Gap Acceptance Regression Model at Un-Signalized Intersections … · 2016-05-26 · Gap Acceptance Regression Model at Un-Signalized Intersections 5 Table (1): Roads Surveyed in

International Journal of Civil Engineering Research.

ISSN 2278-3652 Volume 7, Number 1 (2016), pp. 1-13

© Research India Publications

http://www.ripublication.com

Gap Acceptance Regression Model at Un-Signalized

Intersections (Major-Minor Roads) in Amman-

Jordan

Eng. Wlla Al-Mhairat

Al-Zaytoonah university of Jordan, Amman, Jordan

E-mail:[email protected], [email protected]

Abstract

The main purpose of this work is to identify the most influential factors on

gap acceptance decisions and to determine the critical gap that will be

accepted by local drivers, identify parameters that affect the driver’s gap

acceptance decision under local conditions, observe the type of distribution of

local gaps accepted in Amman, Jordan and to develop a gap acceptance

microscopic model.

Provide an idea about the local gap acceptance decisions and critical values.

Key words: gap acceptance, model, intersection, capacity

1.Introduction:

The traffic flow process at unsignalized intersections is complicated since there are

many distinct vehicular movements to be accounted for and most of which conflict

with opposing vehicular volumes. The absence of adequate gap acceptance

distribution results in decreasing capacity, increasing delays and increasing potential

for traffic accidents. A driver waiting at a given way sign on a minor road and wishes

to turn into the major road stream is faced with a series of gaps. Drivers must base

their decision on the size of the gaps between the oncoming traffic. Gap acceptance

and rejection are important parameters in determining the capacity of intersections.

Gaps are either accepted or rejected depending on a number of factors like driver age

and gender, intersection geometric, acceleration capability of a vehicle and other

factors[1].

Identification of the parameters that influence gap acceptance decision is very

beneficial for traffic operation and traffic planning. The headway distribution on

major roads along with the gap acceptance behavior enables the derivation of the

potential capacity of the minor road. Thus, the results of this study analysis assist the

mailto:[email protected]

2 Eng. Wlla Al-Mhairat

concerned authorities to develop their corporate plans for traffic operation's

improvements. It is very important to determine the average minimum gap length

(critical gap) that will be accepted by drivers to use in analyzing gap acceptance.

Determining this gap will help in evaluating delays of vehicles on minor roads

wishing to join a major road traffic stream at unsignalized intersections. Also

shedding light on the delay of vehicles on a ramp wishing to join an expressway. So it

therefore requires the acknowledgement of the frequency of arrivals of gaps that are at

least equal to the critical gap. This in turn depends on the distribution of arrivals of

main stream vehicles at the area of merge; it is assumed that for light to medium

traffic the distribution of main stream arrival is Poisson.The application of the gap

acceptance model can contribute greatly in many fields. For example, in the

intelligent transport system (ITS), gap acceptance, merging and lane change are the

main elements [2, 3].

Indicated that Drivers with low acceptance thresholds are more likely to accept the

first gap offered to them, whereas drivers who want long gaps will often reject the lag

and several gaps before obtaining an acceptable gap. The resulting effect of this bias

is that the reported critical gap is somewhat larger than the actual critical gap[4].

Described estimation procedures for critical gaps at unsignalized intersections.

stipulated that not all gaps presented to the driver should be considered in the process

while waiting at an intersection. showed that nearly all gaps longer than 12 seconds

are accepted and, therefore, should not be considered when determining the critical

gap[5, 6].

Offered two approaches to driver’s critical gap values: the deterministic and the

probabilistic approach. The deterministic critical values are treated as a single average

value. The fundamental assumption is that drivers will accept all gaps that are larger

than the critical gap and reject all smaller gaps. Highway Capacity Manual (HCM)

has adopted the deterministic approach in the two way stop controlled roads (TWSC)

capacity formula. As an alternative, probabilistic models solved some of the

inconsistency elements in gap acceptance behavior by using a statistical treatment of

minor street drivers' gap acceptance behavior [7, 8, 9]. Explained how a long queue-

waiting time may reduce the driver's critical gap. Drivers' frustration may increase as

length of the queue and queue time increases. In addition, the pressure on the driver

that is first in line from other vehicles queued behind will encourage the driver to

accept a shorter gap. Finally, the longer the time a driver spends in queue, the better

he or she will be able to estimate the size of upcoming gaps and the driver may come

to accept a shorter gap [10, 11]. Also found evidence that drivers accept smaller lags

and gaps during peak periods than during off-peak hours. Older drivers have problems

to adequately detect, perceive and accurately judge the safety of a gap as indicated by

[12, 13, 14]. Therefore, older drivers may experience greater difficulties at non-

signalized intersections as the result of diminished visual capabilities, such as depth

and motion perception. Prior results indicated that judgments about whether a

potential collision would occur were less accurate for older drivers (40–64 years)

compared with younger drivers (18–29 years) [15, 16, 17].

Collected gap acceptance data as a function of driver age for left turn, right turn, and

through movements at stop-controlled intersections.The findings indicated that

Gap Acceptance Regression Model at Un-Signalized Intersections 3

younger drivers (20–40 years) accepted shorter gaps than older drivers (over 65 years)

[18]. Through both simulator and field measures, indicated that older drivers show

relative insensitivity to vehicle approach speed in left-turn maneuvers across the

major road traffic when compared with younger drivers. This may increase the risk of

accidents if there is a lone speeder in the traffic scheme [19, 20]. Concluded that older

drivers generally over-estimate the speed of vehicles traveling at low speeds, while

under-estimating the speed of those traveling much faster, which could explain the

over-involvement of elderly drivers in accidents at junctions. Stochastic models of the

gap-acceptance behavior of left-turn drivers on major roads at unsignalized

intersections were programmed using (SLAM II), a simulation computer language

[21].

Critical gap is the threshold by which drivers in the minor stream judge whether to

accept a gap. If the gap is larger than critical gap, drivers accept it and enter the

intersection; otherwise, drivers reject the gap and wait for the next gap. At “a priority-

controlled intersection” concluded that, critical gap is usually considered as a fixed

value or to follow a certain distribution[22, 23].

2. Data Collection:

Six unsignalized intersections in Amman city were investigated in typical days. The

intersections were chosen to be on major roads, and of high importance to all road

users; as nearby areas contain many places of interest that attract many people. These

intersections are shown in Figures (1 through 6).

Figure (1): Loop Intersection for Queen

Rania Road and Al-Madina.

Figure (2): Loop Intersection for Istiqlal

Road and Jordan Road. Al-Monawra

Road


Figure (3): Loop Intersection for Airport

Road and Mgableen Road.

Figure (4): (90º) Intersection between

Zahran Road and Hashem Otbeh Road.


Mecca Road and King Faisal Abd-

Alazeez. Road


Yarmouk Road and Abd-Alrahman

Kawakby Road.

The selected unsignalized intersections were divided into two groups: loop geometry

including three intersections, and three (90◦) intersections geometry. Those are

mentioned in Table (1).


Table (1): Roads Surveyed in the Study

Type of intersection Intersection Name

Loop Queen Rania

Loop Istiqlal

Loop Airport

(90◦)Intersection Zahran

(90◦)Intersection Mecca

(90◦)Intersection Yarmouk

3. Calculations and Results:

To obtain the critical gap in accordance with Raffs definition, the cumulative number

of accepted gaps and rejected gaps were calculated for each gap size. Graphical

representations of the previous data were made, and then the critical gap was obtained

from the intersection of the two curves (Cumulative accepted and cumulative rejected

gaps).

Figure(7): Critical Gap Determination for

Queen Rania Road in Peak Period.

Figure (8): Critical Gap Determination for

Queen Rania Road off Peak Period.

Figure (9): Critical Gap Determination for

Istiqlal Road in Peak Period

Figure (10): Critical Gap Determination

for Istiqlal Road off Peak Period.



for Airport Road in Peak Period.


for Airport Road off Peak Period.


for Zahran. Road in Peak Period.


for Zahran Road off Peak Period.


for Mecca. Road in Peak Period.


for Mecca Road off Peak Period.



for Yarmouk. Road in Peak Period.


for Yarmouk Road off Peak Period.

The results of previous figures are illustrated in Table (2):

Table 2: Critical gap values for each intersection

Critical Gap Value (sec) Road Name

Off-Peak On-Peak

5.5 3.3 Queen Rania

5 3.3 Istiqlal

5 3.3 Airport

4.5 3.1 Zhran

5 3.5 Mecca

5.1 3.3 Yarmouk

5.02 3.3 Avg. (sec)

Results showed that the mean critical gap values were equal to 3.3 seconds in peak

periods and 5.02 seconds for off peak periods. The results of this study agrees with

several previous studies.

4.1 Analysis of Parameters Affecting Gap Acceptance:

Data were inspected by logistic analysis in accordance with previous studies to

determine the variables that affect gap acceptance. The results of this analysis are

shown in Table (3). Input parameters that were considered; driver age and gender, the

flow on major and minor road, the geometric of the roads, and speed of vehicles on

major road.

Table (3) shows the results through the logistic analysis. The dependent variable was

the driver decision on acceptance or rejection of a gap; the independent variables were

driver age, driver gender, traffic flow on major road, traffic flow on minor road, speed


of vehicles on major road on the lane in which vehicles are merging, type of vehicles

on minor road wishing to merge, and intersection geometry type.

Table 3: The SPSS Output for the Logistic Model

-value R Significance Level coefficient Variable

0.376 0.000 - Model

- 0.000 -0.078 Driver age

- 0.000 3.029 Driver gender

(male=1, Female=0)

- 0.027 0.435 Traffic flow on major road

(on-peak=1, off-peak=0)

- 0.000 1.642 Traffic flow on minor road

(on-peak=1, off-peak=0)

- 0.000 -0.110 Vehicle speed on major road

- 0.021 0.412 Vehicle type on minor road

(pc=1, others =0)

- 0.039 3.815 Intersection geometry type

(Loop=1; T@ 90º=0)

Therefore, the obtained logistic model is:

D =-0.078*DA + 3.029*DG + 0.435 * F major + 1.642*F minor-0.110 * M +

0.412* VT + 3.815* IG + E

Where

D: decision to accept or reject.

DA: driver age.

DG: driver gender.

F major: traffic flow on major road.

F minor: traffic flow on minor road.

M: vehicle speed on major road.

VT: vehicle type on minor road.

IG: intersection geometry type.

E: error.

4.2 Analysis of Gap Acceptance Model:

Previous model was established to determine decision on gap acceptance. In order to

establish a model to estimate the size of the gap, multiple regression model was used

on the surveyed intersections.

Table (4) shows the results of the multiple regression analysis. The dependent

variable was to accepted gap size; the independent variables were driver age, driver

gender, traffic flow on major road, traffic flow on minor road, speed of vehicles on

major road on the lane in which vehicles are merging, type of vehicles on minor road

wishing to merge, and intersection geometry type according to [24, 25].


Table 4: The SPSS Output for the Multiple Regression Model

-value R Significance

Level

Coefficient Variable

0.633 0.000 - Model

- 0.000 0.090 Driver age

- 0.000 -0.601 Driver gender (male=1, Female=0)

- 0.002 -0.024 Log(traffic flow on major road)

- 0.039 -0.071 Log(traffic flow on minor road)

- 0.000 0.040 Vehicle speed on major road

- 0.042 -0.101 Vehicle type on minor road (pc=1, others =0)

- 0.047 -0.008 Intersection geometry type (Loop=1; T@90º=0)

Therefore, the obtained multiple regression model is:

AGS = 0.009*DA-0.601* DG-0.024* F major – 0.071* F minor + 0.004* M-0.101*

VT – 0.008* IG + E

Where

AGS: the accepted gap size.

DA: driver age.

DG: driver gender.

F major: the traffic flow on major road.

F minor: the traffic flow on minor road.

M: vehicle speed on major road.

VT: vehicle type on minor road.

IG: intersection geometry type.

E: error.

Applying the obtained multiple regression model on surveyed data in different

locations, for example, if;

Driver age: 60 years old.

Driver gender: male.

Vehicle speed = 60 km/hr.

Vehicle type: passenger car.

Intersection type: loop.

Gap = 6 seconds.

Traffic flow on major road =2073 veh/hr.

Traffic flow on minor road = 858 veh/hr.

Peak period.

Implementation of the previous data in the multiple regression model, the answer was

6.8 seconds. The significance levels show that the effects of the studied variables

were significant, and were less than 0.05. This means that the selected variables have

a significant effect on determining the accepted gap size.


Analyzed data show that each factor in this model has an effect on the accepted gap

size. Multiple regression model shows positive sign for driver age, which means in

case of increasing in driver age; the required gap size increased.

For driver gender, model shows positive sign for female, this means that females use

larger gap size more than males, because females more cautions for ending their

waiting time. For intersection geometric factor, model shows positive sign for (90◦)

intersection and negative sign for loop geometry type. This is because merging

vehicles in (90º) intersections need larger gap size than loop type. For traffic flow on

major stream, model shows negative sign because drivers accept smaller gap size in

peak period. Vehicle type factor have negative sign for passenger car because it needs

smaller gap size compared with buses. Finally, Model shows negative sign for vehicle

speed on major road, because it shortens the accepted gap size [26].

4.3 Applications of Models:

The phenomenon of gap acceptance can be used in many important aspects such as

queue lengths, delays and road capacities. Results shown in Table (5) indicate the

existence of short queues in some roads (3-4 vehicles) and long queues (9-16

vehicles) on other roads. Despite the length of the queue the delay seems to be

significant (8-14 sec/veh). This can be explained by that roads dimensions are small in

general, and therefore, are affected significantly even by small queue.

Table 5: Summary of Results

Off-Peak Period Peak Period Road

Name Calculat

ed

capacity

Ccal.

(veh/hr)

Estimated

capacity from

GREATER

AMMAN

MUNICIPALI

TY C est. (veh/hr)

Delay

D

(sec/veh)

Queu

e

length Qι(ve

h)

Calculat

ed

capacity

Ccal.

(veh/hr)

Estimated

capacity from

GREATER

AMMAN

MUNICIPALI

TY C est. (veh/hr)

Delay

D

(sec/veh)

Queu

e

length Qι(ve

h)

3393 3700 6.51 2 3470 3700 8.96 9 Queen

Rania 3023 3700 9.16 9 3100 3700 11.52 16 Istiqlal 3559 3800 6.2 2 3634 3800 6.86 3 Airport 837 950 10.8 2 910 950 14.17 4 Zahran 755 845 11.82 2 830 845 13.97 3 Mecca 1038 1200 9.05 1 1115 1200 11.89 4 Yarmou

k

It was noticed that the calculated capacity in peak and off-peak periods are less than

the estimated capacity obtained from (GREATER AMMAN MUNICIPALITY), this

result explains the high levels of congestion in the studied roads.

4.4 Comparing with HCM:


Capacity values obtained from GREATER AMMAN MUNICIPALITY and HCM

were compared and examined using the T-test. The HCM formula is shown below.

c = v*((e^ (−v*tc /3600)) / (1 – e^ (−v*tf /3600))) (1)

where:

c = capacity of minor road (veh/h).

v = flow rate for major road (veh/h).

tc = critical gap(s).

tf = follow up time(s).

Table (6) shows the results for T-test. It was noticed that the actual capacity of minor

road calculated using the HCM equation is less than the values that was obtained from

GREATER AMMAN MUNICIPALITY by ratio equal to 0.93. Also the significance

level shows that the studied variables were significant and were less than 0.05.

Table 6: The SPSS output for T-test

Number of readings Mean value Standard deviation Significance level

6 0.93 0.05 0.00

5. Conclusions

Based upon the analysis performed in this study, the following conclusions were

made:

1. The critical gaps at the six locations in Amman (the capital city of Jordan)

ranged between (3.1-3.5 seconds) for peak periods and between (4.5-5.5

seconds) for non-peak periods.

2. Gaps investigated in the study followed Poisson distribution.

3. For gap acceptance decision, a logistic model is developed. The obtained

logistic model is:

D =-0.078*DA + 3.029*DG + 0.435 * F major + 1.642*F minor-0.110 * M

+ 0.412* VT + 3.815* IG + E

4. For determination of accepted gap size, a multiple regression model is

developed. The obtained multiple regression model is:

AGS = 0.009*DA-0.601* DG-0.024* F major – 0.071* F minor + 0.004*

M-0.101* VT – 0.008* IG + E

5. The analysis indicated that there is a decrease in the roads capacities, and

increase in delays due to the absence of adequate gap acceptance. These

results require more attention from traffic engineers in solving congestion,

delays, capacities problems, and level of service. It can be concluded that

operations on ramps studied in this research may be improved by using control

system, for example, ramp metering. Ramp metering is defined as the process

of facilitating traffic flow on freeways by regulating the amount of traffic

entering the freeway through the use of control devices on entrance ramps to

allow vehicles to enter the freeway at a predetermined rate. This will ease

congestion by controlling the rate of flow of merging vehicles. This will also


assist in reducing pollution and energy waste. An alternative solution is to

provide an additional lane; this will increase the capacity. Selection of most

appropriate solution will require cost-benefit analysis.

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Gap Acceptance Regression Model at Un-Signalized Intersections … · 2016-05-26 · Gap Acceptance Regression Model at Un-Signalized Intersections 5 Table (1): Roads Surveyed in