicle depends on the start-up behavior. The start-up behavior which is modeled in thisproject includes the start-up response time (SRT) and the entering acceleration rate. After the
SRT, the first entering vehicle will accelerate with the entering acceleration rate. The vehicle
will use this acceleration rate until it passed through the conflict area with right turning trafficof the opposite phase. After that, the entering vehicle will use the acceleration rate as shown inEquation (5.4). For other vehicles, the speed behavior is the same behavior with vehicles atlane moving segments.
Right-turning vehicles
1. Approaching intersection: In this segment vehicles prepare to turn as shown in Figure 5.15.
An ideal speed profile is generated when vehicles start running at this segment as described in
Section 2.3. The speed profile model is developed for free flow vehicles. It is necessary to
distinguish between free flow vehicles and vehicles running in a platoon. Assuming a thresholdof 3 s of headway between vehicles (HCM 2000) is used to distinguish between free flow
vehicles and in-platoon vehicles. For in-platoon vehicles and vehicles with a speed lower thanthe minimum speed vmin, the speed choice behavior is the same with through vehicles at thesame segment. For free flow vehicles which have a speed greater than vmin, ideal speeds will beapplied.

Approaching


i

i-1 …

1



Figure 5.15 Right turning vehicles are running at the approaching segments
2. Entering segments: For the first entering vehicle at the onset of green; the speed of the vehicle
depends on the start-up behavior. However, start-up behavior for right turning vehicles has notbeen developed yet. In this case, SRT is assumed as 0.7 s. The first entering vehicle will use an
acceleration rate calculated as in Equation (5.4). For other vehicles, the speed depends onwhich type of speed model they use before entering the intersection. They will continue using
the speed model they used in the approaching segment.
66

Left-turning vehicles
1. Approaching segment: In this segment, left turning vehicles behave like the right turning
vehicles.
2. Entering segment: In this segment, left turning vehicles react to pedestrians at the crosswalk
as shown in Figure 5.11. Three types of speed profile models are developed as described in
Subsection 4.5.1 and illustrated in Figure 4.9 (ideal speed profile, clearing profile and stopping
profile). For left turning vehicles approaching the crosswalk, the speed choice depends on the
gap acceptance model (Section 4.3). The loop outlined in Figure 5.16 and described in detail in
Section 4.5 will be applied with a decision update interval of 0.5 s until the vehicle passed thecrosswalk. In case vehicles reject all gaps until they reach the crosswalk, they will stop andwait at the crosswalk until an accepted gap appears. When an acceptable gap becomes available,
drivers will use the acceleration rate estimated by Equation (5.4) to pass through the crosswalk.

Start
Approaching
crosswalkti = ti-1 + 0.5 sec

Pedestrians at crosswalk?
Lag searchingNo

Lag accepted?

Ideal profile

No

No

Yes
Preparing to stop?

Full-stop profile

Yes
Clearing profile
Yes
Crosswalk?
Yes

End
Figure 5.16 Speed choice algorithm of left turning vehicles approaching crosswalks
Pedestrian movement models
Due to the high complexity of pedestrian behavior, so far only a simplified model is implemented
for pedestrians crossing the crosswalk. It is assumed that pedestrians do not change their direction
while crossing. The origin and destination positions of pedestrians are randomly generated. A
simplified model is used to reflect the effect of signal timing, crosswalk length and pedestrian67direction of movement on pedestrian speed while crossing. The detailed information about thesemodels is presented in Subsection 4.2.4.

68

6 Simulation Validation and Case Study
6.1 Overview
In order to verify that the simulation is working reasonably, a case study is conducted. The
simulation output related to the models not yet validated and related to safety is compared toobserved data. The case study also serves as a platform to highlight the potential of the safetyassessment approach. Nishi-osu (西大須) intersection in Nagoya is selected for the case study.
Table 6.1 shows the layout of Nishi-osu intersection and the operational characteristics.
Table 6.1 The characteristics of Nishi-osu intersection in Nagoya City 国道 19 号線と市道が交差する交差点であり，交通量は昼夜を問わず非常に多い
 付近には娯楽施設や商店街が立地しており，歩行者，自転車利用者が多く，特に横断歩道上での右左折車両との交通事故が多発
 交差点サイズが大規模であり，右左折車両
が高い速度のまま横断者間を縫うように走行しがちであり，接触直前のニアミスが起
こりやすい

φ1

φ2

φ3

φ4

Green

52

7

67

12

Yellow42

42

Phase No.

φ5

Phasing

Duration(sec)

All-redCycle length (sec)

5

5
160

Vehicle behavior
Observation times(Shooting hours)

ApproachStart-up

Stop-go decision

Vehicle maneuver

TH

TH

LT

RT

RT

Pedestrian
behavior

RT

East
9:00～12:00(8:45～12:30)

West

●

●

South

●

●

North

●

●

●

Note：● Analyzed item

69

Table 6.2 Observed demands of the analyzed movements at Nishi-osu Intersection

Intersection

Approach

Nishi-osu

North
West
South

Vehicular Traffic volume
veh/lane/hr
Through
Left turnRight turn147
454

Pedestrians demand
ped/hrNear-side
Far-side
96

64

284
276

This site is characterized by a significant number of collisions, especially between pedestrians andleft-turning vehicles. Data was collected at three approaches of the intersection. Collected data
includes pedestrian maneuver data, turning and through traffic maneuver data.
The simulation program is calibrated using the observed vehicle and pedestrian demands for the
analyzed movements as shown in Table 6.2. Pedestrian demand in the north approach refers to thepedestrians who use the crosswalk in the north approach.
The geometric layout of Nishi-osu Intersection and its representation in the simulation is shown in
Figure 6.1.

a) Aerial photob) Representation of the intersection in thesimulation

Figure 6.1 Photos of Nishi-osu intersection in reality and in the simulation program70

6.2 Car following model
6.2.1 Introduction
Car following models are one of the essential models in the traffic simulation environments. Thesemodels are complicated and validating them requires a lot of empirical data. In this part, a simple
calibration and verification process is conducted for the car-following model integrated into thesimulation, the Intelligent-Driver Model (IDM).
6.2.2 Calibration methodology
Step 1: Calibration parameters:
The car following behavior can be presented by time headway and speed of vehicles. In this study,
the queue discharge headway and queue discharge speed at the stop line are used as calibration
parameters. Queue discharge headway (sec) is defined as the time difference between two
consecutive vehicles in a platoon passing the stop line of an intersection while queue discharge
speed (m/sec) is the departure speed at the stop line during the saturated part of the green period(Akcelik 1999). Initially, the parameters of the Intelligent-Driver Model (IDM) are set to default
values as shown in Table 5.4.
Step 2: Data collection:
Due to the limited data only one site is selected for calibration and verification this time. The
selected site is the second through lane (determined from the edge of the sidewalk) of the west
approach of Nishi-osu Intersection. Signal timing and traffic characteristics of Nishi-osu
intersection are described in Table 6.1 and Table 6.2. Observed queue discharged headways andqueue discharged speeds of queued vehicles at the stop-line is collected by using the image
processing program TrafficAnalyzer (Suzuki and Nakamura, 2006).
Step 3: Adjustment and verification:
By comparing observed data with estimated results (using default values), the parameters of the carfollowing model are tuned. These parameters are assumed as fixed values or follow a normal
distribution as shown in Table 6.3. To calibrate all these parameters, a lot of empirical data isnecessary, however available data is limited, thus the parameter of acceleration exponent (δ,cf. Equation (5.2) and Table 5.4) is chosen to tune the car following model IDM. The parameter ofacceleration exponent (δ) is one of the most significant ones since it defines how the vehicles react
to other vehicles in front of them or in other words it shows how vehicles adjusted theiracceleration rate while running.
71

Table 6.3 Adjusted factors of car following model (IDM model)

No

Parameters

Meaning

Passenger Car

Heavy vehicle(Bus and SUT)12v0 (km/h)
T (sec)3s0 (m)

4
5
6

a (m/sec2)b (m/sec2)

Desired speed
Minimum time headway
Minimum bumper-to-bumper
distance to front of vehicle
Maximum acceleration
Maximum deceleration
Acceleration exponent

Normal Dis. (45,5.0)
1
Normal Dis. (2.0,1.0)
s0 >=1.0
Normal Dis. (2.5,0.2)-3.6
4

Normal Dis. (40,5.0)
1.2
Normal Dis. (3.0,1.0)
s0 >=2.0
Normal Dis. (1.25,0.1)
-3.6
4

δ (-)

If the parameter of acceleration exponent (δ) is equal to one, the change in acceleration rate isconstant as shown in Figure 6.2. It is concluded that δ need to be more than one to enhance startup
behavior as shown in Figure 6.2.

Maximum acceleration rate

Figure 6.2 Changing of acceleration rate with different values of parameter of acceleration
exponent parameter (δ: delta)
6.2.3 Verification
Figure 6.3 compares observed and simulated discharge headways at the second through lane(determined from the edge of the sidewalk) of the west approach of Nishi-osu Intersection. The
observed average discharge headway is about 1.83 sec (calculated from the 5th vehicle, passenger
cars only) while average simulated discharge headway is about 1.81 sec. Additionally, simulated
discharge speeds increase after green start following the same tendency of observed discharge
speeds as shown in Figure 6.4. Moreover the estimated discharge speeds match well the observed
ones. To provide a better view of the performance of the used car following model, the time-space72

diagram of a simulated platoon of vehicles is presented in Figure 6.5. It is clear that following
vehicles behave reasonably by keeping a safe distance to the leading ones.

Figure 6.3 Comparison of observed and estimated discharge headway at the stop line of the west
approach of Nishi-osu intersections

Figure 6.4 Comparison of observed and estimated discharge speed at the stop line of the west
approach of Nishi-osu intersections

73

Figure 6.5 Time – space diagram of a vehicle platoon passing intersection

6.3 Conflicts between clearing right-turning traffic with starting throughtraffic
The model for the path of turning vehicles has already been calibrated and validated in the firstreport. Here the focus is on safety relevant properties of the paths in the context of the simulation.
One important parameter is the lateral distribution of the paths at crucial locations. So far the model
assumes the vehicle to enter and exit the intersection in the middle of the respective lane. In futureversions this lateral entering and exiting position will be randomly modeled to reflect better thereality.
Figure 6.6 shows the distribution of observed and simulated paths of right-turning vehicles at thenorth approach of Nishi-osu Intersection. The lateral path density distribution (D.D.) and the lateral
cumulative distribution (C.D.) at three cross-sections along the turning paths are presented in
Figure 6.6. The density and cumulative distributions are drawn in an interval of 0.5 m. The
distributions of simulated and observed paths are similar in section . The deviation near the entry
and exit are due to the simplified assumption of the lateral entering and exiting position of thevehicles. The sample size of the observed paths is small, thus collecting more data is necessary toprovide a more reliable validation.

74

120

110

100

90

100%

1

80%

Percentage

80

D. C. Observed
C. C. Observed
D. C. Simulated
C. C. Simulated

60%
40%

70

Sample size (Observed) = 15
Sample size (Simulated) = 109

20%

1

0%

0

60

2

4
6
8
10
Distance from the curb (m)

12

14

2

80%

50

D. C. Observed

2

3

40

Percentage

Distance (m)

100%

60%

C. C. Observed
D. C. Simulated
C. C. Simulated

40%

Sample size (Observed) = 15
Sample size (Simulated) = 109

20%
0%

30

6

8

10
12
14
16
Distance from the curb (m)

18

100%

3

80%

20

20

D. C. Observed

Percentage

C. C. Observed

10

60%

D. C. Simulated
C. C. Simulated
Sample size (Observed) = 15
Sample size (Simulated) = 109

40%
20%

SimulatedTrajectory of Passenger Cars (P.C.)
0%

0

0

0

10

20

30

40

50

60

70

80

90

100

2

110

4
6
8
10
Distance from the curb (m)

12

14

120

Distance (m)Figure 6.6 Comparison between observed and simulated paths of right-turning vehicles at thenorth approach of Nishi-osu Intersection

To test how the simulation presents the conflict between clearing right-turning vehicles and starting
through traffic, comparisons between observed and simulated late exit time LET, start-up responsetime SRT and post encroachment time PET are presented. These times depend largely on the speedof the turning vehicles.
Figure 6.7 presents the simulated speed profiles of free flowing turning vehicles. As in reality(Figure 2.3) vehicles reach their minimum speed between the stop line and the downstream
crosswalk.

75

Speed profiles of free flow right-turning vehicles
18
16
14

10
8

Downstream crosswalk

Speed (m/sec)

12

6

Stopline

42

0-50 -40 -30 -20 -10

0

10

20

30

Stop line
Downstream
crosswalk

40 50 60 70 80
Distance to stopline (m)90 100 110 120 130 140 150

Figure 6.7 Simulated speed profiles of clearing free-flow right-turning vehicles at the northapproach of Nishi-osu Intersection

Figure 6.8 shows the distribution of observed and simulated late exit times LETs of clearing rightturning vehicles at the north and south approaches of Nishi-osu Intersection. By conducting
significance test, it is concluded that the mean of the observed and simulated LET distributions are
not significantly different at the 95 % confidence interval.

North Approach Sample Size nObserved Data n = 20
Simulatied Data n = 58

87

Observed D.D.

Frequency

6

100%

20

90%

18

80%

16

70%

14

Simulated D.D.
60%

Observed C.D.

5

50%

Simulated C.D.

4

Frequency

9100%South Approach Sample Size nObserved Data n = 83
Simulatied Data n = 128

90%
80%

Observed D. D.
Simulated D. D.
Observed C.D.
Simulated C.C.

12
10

70%
60%
50%

8

40%

30%

6

30%

20%

4

20%

1

10%

2

10%

0

0%

0

40%

3
2

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

7

8

9

0%

-10 -910Late Exit Time LET (sec)

-8

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

7

8

9

10

Late Exit Time LET (sec)a) North approachb) South approach

Figure 6.8 Comparison between observed and simulated late exit times LETs of clearing rightturning vehicles at the north and south approaches of Nishi-osu Intersection

As presented in Chapter 3, the start-up response time of through traffic is affected by the clearing
behavior of right-turning vehicles. This interaction is quantitatively modeled and implemented76

inside the simulation. Figure 6.9 presents the distributions of observed and simulated start-up
response times. By conducting significance test, it is concluded that the mean of the observed andsimulated distributions are not significantly different at 95 % confidence interval.
30

25Frequency

20

100%

Sample Size (Observed Data) = 78
Sample Size (Simulatied Data) = 186
Observed D. D.
Simulated D.D.
Observed C. D.
Simulated C. D.

80%

60%

15
40%

10
20%

5

0

0%

-10 -9

-8

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

7

8

9

10

Start-up Response Time SRT (sec)Figure 6.9 Comparison between observed and simulated start-up response times SRTs ofstarting through vehicles at the west approach of Nishi-osu Intersection

Since the main objective behind developing the microscopic simulation model is the safetyassessment, it is necessary to verify that the interaction between different conflicting movements isreasonably represented. In the current project, however, only a small number of samples could bevalidated. Figure 6.10 presents a comparison between observed and simulated Post Encroachment
Times PETs of the conflict between right turning vehicles from the north and south approaches of
Nishi-osu intersection with the through vehicles from the west approach of the same intersection
for an observation interval of two hours. Though by conducting significance test, the means of theobserved and simulated distributions for both conflicts are significantly different at 95% confidence
interval due to the small sample size, the distributions cover a similar range. The simplifications
used in the current version of the simulation have to be mitigated for further improvement of theresults.

77

12

30

100%

With right-turners from the North approach
Observed Data Sample Size n = 17
Simulatied Data Sample Size n = 58

Frequency

8

6

Observed D.D.

70%

Simulated D.D.

60%

Observed C.D.

50%

Simulated C.D.

40%

4

30%
20%

2

90%

25

80%

Frequency

10

100%

With right-turners from the South approach

90%

80%
70%

20

Observed Data Sample Size n = 17
Simulatied Data Sample Size n = 58

15

Observed D.D.

50%

Simulated D.D.

40%

Observed C.D.

30%

10

Simulated C.D.
5

0%

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

0

0%

0

20

20%

10%

10%

0

60%

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

PET(sec)

PET(sec)a) With right-turners from the north approachb) With right-turners from the south approach

Figure 6.10 Comparison between observed and simulated PETs of the conflict between throughtraffic from the west approach of Nishi-osu intersection and right-turners

6.4 Conflicts between left-turning traffic with pedestrians
To verify the performance of the path model for left-turning vehicles, Figure 6.11 and Figure 6.12
compare the distributions of observed and simulated paths of left-turning passenger cars and heavy
vehicles at the west approach of Nishi-osu Intersection. The lateral path density distribution (D.D.)
and the lateral cumulative distribution (C.D.) at three cross-sections along the turning paths arepresented in Figure 6.11 and Figure 6.12. The density and cumulative distributions are drawn in aninterval of 0.5 starting from the curb of the intersection. It’s clear that the distributions ofsimulated and observed paths of passenger cars are quite similar and they have the same tendency.
The difference is mainly referred to the assumption that the exiting position of the vehicles is in thecenterline of the lane while observations show that the exit positions are widely distributed
throughout each exit lane. This assumption affects the parameters of the estimated paths. Thus
incorporating a lateral exit position model in the simulation will significantly improve the
distribution of estimated paths.

78

120

80%

120

100%

1

80%

D. C. Observed

110Percentage

Percentage

90

60%

D. C. Simulated
C. C. Simulated
Sample size (Observed) = 294
Sample size (Simulated) = 361

40%

C. C. Simulated

40%

Sample size (Observed) = 294
Sample size (Simulated) = 361

0%

80

0%
0

2

70

4

6
8
10
Distance from the curb (m)

12

14

60%

C. C. Observed
D. C. Simulated

40%

C. C. Simulated
Sample size (Observed) = 294
Sample size (Simulated) = 361

20%

20%

80
0

2

4

0%

6
8
10
Distance from the curb (m)

12

0

14

2

4

6
8
10
Distance from the curb (m)

12

14

220

230

70

60

60

50

Distance (m)D. C. Simulated

100

90
20%

D. C. Observed

C. C. Observed
60%

3

80%

D. C. Observed

C. C. Observed

100

100%

2

Percentage

100%

110

50

3

3

40

2

1

30

40

1

30

20

2

20

10

10

Observed trajectory of Passenger Cars (P.C.)

SimulatedTrajectory of Passenger Cars (P.C.)

0

0

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

180

190

200

210

Distance (m)Figure 6.11 Comparison between observed and simulated paths of left-turning passenger cars at
the west approach of Nishi-osu Intersection

Regarding heavy vehicles, it is important to note that the sample size of the observed paths for theverification is very small; this might be the reason why simulated paths are significantly different
than observed ones at 95 % confidence interval as shown in Figure 6.12. Furthermore, theassumption of lateral exiting position contributes to the differences as well.
To test how the simulation presents the conflict between left-turning vehicles and pedestrians, thespeed profiles of free-flow, stopping and yielding left-turning vehicles are presented in Figure 6.13.
Stopping and yielding profiles reflect the interaction with pedestrians. Generally, generated speed
profiles are reasonable. However, when analyzing observed profiles it can be seen that undercertain circumstances driver behavior follows more complex patterns as highlighted in Figure 6.14
and Figure 6.15. While the respective right patterns are well represented by the assumed speed
profiles and decision making processes, the respective left patterns show stages with different
acceleration rates (slight deceleration possibly due to some uncertainty of the driver on whether toproceed or to stop, followed by higher deceleration). These more complex patterns have to beincorporated into future versions of the simulation.

79

240

120

90

80

C. C. Observed
D. C. Simulated

60%

C. C. Simulated
Sample size (Observed) = 54
Sample size (Simulated) = 4040%D. C. Observed

0%
4
6
8
10
Distance from the curb (m)12

D. C. Simulated
C. C. Simulated

Sample size (Simulated) = 40

C. C. Observed

D. C. Simulated

40%

C. C. Simulated
Sample size (Observed) = 54
Sample size (Simulated) = 40

20%

80
0

14

D. C. Observed

60%

90Sample size (Observed) = 54

2

4

0%

6
8
10
Distance from the curb (m)

12

14

0

2

4
6
8
10
Distance from the curb (m)

12

14

220

230

70

60

60

50

Distance (m)C. C. Observed

40%
20%

2

3

80%

100

0%

0

110

60%

20%

70

100%

2

80%

Percentage

100

Percentage

80%

120

100%

1
D. C. Observed

Percentage

100%

110

50

3

40

3

40

2

1

30

1

30

20

2

20

10

10

Simulated trajectory of heavy vehicles (H.V.)

Observed trajectories of heavy vehicles (H.V.)
0

0

0

10

20

30

40

50

60

70

80

90

100

120

110

130

140

150

160

170

180

190

200

210

Distance (m)Figure 6.12 Comparison between observed and simulated paths of left-turning heavy vehicles at
the west approach of Nishi-osu Intersection

Simulated speed profils of left-turning vehicles
Downstream Crosswalk

16
14

Speed (m/sec)

12
10
8
6
Free-flow profile

4

Full stop profile

Downstream
crosswalk
Stop line

Stopline

Yielding profile

2
0
-50

-40

-30

-20

-10

0

10

20

30

40

50

60

70

80

90

100

Distance to stopline (m)Figure 6.13 Simulated speed profiles of left-turning vehicles at the west approach of Nishi-osu
Intersection

80

240

2

20

18

1.5

18

Speed (m/s)

14
12

0.5

10

0

8

-0.5

6

-1

4

2

437

0
0

5

10

1.5

16

1

14

Speed (m/s)

1

Acceleration (m/s²)

16

2

12

0.5

10

0

8

-0.5

6

-1

4

-1.5

2

-2

0

-1.5
494

0

15

5

10

-2

15

Time (s)Time (s)SpeedAcceleration (m/s²)

20

Speed

Acceleration

Acceleration

Figure 6.14 Different observed stopping profile types
2

20

18

1.5

18

Speed (m/s)

14
12

0.5

10

0

8

-0.5

6

-1

4

2

517

0
0

5

10

1.5

16

1

14

Speed (m/s)

1

Acceleration (m/s²)

16

2

12

0.5

10

0

8

-0.5

6

-1

4

-1.5

2

-2

0

15

-1.5
506

0

Time (s)SpeedAcceleration (m/s²)

20

5

10

-2

15

Time (s)Acceleration

Speed

Acceleration

Figure 6.15 Different observed yielding profile types

6.5 Sensitivity analysis
To demonstrate the potential of the developed simulation model, the effects of modifying thegeometric layout of Nishi-osu intersection towards compact design upon Angle Collision Index
ACI is analyzed. Figure 6.16 shows the layout plans for two scenarios; Scenario 1 is the existinggeometric layout while Scenario 2 is a proposed compact layout.

81a) Scenario 1, existing layoutb) Scenario 2, compact layout

Figure 6.16 Existing and compact layout of Nishi-osu intersection

In the case of a compact layout (Scenario 2) as shown in Figure 6.16b, it is advisable to modify thesignal timing parameters. The all-red interval is reduced from 5 s to 3 s. By using the vehicle
demands in Table 6.2, the simulation is run for three hours for each scenario defined in Figure 6.16.
The Angle Collision Index (Section 3.6) is estimated for both scenarios. To calculate the ACI, themasses of the conflicting vehicles are assumed as 1500 kg (standard weight of a passenger car).
With the Post Encroachment Time PET in the unit of seconds and the vehicle speed in m/s
Equation (3.5) can be used to calculate the ACI.
Figure 6.17 shows the distributions of ACI for the two conflicts between though traffic from west
approach and the right-turners from the north approach (Figure 6.17a)) and the south approach(Figure 6.17b) of Nishi-osu intersection for different vehicle speeds. It is important to note that thevalue of ACI is estimated based on Equation (3.5) by using the speeds of the conflicting vehicles
and the Post Encroachment Time PET. However ACI is very sensitive to PET, thus most of thevery high values of ACI correspond to very small PET values.
Figure 6.17 shows that the number of conflicts, particularly the number of severe conflicts (highvalues of ACI), is reduced by implementing the compact geometric layout (Scenario 2). The
compact layout, hence, improves the safety appreciably. Due to the higher demand of right-turning
traffic from the south as compared to right-turning vehicles from the north, the number of conflicts
between through traffic and right-turners from the north approach (Figure 6.17a) is smaller thanthat of the conflicts with right-turners from the south approach (Figure 6.17b). However, theconflicts between right-turning vehicles from the north and through traffic from the west are more

82

100

100

90

90

Scenario 1 (Right-turners from North App.)80

Scenario 2 (Right-turners from North App.)70

Scenario 2 (Right-turners from South App.)

50

Angle Collision Index ACI

80

76

More

72

68

64

60

56

52

48

44

40

36

32

28

24

0

80

76

More

72

68

64

60

56

52

48

44

40

36

32

28

24

20

16

0

8

10

0

12

20

10

4

30

20

20

40

30

16

40

60

8

50

12

60

4

Frequency

700Frequency

Scenario 1 (Right-turners from South App.)

80

Angle Collision Index ACIa) ACI of the conflict with right-turners
from the north approachb) ACI of the conflict with right-turners
from the south approach

Figure 6.17 Comparison of ACI for the conflict between through traffic and right-turners at
Nishi-osu intersection for the two geometric layout scenarios
severe due to the adverse angles (Figure 6.17a) and the shorter distance from the stop line to theconflict area as shown in Figure 6.17a).
A distinct change from Scenario 1 to Scenario 2 can also be recognized for the conflicts of leftturning vehicles with pedestrians as underlined by the Vehicle Pedestrian Index (VPI). This index
incorporates both the likeliness of conflicts (expressed by the post-encroachment time) and theirseverity (expressed by the kinetic energy of the vehicle). The compact intersection (Scenario 2)
leads to a reduction of the severity and in most cases also the frequency of conflicts as ishighlighted in Figure 6.18. Only for gap type E (Figure 2.10 shows the defined lags/gaps types) no
significant improvement can be seen, and for gap type B the situation slightly deteriorates.
Another result is the severity of the conflicts as compared between the different gap types. Gaps
with individual pedestrians arriving from one side only (type A and type B) are distinctly more
severe than the other types, where more than one pedestrian is involved (mind the different scale ofthe y-Axis). This might indicate that drivers behave more cautious when several pedestrians arevisible on the crosswalk.

83

180

100%

160

90%
80%

140

70%

Frequency

120

Scenario 1
100

60%

Scenario 2

50%

80

Cumulative (Scenario 1)%

60

Cumulative (Scenario 2)%

40

Sample size (Scenario 1) is 205
Sample size (Scenario 2) is 175

40%
30%
20%

20

10%

0

0%

Pedestrian Vehicle Index PVIa) Conflict location
250b) Lags of Type A
100%

80

90%
200

100%
90%

70

80%

80%
60

Scenario 1

150

Scenario 2

Cumulative (Scenario 1)%

100

70%

Frequency

Frequency

70%
60%
50%
40%

Cumulative (Scenario 2)%
Sample size (Scenario 1) is 123
Sample size (Scenario 2) is 239

50

Scenario 2
40

Cumulative (Scenario 1)%
Cumulative (Scenario 2)%

30

30%

Sample size (Scenario 1) is 97
Sample size (Scenario 2) is 67

20
20%
10

10%
0

Scenario 1500%c) Lags of Type Bd) Gaps of Type C

90%

60%
15

Scenario 1
Scenario 2
Cumulative (Scenario 1)%
Cumulative (Scenario 2)%

10

50%
40%

80%

40

30

20

30%
20%

5

Scenario 1

70%

Scenario 2

60%

Cumulative (Scenario 1)%

50%

Cumulative (Scenario 2)%

40%

Sample size (Scenario 1) is 103
Sample size (Scenario 2) is 75

30%
20%

10

10%
0

10%

0%
0

20%

100%

50

80%

Frequency

Frequency

60

90%

70%

20

30%

500 1000 1500 2000 2500 3000 3500 4000 4500 5000 More

Vehicle Pedestrian Index VPI

Sample size (Scenario 1) is 85
Sample size (Scenario 2) is 63

25

40%

0%

Pedestrian Vehicle Index PVI

100%

50%

10%

0
0

30

60%

0

500 1000 1500 2000 2500 3000 3500 4000 4500 5000 More0%0500 1000 1500 2000 2500 3000 3500 4000 4500 5000 More

Vehicle Pedestrian Index VPI

Vehicle Pedestrian Index VPIe) Gaps of Type Df) Gaps of Type E

Figure 6.18 Comparison of VPI for the conflict between left-turning traffic and pedestrians at
Nishi-osu intersection for the two geometric layout scenarios84

7 Conclusions and Outlook
7.1 Conclusions
The improvement of safety at signalized intersections still poses a challenge to authorities andtraffic engineers. So far the safety assessment is mainly based on behavioral and accident analysis.
An a priori evaluation of alternative layouts, regulations and signal control regimes before theirimplementation is, thus, not possible. This project aimed at overcoming this limitation by
developing a microscopic simulation tool incorporating models for the driving behavior insidesignalized intersections.
For clearing right-turning vehicles and the conflict with entering through-traffic and for left-turning
traffic and the conflict with pedestrians detailed models have been developed, calibrated andverified, that not only give a realistic representation of the traffic flow, they are also sensitive tointersection geometry and signal control. These two conflicts have been identified as the mostfrequent conflict types at signalized intersections.
The models and their sub-models have been incorporated into a microscopic simulation tool. The
software provides an intuitive user interface for the simulation of isolated intersections. Traffic
demand as a lane based origin-destination matrix and the intersection geometry including curb radii,
position of the hard nose, and crosswalk widths are the input data. The simulation outputs vehicle
trajectories and several safety indices like post-encroachment times (PET).
For the safety assessment of the mentioned conflicts, two new safety indices have been proposed(Angle Collision Index, ACI, and Vehicle Pedestrian Index, VPI), which incorporate not only the
conflict probability, but also the likely severity based on kinematic concepts.
A case study illustrates the potency of the new tool. Though the focus is yet limited to only two
conflict types and many simplifications have yet to be avoided, the project underlines the potentialof this new research approach to the safety assessment of signalized intersections.

7.2 Outlook
The developed models and their realization in a simulation software proves the validity of the new
approach to the safety assessment of signalized intersections. However, the achievements can only
be seen as a starting point for further research. Four areas for improvement have to be highlighted:•

Consideration of more conflict types, namely angle collisions of right-turning vehicles with
opposing traffic and with pedestrians.
85•Calibration and improvement of the stop-go decision, gap acceptance, and start-up behavior
models for all possible movements in intersections (left-turning, right-turning, and throughtraffic).

•

Improvement of existing models by collecting more data to increase the sample size and get
more reliable results for the impact of different factors on the model parameters.

•

More realistic and flexible pedestrian behavior modeling.

Figure 7.1 illustrates the major models and conflict types which have not yet been developed.

conflict types not yet assessed
conflict types already assessed

gap acceptance (veh/ped)
angle collisions(with opposing traffic)

stop-go behavior

pedestrian behavior
gap acceptancemodelsstart-upbehavior(LT, RT)
rear-end
collisions

stop-gomodel(through, LT)

Figure 7.1 Illustration of models and conflict types which need further attention

86

The simulation tool proved to be a flexible base for the incorporation of further models. As
compared to existing micro-simulation software, the developed tool offers a much more detailed
representation of traffic flow at intersections. As an overall traffic flow simulator in networks it
will remain, of course, only a test platform. Some simplifications and limitations, nevertheless, canbe overcome in future versions: the limitation to an isolated intersection, the neglect of lanechanging behavior, the restriction of the number of vehicle types, to name a few.
A long term perspective will be the incorporation not only of realistically modeled pedestrians in
the intersection area, but also of bicycles and motorbikes and the interaction of them with eachother. The models will be provided for the inclusion in existing micro-simulation tools to combine
the strengths of existing and the newly developed tools.

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