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Title: Modeling Crossing Behavior of Drivers and Pedestrians at

Uncontrolled Intersections and Mid-block Crossings

Objectives

The goal of this study is to advance the state of the art in understanding traffic characteristics and

modeling drivers’ and pedestrians’ behavior at uncontrolled intersections and mid-block crossings

respectively. Based upon the existing research needs and the potential for utilizing data collected

at various locations, the following research objectives are established to address goals of this

research initiative:

Research Objective 1 – Traffic Characterization

To study the microscopic traffic characteristics at the functional area of unsignalized intersections,

such as, vehicle category wise speeds on the major and minor legs, relative speed between the

inner lane and outer lane of major road, conflict point study and vehicle trajectories study.

Research Objective 2 – Drivers and Pedestrian Gap Acceptance Analysis

Analyzing the driver and pedestrian behavior while crossing uncontrolled intersections and mid-

block crossings respectively, which involves quantifying driver and pedestrian gap acceptance

and gap rejection behavior, identification of the factors that affect drivers’ and pedestrians’

crossing behavior.

Research Objective 3 – Dilemma Zone for Low Priority Streams

Studying the dilemma of crossing vehicles and pedestrians.

Finding location and length of the dilemma zone using probabilistic approach at uncontrolled

intersections for vehicles and at uncontrolled mid-block crossings for pedestrians.

Summary of previous work.

Understanding traffic parameters such as speed, traffic composition, gap acceptance, and conflict

points at microscopic level is necessary for developing performance evaluation models. These

parameters also help to evaluate facilities with respect to safety. Many studies are found in the

literature that focus on microscopic traffic characteristics at various transportation facilities in

developed countries where traffic is disciplined. Very few studies are found that analyze traffic

behavior at unsignalized intersections and mid-block crossings in India. The traffic behaves

significantly different at unsignalized intersections and mid-block crossings in developing

countries like India than at the intersections and crossings in developed countries which are

controlled by stop and yield signs. The situation is more severe in India, because drivers and

pedestrians do not follow the traffic rules strictly; major road drivers usually do not yield to minor

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road traffic even in the presence of yield sign. This condition further makes more challenging task

to analyze the traffic characteristics. The identified research gaps after doing through literature

review are outlined below.

Gap acceptance theory is limited to finding Capacity and LOS of the intersections and mid-

block crossings, only few studies have used gap acceptance theory for highway safety

considerations. Many gap acceptance studies are reported for homogenous traffic conditions

where lane discipline and priorities are respected. Modeling heterogeneous traffic conditions

is more challenging and complex task.

A majority of the research used time based gap/lag data for modeling driver and pedestrian

gap acceptance behavior. Spatial gap acceptance behavior of drivers and pedestrians at

uncontrolled intersections and mid-block crossings is not comprehensively studied.

Dilemma behavior of drivers at uncontrolled intersections and pedestrians at mid-block

crossings is not yet studied.

A few studies have examined the effect of night time on drivers’ behavior. For the most part,

data collected in these studies have not included speed, distance, and vehicle type of

conflicting vehicle. Thus, only a very few of these studies have been able to use and study

detailed traffic characteristics.

Methodology Overview

The methodology presented in this research rests on the assumption that driver and pedestrian

behavior can be modeled through a set of descriptive parameters, which can be calibrated from

filed data. The research presented in this study involves several tasks, as follows:

Selection of Intersections and Mid-block Crossings

Seven uncontrolled road intersections and two mid-block crossings with their approach segments

are identified for data collection. Each intersection having different vehicle composition is studied.

One intersection from town, two typical inner-city intersections, three intersections from outer

suburban road and one intersection on rural fast road are studied

Classification of Intersections

Selected intersections are classified/labeled as Type-I, Type-II, and Type-III intersections. Type-I

intersections are located at the city centre; Type-II intersections are located on outer link road

while Type-III intersections on rural national highway. Snapshots of three intersections, one in

main city, one in a suburb, and one in the outskirt of city are shown in Figure 1.

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Figure 1: Typical examples of type I, type II and type III intersections

Data Extraction

Except geometric data, all required data are extracted from the video recorded. For gap acceptance

and dilemma study, vehicle and pedestrian yielding behavior, accepted and rejected gaps, traffic

volume data are recorded at study sites and analyzed. The data extracted has total 1234 gap/lag

observations at three 4-legged intersections located on outer link road; 1469 and 1103 gap/lag

observations at one 3-legged intersection located on rural national highway for day and night

respectively, and 1107 gap/lag observations for pedestrians at two mid-block crossings.

Data Analysis

The data extracted is then analyzed for studying drivers and pedestrians gap acceptance and

understanding their dilemma at uncontrolled intersections and mid-block crossings respectively.

Gap acceptance study involves temporal as well as spatial gap analysis. For dilemma analysis,

variations in temporal and spatial gap acceptance behavior are analyzed to arrive at dilemma zone

boundary values.

Summary of Input Data

The preliminary analysis is done to understand different traffic parameters at uncontrolled

intersections. The preliminary analysis includes understanding of traffic composition, lane

preference, speed analysis, traffic conflict points, distribution of gaps, and vehicle trajectories.

Traffic Composition and Lane Preference

It is observed that Type I intersection is handling much higher traffic compared to others, and

Type II intersection traffic is higher than that of Type III. The traffic composition clearly shows

that very high proportions of two-wheelers are used in most cities of India. Similar observations

are reported in other studies (Sangole, 2011). The proportion of two-wheeler is highest at Type I

intersections. This is mainly because two-wheelers are preferred for shorter trips and in the areas

of high congestion.

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Table 1: 20-Minutes Volume Statistics in % with Type and Lane Choice

Inter. Type Lane 2W Car HMV Rickshaw Bicycle Total

Type I

Outer 40 30 5 60 95 42

Inner 60 70 95 40 5 58

Total % 71.89 10.51 1.71 13.28 2.61 2341

Type II

Outer 48 33 21 95 92 49

Inner 52 67 79 5 8 51

Total % 52.03 27.36 5.91 13.20 1.49 1674

Type III

Outer 3 30 40 100 0 21

Inner 97 70 60 0 0 79

Total % 48.17 29.74 19.27 2.83 0.00 955

Speed Analysis

Vehicle speeds are calculated at different distances by noting the vehicle crossing time at cross

grid lines along a vehicle path. The speed variations of vehicles along its path for a major approach

and a minor approach are depicted in Figure 2. The speed values at centre of intersection (0-0 m)

are much lower since vehicles have to slow down or stop because of crossing or merging of traffic

from other approaches and large number undisciplined pedestrian movements.

Figure 2: Speed variations for major road and minor road at type I intersection

Vehicle Conflict Points

Good understanding of how and where conflicts occur is required for the proper geometric design

and implementing efficient traffic control measures. Vehicle trajectories on the angular view from

video and the transferred trajectores on a plan are shown in Figure 3. One important observation

from the trajectory path is that the two-wheelers taking turns are not at the centre of the lane. As

far as possible the vehicles are on extreme right of an approach; this minimizes the crossing time

for a vehicle. Howerver, the standard 32 points conflict diagram is based on the assumption that

vehicle move at the center of a lane.

Distributions of Gaps and Observed Trajectory Data

The histograms for temporal and spatial gap along with the various distributions (Exponential,

Lognormal, Gamma and Weibull) fitted for all available gaps (accepted and rejected) are shown

0.0

10.0

20.0

30.0

40.0

50.0

Sp

eed

(k

m/h

r)

Distance (m)

Major Road (West Bound )

0.0

10.0

20.0

30.0

40.0

50.0

Sp

eed

(k

m/h

r)

Distance (m)

Minor Road (South Bound)

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in Figure 4. Based on Kolmogorov-Smirnov (K-S) test, it is observed that lognormal distribution

fits temporal gaps well, whereas the spatial gaps follow Gamma distribution.

Figure 3: Plotting of vehicle trajectories and comparison of conflicts between right turning vehicles

Figure 4: Distribution fitting for available temporal gaps and spatial gaps at 4-legged intersection

The distance of the vehicle and its speed travelling over a major road are plotted when the vehicle

on minor road is waiting to accept the gap. Figure 5 depicts the graphical representation of

locations and speeds of observed main line stream vehicle either during the acceptance or rejection

of gap or lag by minor road vehicle to cross the major road.

Figure 5: Observed speeds and distances of main line stream vehicles while acceptance and rejection of

gap by minor road vehicles for (a) 4-Legged intersection, (b) 3-Legged intersection (Day)

Analysis Overview and Main Results

Modeling Driver and Pedestrian Behaviour Using Binary Logit Models

A binary-logit model is recognized as one of the important modelling tool for studying discrete

choices. It has two alternative outputs from which an individual can choose. In present case, a

minor road vehicle or a pedestrian waiting for a sufficient gap has to choose between the two

0 2 4 6 8 10 12 14 16 18 200

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Gap (Sec)

D e

n s

i t

y

Histogram

Exponential

Lognormal

Gamma

Weibull

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 1500

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

Gap (Meter)

D e

n s

i t

y

Histogram

Exponential

Lognormal

Gamma

Weibull

0

10

20

30

40

50

60

70

0 20 40 60 80 100 120 140

Sp

eed

(k

m/h

r)

(a) Distance (m)

Accepted

Rejected

0

20

40

60

80

100

120

140

0 50 100 150 200 250

Sp

eed

(k

m/h

r)

(b) Distance (m)

Accepted

Rejected

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alternatives from an available gap: accept the gap or reject the gap. A linear-utility expression can

be expressed as shown in Equation 1:

𝑃𝑘(𝑖) =1

1 + 𝑒−𝑈𝑖

(1)

𝑈𝑖 is a utility of gap i , expressed as:

𝑈𝑖 = 𝛽1𝑋1 + 𝛽2𝑋2 + 𝛽3𝑋3 + … + 𝛽𝑛𝑋𝑛 (2)

Where, 𝑋1, 𝑋2 , … , 𝑋𝑛 are the variables that influences the decision of drivers and

𝛽1, 𝛽2 , … , 𝛽𝑛 are the corresponding coefficients. We used software tool NLOGIT to calibrate

binary logit model. Various dummy variables tried while developing model along with their

definition and share in the total data set are given in Table 2.

Table 2: Definitions of Dummy Variables

Dummy Variables Definition

% observation with value 1 0 1

Gender of the subject vehicle driver Female Male 85%

Whether Lag or Gap Gap Lag 21%

Position of conflicting vehicle Lane1 Lane2 19.6%

Conflicting vehicle: two-wheeler No Yes 42%

Conflicting vehicle: Auto Rickshaw No Yes 8%

Conflicting vehicle: Car No Yes 34%

Conflicting vehicle: Truck No Yes 11%

Subject vehicle: two-wheeler No Yes 71%

Subject vehicle: Auto Rickshaw No Yes 11%

Subject vehicle: Car No Yes 17%

Subject vehicle: Truck No Yes 1%

Separate models for spatial and temporal gaps are developed. We tried various combinations of

variables affecting the gap acceptance decision and shortlisted two models each for spatial and

temporal gaps. Model 1 and 2 are developed by taking various combination of variables from

Table 2. Table 3 gives values of t-statistics for variables used and R2 for the models developed.

Model 1

𝑈𝑖 = − 7.292 + 1.921(𝑇) + 1.08 (𝐿𝐺) − 1.494 (𝑇𝑊_𝑇) + 1.230 (𝑇𝑊_𝑇𝑊) − 0.616 (𝑇𝑊_𝐶) (5)

Model 2

𝑈𝑖 = − 0.606 − 0.189(𝑆) + 0.194 (𝐷) + 1.08 (𝐿𝐺) − 1.273 (𝑇𝑊𝑇) + 1.273(𝑇𝑊_𝑇𝑊) − 0.539 (𝑇𝑊_𝐶) (6)

The probablity of accepting spatial lag or gap is shown in Figure 6(a). From the figure, it is clearely

evident that for a given value of lag/gap, drivers are more willing to accept lag i.e. first gap. Figure

6(b) shows the probability of accepting spatial gap by two wheelers for different types of

conflicting vehicles.

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Figure 6: (a) Probability of acceptance of spatial gap and lag and (b) Probability of accepting spatial gap

by two wheelers for different types of conflicting vehicles

Table 3: Results of the Estimation of the Logit Model

Variable Description Model 1 Model 2 Model 3 Model 4

t-stat t-stat t-stat t-stat

Constant Constant -16.215 -1.369 -13.869 -0.924

T Time 14.942 - 14.052 -

S Speed - -7.820 - -8.181

D Distance - 14.841 - 13.986

LG Lag/Gap - - 3.102 3.092

TW_T 2Wheller_Truck - - -3.003 -2.697

TW_TW 2Wheller_2Wheller - - 3.411 3.590

TW_C 2Wheller_Car - - -1.570 -1.380

McFadden Pseudo R-squared 0.68 0.67 0.72 0.71

Comparison of Critical Gaps

As per HCM 2000, critical gap is the minimum time between successive major street vehicles

where minor street vehicles make a maneuver. Critical gap may differ for different drivers based

on driver’s characteristics such as driving experience, age, gender, and psychological condition.

The summary of temporal and spatial critical gap values for through traffic, right turning, and

through and right combined is listed in Table 4.

Table 4: Summary of Critical Gap Values Calculated from Different Methods

Method

Critical Gap

Through Traffic (Minor Rd. to Minor Rd.)

Right Turning

(Minor Rd. to Major Rd.) Combined Traffic

Temporal (s) Spatial (m) Temporal

(s) Spatial (m) Temporal(s) Spatial(m)

Raff's Method 3.7 36 3.4 29 3.8 36

Logit Method 3.6 36.4 3.7 37.3 3.7 31.2

MLM 3.5 35.6 3.5 36.2 3.6 35.8

Lag Method 3.1 30 3.8 33 3.6 31

Ashworth 3.0 n/a 3.7 n/a 3.3 n/a

0

0.2

0.4

0.6

0.8

1

0 20 40 60 80

Pro

bab

lity

(a) Distance (m)

Lag

Gap

Lag (36 km/hr)

Gap (36 km/hr)

0

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50 60 70 80

Pro

bab

lity

(b) Distance (m)

Two Wheeler_Two Wheeler

Two Wheeler_Car

Two Wheeler_Truck

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Critical Gaps for Pedestrians

The critical gap values estimated using different methods are shown in Table 5. The probabilistic

methods (logit method and maximum likelihood method) are relatively close in their estimation

of the mean pedestrian critical gaps. Critical gaps estimated using Raff’s and Ashworth’s methods

are on lower side.

Table 5: Critical Gap Comparison by Different Methods

Temporal critical gap

(Adequate Gap)

(s)

spatial critical gap

(Adequate Gap)

(m)

Critical gap accepted by pedestrian

( Found using different methods)

Method Temporal

(s)

Spatial

(m)

11.5*

8.6**

198*

148**

Raff's Method 3.6 60

Logit Method 4.3 73

MLM 4.3 71

Ashworth’s Method 3.6 N/A

N/A not applicable; * Adequate Gap using HCM default values; ** Using observed field values

SVM for Classification of Gaps

The basic idea of the SVM is to construct a hyperplane as the decision plane, which separates the

trajectories of accepted and rejected gap classes with the largest margin. The data are divided into

two classes: positive (+1) which are accepted gaps and negative (-1) which are rejected gaps (see

Figure 7). The two classes in present situation are linearly non-separable. Figure 7 shows the

profiles of both accepted and rejected spatial gaps for various speed ranges for a 4-legged

intersection. The 10-fold cross-validation method was used for training and validating.

Figure 7: Hyperplane separating two classes accepted and rejected for 4-legged Intersection

Dilemma Zone for Low Priority Streams

The study defines “Dilemma zone” as a roadway segment of a major road over which if a vehicle

is present with a certain speed, creates dilemma to minor road vehicle regarding maneuvering.

When a conflicting vehicle is in this zone, minor road vehicles may take incorrect decision, and

this unsafe behavior may lead to crashes at intersection. This observation leads to the evaluation

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 15010

20

30

40

50

60

70

Distance (m)

Sp

eed

(k

m/h

r)

Accepted

Rejected

Support Vectors

Mean Speed Critical Gap = 30m

Critical Gap Line

(Hyperplane)

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of upper and lower limit of accepted/rejected gaps which are stated as outer (D0) and inner (Di)

boundaries of dilemma zone. Using probabilistic approach, we have found the dilemma zone

which is modeled as the road segment or a zone where more than 10% and less than 90% of the

drivers would choose to reject the gap. Binary discrete choice models are developed to determine

the probability of rejection of gap for a given distance and speed of the conflicting vehicle. Table

6 depicts parameter estimates and statistical significance of the logit models for selected

intersections. Table 7 shows the dilemma zone boundaries for probability of 10% and 90%

stopping for 4-legged intersection.

Table 6: Parameter Estimates and Statistical Significance of the Logit Model for Selected Intersections

Variable Description 4-legged inter. 3-legged inter. (Day)

3-legged inter.

(Night)

Coefficient t-stat Coefficient t-stat Coefficient t-stat

Constant Constant -0.814 -1.369 -0.642 -1.534 -0.669 -1.421

S Speed -0.155 -14.841 -0.063 -9.006 -0.982 -8.240

D Distance 0.172 7.820 0.058 17.500 0.067 15.429

McFadden R2 0.70 0.58 0.58

Table 7: Dilemma Zone Boundaries for Probability of 10% and 90% Stopping for 4-legged Intersection

Approach Speed (km/hr) 4-legged intersection

90% 10%

25 14 m 40 m

35 23 m 48 m

45 32 m 58 m

Effect of Vehicle Type on Dilemma Zone Boundaries

The distribution of the dilemma zones are found varying with different type of vehicles. Vehicle

types such as truck, car and two wheeler were found to have statically significant effect on length

and location of dilemma zone boundaries. Analysis result indicated that the dilemma zone

distribution shifts away from the intersection as vehicle size increases. Time of the day (i.e., day

vs night) had a statically significant effect on both length and the location of dilemma zone.

Main Conclusions

Preliminary Data Analysis

It is well know that two-wheelers form a major component of the traffic in India. At one

intersection, the proportion of two-wheelers is more than 70% and at two intersections, it is close

to 50%. It is also observed that the traffic speed on inner lane is higher than that on outer lane.

Vehicles at type II and type III intersections maintain much higher speed than the posted speed

limit. From the vehicle trajectories analysis, it is concluded that the conflict points of right turning

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two-wheelers are located significantly away from the conflict points arrived assuming vehicles

move at the center of a lane.

Gap Acceptance Analysis

It is observed that, approach speed of major stream affects the spatial gap acceptance but not the

temporal gap acceptance. Type of conflicting vehicle also has a major impact on crossing vehicle

and pedestrian gap acceptance behaviour. It was found that, as size of conflicting vehicle

increases, the probability of accepting the available gap decreases. At 4-legged intersection, the

temporal critical gap values for through movement vary from 3.0 sec by Ashworth method to 3.7

sec by Raff’s method. The values for right turning movement vary from 3.4 to 3.8 seconds. This

study also demonstrates the feasibility of SVM to classify and predict gap acceptance/rejection

for uncontrolled intersections and midblock crossing.

Dilemma Zone for Low Priority Streams

The empirical results have clearly indicated that the existence of dilemma zone vary with the

traffic and geometric characteristic. Separate dilemma zones for trucks, cars and two wheelers are

analyzed. The start and end point of dilemma zone for medium speed intersection for different

conditions varies from 10 to 40 m and 32 to 62 m, whereas for high speed intersection these values

vary from 12 to 88 m and 76 to 148 m.

Suggested Further Research

The aggressive behavior of drivers and pedestrians reported could be partly due to the poor

enforcement of the priority rules. The study can be extended to analyze the variations in gap

acceptance for different traffic volumes at different time periods. The effect of

driver/pedestrian age, and education level can also be studied.

Gap acceptance depends upon various traffic and geometric factors. The selected intersections

had level approaches, central refuge area and 90 degree intersecting approaches. Intersections

having peculiar traffic and geometric characteristics (traffic encroachment, speed breakers

etc.) can also be analyzed. Selected pedestrian crosswalks in this study were on high speed

arterials. Thus, the transferability of behavioral models for different locations needs to be

checked.

Dilemma zone and prediction of gap acceptance at uncontrolled road sections can be important

to develop real time applications such as Advanced Warning and Safety System (AWSS) and

Advanced Traffic Management Systems (ATMS). These systems will help drivers and

pedestrians to make an appropriate choice of action during crossing at intersections and mid-

block crossings. Future studies should apply the SVM technique to data from different cities

and check the applicability of the models developed.