ESTIMATING CRITICAL GAP ACCEPTANCE FOR UNSIGNALISED T- INTERSECTION UNDER MIXED TRAFFIC FLOW CONDITION

ESTIMATING CRITICAL GAP ACCEPTANCE FOR UNSIGNALISED T- INTERSECTION UNDER MIXED TRAFFIC FLOW CONDITION Wan Hashim WAN IBRAHIM Associate Professor, Department of Civil Engineering, Faculty of Engineering, UNIMAS, 94300 Kota Semarahan, Sarawak, Malaysia, Email: cewhwi@yahoo.com Mohd Erwan SANIK Research Assistance, School of Civil Engineering, Universiti Sains Malaysia, Engineering Campus, 14300 Nibong Tebal, Malaysia Abstract: Critical Gap Acceptance procedure is still widely used for estimating capacity of unsignalised intersection. In Malaysia, the critical gap acceptance is still being used as in the existing guideline for unsignalised intersection (Arahan Teknik (Jalan) 11/1987). However, the use of the gap acceptance procedure does not take into consideration the mixed traffic flow condition prevalent on Malaysian road. In this study, critical gap acceptances under normal saturation flow condition were estimated for unsignalised T- Intersection in Malaysia using the Maximum Likelihood Method. The results indicate that there are significant differences between the critical gap of passenger cars and motorcycles. In this study, the composite critical gap that takes into consideration the differences in traffic compositions were proposed. The composite critical gap enables the use of single representative gap acceptance value for estimating capacity of unsignalised T-intersection based on Malaysian traffic condition. Keywords: Composite Critical Gap, Maximum Likelihood Method, Unsignalised T- Intersection, Mixed Traffic Flow Condition 1. INTRODUCTION There are several methods available for estimating capacity of unsignalised intersection. The first method is based on the gap acceptance and follow-up times of vehicles on minor roads which are mainly used in the United States and several European countries. The second method is empirical regression approach which is mainly based on research investigation from British result (Kimber and Combe, 1980). The third approach is conflict technique which is based on the mathematical formulation of interaction and impact between flows at intersection (Prasetijo et al. 2006). However, a number of researchers had addressed critical gap estimation methods and procedures for estimating capacity of unsignalised intersection (Cassidy et al. 1994, Troutbeck 1992, Hewitt 1985, Harder 1976, Salter,1976, Sieglog 1973, Miller 1972, Ashworth 1970, Hughes 1989, Velan and Van Aerde 1996, Hamed et al.1997, Gattis and Low 1999 and Raff 1950). Furthermore, currently the available method used to analyze unsignalised intersection in Malaysia is also using the gap acceptance method (Arahan Teknik Jalan 11/1987) which were adapted from the US HCM 1985 (TRB, 1985). In Malaysia, the traffic characteristic consists of several types of vehicles as shown in Table 1 where the percentage of motorcycles is very high and is greater than the percentage of passenger cars. All of the existing critical gap acceptance procedure did not take into consideration the differences in traffic composition especially taking into consideration the characteristics of

motorcycles. The queuing characteristics of motorcycles usually did not follow the conventional traffic rules i.e. First In First Out or Last In Last Out. Motorcycles usually follow the First In First Out and Last In First Out rule due to the small size and agility of the motorcycles. Therefore due to the high number of motorcycles on the road, it is important to take into consideration the effect of motorcycles on the estimated value of critical gap acceptance. The use of the gap values would lead to inaccurate interpretations of the results of the analysis as all parameters and variables used are not based on local traffic characteristics. In this paper, the critical gap acceptance method incorporating the mixed traffic flow condition is discussed. The critical gap acceptance under normal saturation flow condition for passenger cars and motorcycles were estimated separately and a composite critical gap acceptance formulation is proposed in this paper to take into consideration the differences in vehicle characteristics. Estimation of critical gap under nearsaturation or over-saturation condition requires further research. Table 1: Motor Vehicle Registration Malaysia - By Vehicle Types From 1986 2005 (JKR, 2005) Year Motorcycle Car Taxi Bus Lorry & Van Hire Car Trailer Other Total 1987 2,611,396 1,479,871 24,628 21,901 319,114 3,810 26,625 113,039 4,600,384 1988 2,702,932 1,549,600 25,132 23,346 328,594 4,154 26,503 122,655 4,782,916 1989 2,848,717 1,658,567 26,078 24,828 349,737 4,725 26,807 132,327 5,071,786 1990 3,035,930 1,811,160 28,811 26,803 380,330 5,666 27,348 146,730 5,462,778 1991 3,251,289 1,970,934 31,842 28,229 411,149 6,181 27,998 159,554 5,887,176 1992 3,473,643 2,107,005 34,178 30,013 442,401 6,791 28,744 172,733 6,295,508 1993 3,703,838 2,255,420 36,458 33,358 466,871 7,586 29,077 179,871 6,712,479 1994 3,977,047 2,426,546 40,088 34,771 495,736 10,279 28,788 196,834 7,210,089 1995 3,564,756 2,532,396 27,276 35,224 430,716 28,969 No data 183,038 6,802,375 1996 3,951,931 2,886,536 49,485 38,965 512,165 9,971 No data 237,631 7,686,684 1997 4,328,997 3,271,304 51,293 43,444 574,622 10,826 No data 269,983 8,550,469 1998 4,692,183 3,452,852 45,643 54,590 599,149 10,142 No data 269,983 9,124,542 1999 5,082,473 3,787,047 55,626 47,674 642,976 10,020 No data 304,135 9,929,951 2000 5,356,604 4,145,982 56,152 48,662 665,284 10,433 No data 315,687 10,598,804 2001 5,592,150 4,528,490 56,464 49,669 688,367 10,053 No data 327,369 11,252,562 2002 5,825,960 4,974,850 57,920 51,008 711,738 10,107 No data 344,058 11,975,641 2003 6,164,958 5,428,774 60,723 52,846 740,482 10,210 No data 361,275 12,819,268 2004 6,572,366 5,911,752 65,008 54,997 772,218 10,661 No data 377,835 13,764,837 2005 6,604,042 5,960,253 65,504 55,231 775,021 10,971 No data 380,627 13,851,649 2. DATA COLLECTIONS In this paper, the unsignalised intersection being investigated are the two-way stop controlled T-Type intersections that are prevalent throughout Malaysia. The sites chosen for carrying out this study are located throughout major cities in the West Course of Malaysia. The typical layout and movement at the intersections is as shown in Figure 1. There are six different types of traffic movements at the T-intersection. The unsignalised T-intersection has three levels of conflicting streams that should be considered; i.e. right turn movement from major stream (MajRT), left turn movement from minor stream

Proceedings of the Eastern Asia Society for Transportation Studies, Vol., 2007 (MinLT) and right turn movement from minor stream (MinRT). The conflicting streams mean that the movements cannot cross the junction except when one driver gives priority to another movement with lower degree of conflict and high saturation flow. Right turn movement from major road is the highest priority conflicting stream because this movement is made from a major stream into a minor stream. Drivers from minor stream should be aware of all right turning vehicles from major stream and must give priority to all those vehicles. The second priority conflicting stream is left turn movement from minor stream. The third and the last priority conflicting stream at unsignalised T- intersection is right turn from minor stream. Major Stream MinLT MajRT MinRT Major Stream Minor Stream Figure 1: Typical Layout and Movements at Unsignalised T-Intersection (Asmi, 2003) At unsignalised intersection, each major stream vehicle is able to pass the intersection without any delay. Referring to Figure 2, a minor street vehicle can only enter the conflict area if the next major vehicle is far enough to let the minor vehicle safe passage of the whole conflict area (Brilon et al., 1999). According to Brilon et al. (1999), far enough is defined as the situation that the next major street vehicle will arrive at the intersection at an instant that will happen t c seconds after the previous major stream vehicle or t c seconds after the minor vehicle s arrival. This value t c is called the critical gap, which is the minimum time gap in the priority stream that a minor street driver is ready to accept for crossing or entering the major stream conflict zone.

Minor stream Major stream q p Conflict area q n Figure 2: Illustration of conflict area at an Intersection (Brilon et al., 1999) According to the U.S. HCM 2000, critical gap, t c, is defined as the minimum time interval in the major-street traffic stream that allows intersection entry for one minorstreet vehicle (TRB, 2000). Thus, the driver critical gap is the minimum gap that would be acceptable. A particular driver would reject any gaps less than the critical gap and would accept gaps greater than or equal to the critical gap. Estimates of critical gap can be made on the basis of observations of the largest rejected gap and smallest accepted gap for a given intersection (TRB, 2000). In this study, gap acceptance is measured based on the headway between two consecutive conflicting vehicles in the major streams while passing the conflict area. Unlike the gap acceptance, lag is measured based on the arrival of the minor stream vehicle at the stop line and the arrival of front bumper of first vehicle on major stream crossing the entrance line of the conflict area. In this study, two types of two-way stopped controlled unsignalised intersections were considered i.e. multi-lane and single lane intersection. The stop line for minor approach and entering queue position of the junction should be clearly identified. In every major approach, define clearly the conflict area and exit line of the conflict area. The stop line is the position at which vehicles from minor stream enter the intersection and leave the approach. In this study, a video camera is used to capture traffic information on site and the video camera should be strategically located at the intersection. Gap acceptance for different type of vehicles such as passenger cars and motorcycles were observed in the traffic lab based on the recorded events.

3. ESTIMATION OF CRITICAL GAP ACCEPTANCE USING MAXIMUM LIKELIHOOD METHOD In this study, the maximum likelihood method is used for estimating the critical gap acceptance. The Effectiveness of the maximum likelihood method has been evaluated in further studies by Brilon (1995) and Troutbeck (1992). The maximum likelihood technique (Troutbeck, 1992) can reproduce the real critical gap of a driver population quite reliably without depending on external parameters. For this reason, the maximum likelihood technique is used to determine critical gaps in the United State (Kyte et al., 1996) as well as for German empirical investigation. As described by Troutbeck (1992), the maximum likelihood method can be used to estimate critical gap under traffic conditions that are not necessarily oversaturated. The maximum likelihood method of estimating the critical gap distribution is based on the fact that a driver s critical gap is greater than his largest rejected gap and smaller than his accepted gap. The first step is to assume a probabilistic distribution for the critical gaps. For most cases this can be assumed to be log-normal. This distribution is skewed to the right and has non-negative values, as would be expected in these circumstances. The distribution is reasonably general and is acceptable for most studies. Firstly, a function F which represents the distribution of the critical gaps, is assumed in applying the maximum likelihood procedure. Troutbeck (1992) proposed that the function is a log-normal function as shown in equation (1). ( x) x 2 1 F( x ) = 1 1 ln µ ; µ, σ exp dx (1) σ 2π x 0 2 σ where, x = the value at which to evaluate the function (accepted gap and the largest rejected gap) µ = the mean on natural logarithm, ln x σ = the standard deviation of natural logarithm, ln x The likelihood function is defined as the probability that the critical gap distribution lies between the observed distribution of the largest rejected gaps and the accepted gaps as shown in equation (2). where: L L n = [ F( ai ) F( ri )] i= 1 = maximum likelihood function a i = logarithm of the accepted gap of driver i r i = logarithm of the largest rejected gap of driver i F ( ) = cumulative distribution function for the normal distribution as in equation (1). (2)

By maximizing equation (2), mean (µ) and variance (σ 2 ) of the gap acceptance distribution were estimated. In this way, the distribution of critical gaps, as well as their mean and variance, can be derived. The critical gap and the mean of the gap acceptance distribution are related in the case where the gap acceptance distribution is normally distributed. The formulation for estimating critical gap is given by equation (3). Critical gap = µ σ 2 q / 2 where, µ = mean σ 2 = variance q = flow rate in both directions of major road (3) 4. COMPOSITE CRITICAL GAP ACCEPTANCE In this paper, critical gap acceptances for all vehicles, passenger cars, and motorcycles were estimated. Critical gap acceptance for heavy vehicle cannot be estimated due to lack of data throughout the sites. Typical cumulative distribution function of passenger cars gap acceptance using the maximum likelihood method is as shown in Figure (3).

Cumulative Distribution Function Of A Passenger Car's Gap Acceptance 1.00 Cumulative Function 0.50 Accepted Gap The Largest Rejected Gap Accepted Gap - The Largest Rejected Gap 0.00 0 1 2 3 4 5 6 7 8 Gap (sec) Figure 3: The example of cumulative distribution function of passenger car's gap acceptance using Maximum Likelihood method of Left turn from minor road of Jalan Burma - Brown Intersection in Penang As shown in Figure 3, the cumulative distribution function of the accepted gap, the largest rejected gap, mean for left turn from minor road of Jalan Burma-Brown Intersection in Penang are shown. The standard deviation value is estimated when the curves intersect the cumulative distribution function of 0.5. In this particular example, the standard deviation is 1.0, i.e. [(4.5-2.5)/2 = 1.0]. The mean value of critical gap is 3.5 sec. If the volume for both directions in major road is 0.57 veh/sec, the critical gap calculated using equation (3) is 3.2 sec. The estimated critical gaps for all sites are as shown in Table 2. As expected, there are significant differences between the critical gap of passenger cars and motorcycles. The critical gap values for motorcycles are much lower than the critical gap of passenger cars. Similarly, the critical gap for multilane intersection is much higher than the critical gap for single lane intersection. By using a two sample T-test, at a 95% confident level, there is a significant different between critical gap of passenger car and motorcycle. Practically, it is impossible to use two different types of critical gaps to estimate capacity of unsignalised intersection. It would be impractical to estimate capacity of the same facility using critical gap of passenger cars and also to use the critical gap of motorcycles at the same time.

Table 2: Critical Gap Acceptance Values Vehicle Types passenger car Motorcycle All vehicles no. of lane on Critical Gap (sec) major road RTMaj LTMin RTMin Single-lane 3.5 3.2 4.0 Multi-lane 3.7 3.3 4.2 Single-lane 2.8 No Data 3.0 Multi-lane 3.2 2.3 3.3 Single-lane 3.3 2.8 3.9 Multi-lane 3.5 3.3 4.2 Thus, it is proposed that a composite critical gap acceptance formulation need to be developed to take into consideration the differences in vehicle characteristics. The generalized composite critical gap formula is as shown in equation (4) where the equation is used to estimate the overall critical gap as a function of the base critical gap (passenger car critical gap values) and proportion of different vehicles at the particular intersection. Thus, equation (4) can be used to address the issues of estimating critical gap under mixed traffic condition. t c, all, x = tc, base +α c, M PM + β c, HV P HV (4) where, t c,all,x t c,base α c,m P M β c,hv P HV = composite critical gap for movement x (sec) = base critical gap (sec) = estimated coefficient for motorcycle (sec) = proportion of motorcycle = estimated coefficient for heavy vehicle (sec) = proportion of heavy vehicle Using regression analysis, the estimated coefficient for the motorcycles and heavy vehicles are as shown in Table 3 for single-lane facility. As expected the estimated parameters for motorcycle is statistically significant and the coefficient is negative indicating that the higher the proportion of motorcycles in the flow, the lower will be the composite critical gap. However, the estimated coefficient for heavy vehicle is not

statistically significant and can be dropped from the final equation. Similar observation is true for estimated coefficient for motorcycles and heavy vehicles for multilane facilities as shown in Table 4. Table 3: Statistical summary of linear regression for critical gap of single-lane Parameters Estimated Coefficient SE Coefficient t Probability P M -0.425 0.126-3.37 0.002 P HV 0.107 8.302 0.01 0.990 *Standard deviation is equal to 0.209 Table 4: Statistical summary of linear regression for critical gap of multi-lane Parameters Estimated Coefficient SE Coefficient t Probability P M -0.258 0.152-1.70 0.100 P HV 0.515 2.768 0.19 0.854 *Standard deviation is equal to 0.256 The final critical gap acceptance model for single lane facility and multilane facility are as shown in Equation (5) and Equation (6) respectively. Final model for Single Lane Facility t c,all = t c,car 0.424 P M (5) Final model for Multilane Facility t c,all = t c,car 0.252 P M (6) The final R-Squared values for equation (5) and (6) are 0.29 and 0.09 respectively. Further research is required in order to find a better relationship affecting the composite critical gap under mixed traffic condition. The sensitivity of the critical gap formulation is shown in Figure (4) and Figure (5), respectively. As can be seen in the figures, the changes in the value of critical gap significantly influences the control delay and also capacity estimation of the unsignalised intersection. Thus, this paper shows that the estimation of critical gap acceptance need to take into consideration the differences in vehicle compositions under the mixed flow condition.

C o ntro l D elay C hanges versus Variatio n o f C ritical Gap in P ercentage control delay changes (%) 10 8 6 4 2 0-2 -4-6 -8-10 movement 7 movement 9 movement 4-25 -20-15 -10-5 0 5 10 15 20 25 decrease/increase of critical gap (%) Figure 4: Graphical representation of the sensitivity analysis of control delay versus the variation of critical gap for single-lane intersection of Jalan Suka Menanti Jalan Gunung Keriang movement capacity changes (%) Movement Capacity Changes versus Critical Gap Changes in Percentage 15 mov ement 7 10 mov ement 9 mov ement 4 5 0-5 -10-15 -25-20 -15-10 -5 0 5 10 15 20 25 decrease/increase of critical gap (%) Figure 5: Graphical representation of the sensitivity analysis of movement capacity versus the variation of follow-up time for single-lane intersection of Jalan Suka Menanti Jalan Gunung Keriang The comparison of the critical gap acceptance values estimated in this study with other critical gap values are as shown in Table 4. As can be seen in the table, the critical gap acceptance estimated in this study is smaller as compared to the critical gap estimated from other procedures. One possible reason is that the Malaysian drivers are quite aggressive while maneuvering their vehicles at the unsignalised intersection.

Table 5: Comparison of the critical gap values Lane type or no. Critical gap Procedure of lane in major Vehicle type road RTMaj LTMin RTMin This Study Single-lane Base value 3.5 3.2 4.0 (2006) Multi-lane (passenger car) 3.7 3.3 4.2 Arahan Teknik (Jalan) 11/87 (1987) 2 Passenger car (base value with 5.0 average running 4 speed 30 mph or 48.3 km/h) 5.5 2 Passenger car (base value with 5.5 average running 4 speed 55 mph or 88.5 km/h) 6.0 5.5 (s)* 5.0 (y)** 5.5 (s) 5.0 (y) 6.5 (s) 5.5 (y) 6.5 (s) 5.5 (y) U.S. HCM 2 4.1 6.2 7.1 Base value 2000 4 4.1 6.9 7.5 Poland 1*** 5.2 (large towns) Base value 5.4 5.6 2*** 5.7 (Chodur, 2005) *(s) stop-controlled **(y) yield-controlled *** numbers of priority road lanes 6.5 (s) 6.0 (y) 7.0 (s) 6.5 (y) 8.0 (s) 7.0 (y) 8.5 (s) 7.5 (y)

5. CONCLUSIONS In this study, critical gap acceptances were estimated for unsignalised T-Intersection in Malaysia using the Maximum Likelihood Method. The results indicate that there are significant differences between the critical gap of passenger cars and motorcycles. Thus, a composite critical gap formulation is proposed for estimating critical gap of multilane and single lane unsignalised T-Intersection. The adoption of the composite critical gap addressed the issue of mixed traffic where the percentage of motorcycles is higher than the percentage of passenger cars. The use of the composite gap acceptance value enables the usage of single value of critical gaps for the purpose of estimating the capacity of the unsignalised intersection using the critical gap acceptance procedure. The findings of this study are under the normal saturation condition. The application under over-saturated condition requires further research. The proposed findings will be used as an input for Malaysian Highway Capacity Manual for unsignalised T-Intersection condition. ACKNOWLEDGEMENTS The authors would like to express sincere gratitude to The Ministry of Works, Malaysia for proving the funding to carry out this study. REFERENCES Arahan Teknik Jalan No 11/1987, A Guide on Geometric Design of Roads, Kuala Lumpur: Ibu Pejabat Jabatan Kerja Raya, Cawangan Jalan. Ashworth, R. (1970), The Analysis and Interpretation of Gap Acceptance Data. Transportation Research, 4, pp.270-280. Asmi, A. (2003), Estimation of Gap acceptance and Follow-up Time for Unsignalised Intersection based on Malaysian Road Condition, Master s Dissertation, Universiti Sains Malaysia Brilon, W. (1995), Delays at Oversaturated Unsignalised Intersections Based on Reserve Capacities, Transportation Research Board, Washington, D.C. Brilon, W., Koenig, R. and Troutbeck, R.J. (1999), Useful Estimation Procedures for Critical Gaps, Transportation Research, Part A, No. 33 (1999), pp 161-186 Cassidy, M., Sammer, M., Wang, W. and Yang, F. (1994), Unsignalised Intersection Capacity and Level of Service: Revising Critical Gap, Transportation Research Record 1484, pp. 16-23, Washington, D.C. Chodur, J. (2005), Capacity Models and Parameters for Unsignalised Urban Intersections in Poland, Journal of Transportation Engineering, Vol. 131, No. 12, pp 924-930 Gattis, J.L. and Low.T., Sonny. (1999), Gap Acceptance at Atypical Stop-Controlled Intersections, pp.201-207. Available at: http://ojps.aip.org/journal_cgi/getpdf?key=jtpedi&cvips=jtpedi000125000003000 201000001 Hamed, M.M. and Easa, S.M. (1997), Disaggregate Gap-Acceptance Model for Unsignalised T-Intersections, Journal of Transportation Engineering.

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