Exercise 6 - Gap Acceptance and Priority Junction Aditya Nugroho e

EXERCISE 6

GAP ACCEPTANCE AND PRIORITY JUNCTION

CE 5203 TRAFFIC FLOW AND CONTROL

ADITYA NUGROHO

HT083276E

DEPARTMENT OF CIVIL ENGINEERINGNATIONAL UNIVERSITY OF SINGAPORE

2010

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Department of Civil Engineering

CE 5203 Traffic Flow and Control

1.0 INTRODUCTION

Gap acceptance and rejection are important parameters in determining the capacity of stop -sign intersections. Gaps are either accepted or rejected depending on a number of factorsincluding headways, volume of traffic, drivers' characteristics etc. In this Exercise 6 theobjectives are:

Apply gap acceptance analysis Predict junction capacity at Jalan Lempeng

2.0 GAP ACCEPTANCE AND JUNCTION CAPACITY METHOD

2.1 Data collection

A gap can be defined as the time interval between the passage of two successive vehicles onthe major road at a priority intersection. Gap acceptance is the decision of a side-street (minorroad) driver to use a gap created in a major road traffic to merge or maneuver safely with themajor road traffic. A gap may be accepted if it is large enough or rejected if it is too small.

Gaps have been measured using video camera and and data has been extracted usingappropriate MultiTimer software. In this Exercise 6, several variables should be consideredbefore do the measuring of gaps acceptance.

A reference line- a certain line should be set as a reference to count vehicles. Traffic volume major road- Traffic volume of major road were recorded in 30

minutes, to predict junction capacity. Gaps - This was done manually by the use of multimer to time individual vehicles as

they pass the junction from the minor road. The gaps accepted or rejected by the minorroad vehicles were observed and noted also. The time headway of the vehicles on theminor road was simultaneously recorded.

Lags – Differently from gap, this time measurement is between two vehicles ondifferent road. In here, lag is defined as the time it takes a vehicle in the majorroad toreach the front bumper of the vehicle in the minor road.

Vehicles type- Although it is important to measure the gap acceptance by vehiclescomposition where heavy vehicles may affect the gaps acceptance function. However,to simplify our exercise, we do not consider vehicle type.

Therefore a gap is first sought at the conflict point at time t0. Also if vehicles in the prioritystream arrive at the conflict point at times t1, t2, t3,...., then

1 0

1

1,2,3,...i i

lag t tgap t ti

(1)

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2.2 Gaps acceptance and capacity junction measurement

Based on characteristic of Jln Lempeng junction it is assumed that gap models for the driverson the major road are not affected by drivers on the minor road. It is also observed that in thisstudy site, random arrivals of vehicles in main road. Therefore, in order to get generallyapplicable results of gap acceptance models and junction capacity, it is necessary to measuredby following steps.

Finding single estimators of critical gap Approximate probability distribution of gap Calculate junction capacity (random arrivals)

Four single estimators of critical gap were selected for a more detailed analysis: Median accepted gap (50th percentile of Tai)

: ( ) ( )c a c a cF T F T Median critical lag

: ( ) ( )c a a c r a cF T F T Mean critical gap (lag)

1

0 1 2 3 1

1: ( )2

, max , , , ,.., 0

m

c r a ii

r n

a n

T Tm

where T T T T T T nT T

Weighted mean critical lag

1

1

( ) / ( ):

2 1/ ( )

m

r a i r a ii

c m

r a ii

T T T T

T T

3.0 ANALYSIS OF GAPS ACCEPTANCE AND REJECTION

The gaps data were collected from a Jln Lempeng junction. A video camera was mounted onthe roadside, opposite to a reference point, to continuously capture the traffic across thisreference point. The collection of data was done during 30 minutes in morning peak hours.After completing data collection a simplified table is used to calculate critical gaps. Table 1 isexample of a simplified table of gap acceptance/rejection patterns for 30 vehicles in the study.

Table 1 Example of gap acceptance/rejection patterns

No ofvehicle

Accepted Rejected(s) (s) (s) (s) (s) (s) (s)

1 1.06 3.61 1.122 213 11.94 3.79

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5 13.51 3.18 1.456 11.257 24.708 1.5928 21.154 1.1559 13.556

10 15.3511 13.9812 4.69 4.35 2.43 1.0313 14.19 3.09 2.1914 5.632 1.513 1.23315 14.258 1.638

If one were to use only the data in Table 1, not all 15 accepted gaps could be used. Tosimplified the analysis, accepted gaps greater than 20s were discarded. Also, to avoid bias thefirst rejected gap for each vehicles in the minor stream is the one used to determine the criticalgap. The characteristic of the study site of Jln Lempeng junction is Left Turn from the MinorRoad. Gap acceptance studies for this type of maneuver are the most difficult to develop. Leftturn maneuvers have the lowest priority in junction. Therefore, gap acceptance studies for thistype of maneuver should consider gaps available in traffic main stream.

Based on field data observation, it is found that in this juntion has the large gap betweenacceptance and rejection of gaps, therefore choice of appropriate class interval for groupingthe data is a vital step in the analysis. In order to simplify our exercise, the class intervals of2s were considered. To develop the gap acceptance graph, all accepted and rejected gaps aretabulated in Table 2.

Table 2 Gap acceptance and rejection patterns

Sec Frequency CFAG Frequency CFRG0-2 1 1 44 992-4 4 5 39 554-6 15 20 14 166-8 13 33 0 2

8-10 7 40 1 210-12 13 53 1 112-14 8 61 0 014-16 9 70 0 016-18 5 75 0 018-20 3 78 0 0

Total 78 99* By considering headway distribution in Exercise 2 therefore the traffic flow per hour/lane

can be derived, and the outcome of flow is 837 vehicles.* The move up time of vehicle were calculated for those case that more than 2 vehicles

merging in one lag or gap. In average move up time of vehicles is 1.54sec

Critical gap are those gaps that 50% of people will accept or the median of gap acceptancedistribution. Following figure and result represents of single estimator of critical gaps.

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0,00,10,20,30,40,50,60,70,80,91,0

2 4 6 8 10 12 14 16 18 20

Cum

ul a

tive

acc

epte

d g

ap

Median accepted gap

Figure 1 Median accepted gap of left turn maneuver

0102030405060708090

100

2 4 6 8 10 12 14 16 18 20

Cum

ul a

tive

nu

mb

er

Median critical lag

Figure 2 Median critical lag of left turn maneuver

Based on Figure 1 driver majority (50%) will accept gaps in the range 9.8 sec or greater.When accumulated gaps are plotted, the critical lag is the point where both graphs intersecteach other. From Figure 2 critical lag are obtained is 5.9 second. With large different betweencritical lag and critical accepted gap value it shows that there are exist many longer rejectedlags as the number of accepted gaps. Summary of all single estimators are presented in Table3 below.

Table 3 Four single estimators of critical gapEstimators c ValueMedian accepted gap 9.8 sec

Median critical lag 5.9 secMean critical gap (lag) 6.68 sec

Weighted mean critical lag 5.98 sec*Detail calculation of mean and weighted critical lag in appendix

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The gap parameters can be estimated by plotting the probability values against the mid-pointclass values on a normally (or log-normally) the ratio of the number of accepted gaps to totalnumber of gaps. Following figures 4 and 5 represent the result of plotting the gaps data. Ascan bee seen the gaps data do not follow normal distribution and log normal, the gapsdistribution is scattered. Therefore the probit analysis could not perform for next analysis toestimate critical gap parameters.

0 1,5 3 4,5 6 7,5 9 10,5 12 13,5 15

Norm

al

devi

ate

Gap time (s)

-2

-1

0

1

2

3

Figure 3 Normal distribution of gaps data

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Norm

al

devi

ate

Log Gap time (s)

-2

-1

0

1

2

3

Figure 4 Log Normal distribution of gaps data

4.0 JUNCTION CAPACITY

Unsignalized junction capacity at Jln Lempeng are measured by deterministic andprobabilistic approaches. This procedure is based on critical gap acceptance and follow uptimes of vehicles from the minor road. Thus it is necessary before derived minor roadcapacity, we need to modeling gap acceptance behavior. It is assumed that the drivers from

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minor road follow consistent behavior model where person seeking gaps has a characteristicsconstant critical gap.

By apply the deterministic approach therefore gap acceptance function will be,

0,( )

1,c

c

TT

T

Probabilistic approaches of gap acceptance function is using shifted exponential distribution.Shifted exponential is used where gaps accepted is plotted following shifted exponential(appendix). Thus the gap acceptance will be,

min

min

min0,( )

1 ,T

c

TT

e T

From the field data min is 1.46 second and is 7.09

Assuming that the headway distribution of main stream flow following negative exponentialdistribution and the vehicles randomly arrivals therefore the junction capacity can bemeasured by following equations.

( ') ( [ 1] ')

0

'

( 1)

1

c M c M

M c

M

i q i qm M

iq

Mq

Q q i e e

q ec

By using above equations of the deterministic and probabilistic of gap acceptance function,the junction capacity of Jln Lempeng are 724 veh/hour and 752 veh/hour, respectively.

5.0 CONCLUSION

The data in this study are from Clementi Avenue 6 and Jln Lempeng. Such factors geometricdesign of roads, flows, environment, drivers behavior (main important factors in gapacceptance model) and proportion of heavy vehicles, may have an effect on the gapsacceptance. and critical gap These factors would reduce or increase the actual junctioncapacity from the basic capacity.

However a yellow box at Jln Lempeng junction could use as a traffic control measure toprevent gridlock at junctions and vehicles may not enter the area so marked unless their exitfrom the junction is clear (to await a gap in the oncoming traffic flow). It has been shown thatthe methods in the exercise of gap acceptance should be further extend to analyse moreaccurately of the results. Such the method to analysed the drivers behavior, clear sightdistance, and conflict technique which is based on pragmatically simplified concept where

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interaction and impact between flows at junction is brought through mathematicallyformulated by empirical approach.

6.0 REFERENCES

A Policy on Geometric Design of Highway and Streets 2001, 4th Ed. (AASHTO)

Highway Capacity Manual. 2000. Special Report 209, 4th Ed., TRB, National ResearchCouncil, Washington, D.C.,

Traffic Monitoring Guide, 3rd Ed. Federal Highway Administration (FHWA)

Traffic Flow Theory A State-of-the-Art Report (2001). Committee on Traffic Flow Theoryand Characteristics (AHB45). TRB, National Research Council, Washington, D.C.,

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Appendix I

0

0,2

0,4

0,6

0,8

1

1,2

0

0,02

0,04

0,06

0,08

0,1

0,12

0,14

0,16

0,18

0,2

0 5 10 15 20

Dis

trib

utio

n fu

ncti

on

Prob

. de

nsi t

y

Shifted Exponent Distribution

Prob. density Distribution function

Appendix II

Accepted MaxRej Mean Wt Wt Mean1.06 3.61 2.34 0.78 1.83

13.51 3.18 8.35 13.20 110.1224.71 1.59 13.15 24.08 316.6521.15 1.16 11.15 20.29 226.30

4.69 4.35 4.52 4.46 20.1614.19 3.09 8.64 13.87 119.81

5.63 1.51 3.57 4.97 17.7614.26 1.64 7.95 13.65 108.4722.40 3.76 13.08 22.14 289.5516.63 1.14 8.89 15.75 139.97

7.27 3.76 5.52 7.00 38.635.24 4.12 4.68 5.00 23.39

11.92 5.38 8.65 11.73 101.5014.03 4.56 9.29 13.81 128.25

6.96 1.51 4.24 6.30 26.669.59 3.46 6.53 9.30 60.737.11 5.34 6.22 6.93 43.10

17.05 2.34 9.70 16.62 161.179.05 1.84 5.44 8.50 46.30

11.62 1.40 6.51 10.91 71.069.77 1.58 5.67 9.13 51.78

10.33 1.58 5.95 9.69 57.668.97 8.49 8.73 8.85 77.264.29 4.91 4.60 4.09 18.815.49 4.06 4.77 5.25 25.046.13 2.89 4.51 5.78 26.08

11.33 3.56 7.44 11.04 82.18

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5.29 2.84 4.06 4.94 20.0617.41 2.36 9.88 16.99 167.91

6.82 2.94 4.88 6.48 31.6111.00 4.55 7.78 10.78 83.8612.21 5.78 9.00 12.04 108.32

7.21 5.79 6.50 7.03 45.7016.79 2.45 9.62 16.38 157.5115.63 3.87 9.75 15.37 149.88

8.50 3.53 6.02 8.22 49.433.40 9.69 6.54 3.30 21.58

11.73 3.85 7.79 11.47 89.3910.28 8.07 9.17 10.15 93.0916.30 10.02 13.16 16.20 213.2012.47 2.34 7.40 12.04 89.11

4.78 1.03 2.91 3.81 11.074.01 2.92 3.46 3.67 12.705.02 3.60 4.31 4.75 20.474.60 3.09 3.84 4.28 16.446.94 4.37 5.66 6.71 37.976.22 1.28 3.75 5.44 20.426.38 4.34 5.36 6.15 32.975.57 2.04 3.81 5.08 19.343.37 3.54 3.45 3.09 10.66

14.12 4.88 9.50 13.91 132.185.45 1.12 3.28 4.55 14.96

10.44 1.56 6.00 9.79 58.754.92 0.50 2.71 2.92 7.92

11.35 4.88 8.11 11.14 90.416.69 519.81 3476

Exercise 6 - Gap Acceptance and Priority Junction Aditya Nugroho e

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Transcript of Exercise 6 - Gap Acceptance and Priority Junction Aditya Nugroho e