YEAR 2006

By Satish Chandra’ Deepak Kumar2


The paper presents a generalized capacity model for uncontrolled intersections which can consider any number of vehicle categories in the traffic stream. The data collected at an identified four legged intersection were used to determine its capacity considering 2, 3, and 4 categories of vehicles in the traffic stream. It was found that that the capacity of the minor street reduces as the traffic tends to be more heterogeneous.


Intersections are integral part of a road network. The efficiency of a road network is generally governed by the performance of individual intersection. Traffic signals are not considered the best remedies for urban intersection, particularly when they are outside the central business district. In such cases other control devices such as STOP and YIELD sings are used. Uncontrolled intersections are very common in a road network. Although their capacities may be lower than those of other intersection types, they do play an important role in the control of traffic in a network. The performance of unsignalized intersection has long been an area of research and interest. The unsignalized intersections assign priority to major road movement, while the minor road drivers have to find suitable gaps in the major roads in order to make their entry.

Traffic conditions on Indian roads are heterogeneous in nature. Traffic stream consists of fast moving vehicles such as cars, bus, two-wheelers, and slow moving vehicles such as bicycles, Tonga, auto rickshaws etc. These vehicles are widely different in their physical size, power, control and guidance system. The difference in static and dynamic characteristics of different vehicles affect the traffic flow considerably. Due to complex flow process, absence of lane markings, signs and avoidance of regulatory measures, the maneuvering at uncontrolled intersections becomes difficult. Therefore most of the previous work has been mainly done on homogeneous traffic, with very few attempts to study the capacity of unsignalized intersection under mixed traffic conditions.

The present study was undertaken with the objective of modeling the gaps available in a major street of an uncontrolled intersection. The capacity model presented by Li et al. (2003)12 is used to estimate the capacity of an identified uncontrolled intersection considering type of mixed traffic.


Highway Capacity Manual (HCM 2000)7 defined critical gap as the minimum length of time interval that allows intersection to the minor stream vehicle. Cleveland and Capelle (1954)4 assumed that a waiting driver (or pedestrian) accepts the gap, if it is more than his critical gap. Blunden et al. (1962)2 studied the effects of some environmental factors on the critical gap distribution, for left turning maneuvers. Buckley (1962)3 proposed a semi random model of traffic flow on American freeway under conditions of high flow. Pak Poy (1964)13 has shown that the Poisson approximation is valid for condition up to practical capacity of facility being considered in the distribution. Athol (1965) analyzed time headways by dividing the traffic into platoons and groups. The vehicles were considered into a platoon if their headway is less. than critical headway. Dawson and Chimni (1968)6 proposed hyperlang model, which is a linear combination of a translated exponential function and translated Eriang function. The exponential component described free (unconstrained) headways in the traffic stream, and Eriang component described the constrained headways. Cowan (1975V divided the headway into two components; the “tracking” component and the “free” component and found that both the components may be random variables. Katti and Pathak (1985)9 studied headway distribution models for urban road section under mixed traffic conditions. They found that 3-POPEX model is a better choice for high traffic range of 1500 veh/hr and above. Hebert (1963)8 proposed a capacity model of All Way Stop Controlled (AWSC) intersections. Richardson (1987)14 estimated delays based on M/G/1 model of the queuing process. Zion et al. (1990)16 conducted field studies on AWSC intersections and found that delay increased as then intersecting volumes increased, intersections with balanced volumes had lower delays than those without. The percentage of left turns had a noticeable effect on delay. Kyte and List. (1999) performed empirical studies on AWSC intersections to leam about the factors that influence capacity and delay at AWSC intersections. Similar studies have also been reported by Troutbeck (1986)15


Data for this study were collected at an uncontrolled intersection in KM 60 of Delhi - Roorkee Road (NH-58). It was a four legged right angled intersection with single lane approach on each leg. The major road was a straight portion ofNH - 58 and the minor road was Meerut - Barot Road (SH - 14) as shown in Figure 2. Data were collected by video filming the approach of major street for about 90 minutes on a typical weekday. Other information like traffic volume on major and minor streets, follow-up time for different categories of vehicles were collected manually. The recorded film was replayed on a large screen T.V. monitor in the laboratory to extract the desired information. The traffic volume on major road was 474 veh/hr with 37% scooters, 3% three wheelers, 36% cars and 24% heavy vehicles (bus/trucks). The minor road had a traffic volume of 200 veh/hr.


5.1 Fitting ofhyperlandg model

The hyperlang model was derived by Dawson and Chimni (1968)6. This model is a linear combination of translated exponential function and translated Eriang function. The exponential component describes free

of critical gap are taken from IRC: SP 41, 19948 and follow-up time was actually measured in field.

Capacity for Minor Street is estimated as 0.235 veh/s or 850 veh/hr.

5.3.2 Analysis with three categories of vehicles

All vehicles are now divided into three categories as below.
(a) light vehicles (two-wheelers,)
(b) Medium vehicles ( three wheelers Car/jeep/van)
(c) Heavy vehicles (Bus/Truck) The values of parameter are as shown in Table 4.

Solving Equation (13) for these parameters gives a capacity of 0.225 veh/s or 810 veh/hr.

5.3.3 Analysis with four Categories of Vehicles

All vehicles were divided into four categories as below.
(a) Two-wheelers
(b) Three-wheelers
(c) Car/jeep/van
(d) Bus/Truck

Values of Critical gap and follow-up time used are given in Table 5. The capacity is computed as 784 veh/hr.

The above analysis indicates that capacity of a minor street decreases from 850 vehicles per hour to 784 vehicles per hour when heterogeneity of traffic stream is taken into consideration. The results are summarized in Table 6.6. CONCLUSIONS

The study presents a capacity model, which can consider any number of vehicle categories in the traffic stream. Hyperlang distribution is used to find the proportion of free and constrained vehicles. Capacity analysis done by considering three types of vehicles in traffic stream gives the capacity very close to the field capacity. When four categories of vehicles are considered in the traffic stream, the capacity obtained is lower than field capacity. It indicates that the capacity of a minor street of an unsignalized intersection decreases as the number of vehicle categories increases in traffic stream. This type of analysis when carried out at a series of intersections would provide the effect of traffic mix on capacity. The values of critical gaps in present study were adopted from IRC-SP 41,1994s, which are given for all lanes combined in the major road. These values are required lane wise in the capacity model and therefore needs to be investigated further. The effect of turning vehicles on capacity should also be evaluated.


1. Athol, P., (1965) “Headway Grouping”, Highway Research Record 72, National Research Council, Washington DC, ppl36-155.

2. Blunden, W.R., Clissold, M. C and Fisher, R.B.(1962) “Distribution of Acceptance Gaps for Crossing and Turning Maneuvers” Australian Road Research Board, Vol. 1, ppl87-205.

3. Buckely, D.J. (1962) “Road Traffic Highway Distributions” Australian Road Research Board, Vol. 1, ppl53-187.

4. Cleveland, and D.G. Capelle, (1954) “Queuing Theory Approaches”, Highway Research Board, Vol.No.79.

5. Cowan, R.J., (1975) “Useful Headway Models”, Transportation Research. Vol. 9, pp.371-375.

6. Dawson, R.F. and Chimni, L.(1968), “The Hyperlang Probability Distribution-A Genaralized Traffic Headway Model”, Highway Research Record 230, National Research Council, Washington DC, pp.l-14.

7. Highway Capacity Manual (2000), Transportation Research Board, Special Report 209, Washington D.C.

8. Indian Roads Congress, “Guidelines on design ofat-grade intersections in rural and urban areas”, IRC: SP41, 1994.

9. Katti, B.K. and Pathak, R.K.(1985), “A Study of Headway Distribution Models for the Urban Road Sections Under Mixed Traffic Conditions”, Highway Research Bulletin, 26, National Research Council, Washington DC , I.R.C. New Delhi.

10. Kyte, M.; Zegeer, J. and Lall, K. (1991), “Empirical Models for Estimating Capacity and Delay at Stop Controlled Intersections in the United States”, Intersections without traffic signals II (Ed.: W. Brilon, Springer Publications Berlin.

11. Kyte, M. and List, G. (1999), “A Capacity Model for All Way Stop Controlled Intersections Based on Stream Interactions”, Transportation Research, 33A, 313-335.

12. Li, W., Wei, W., Jiang D., (2003) “Unsignalized Intersection Capacity with Mixed Vehicle Flows”. TRB annual meeting CD Rom.

13. Pak-Poy, P.G., (1964)”The Use and Limitation of the Poisson Distribution in Road Traffic”, Australian Road Research Board, Vol. 1.Part 1.

14. Richardson, A.(1987), “A Delay Model for Multiway Stop-sign Intersections”, Highway Research Record No.l 112,,pp. 107-114.

15. Troutbeck, RJ, (1986), “Average Delay at An Unsignalized Intersection with two Major Streams each Having a Dichotomized Headway Distribution. Transportation Science 20 (4) pp. 272-286.

16. Zion, M., List G.F., Manning, (1990). Testing Delay Models with Field Data for Four way. Stop Sign-controlled Inter sections. Transportation Research Record 1225, pp 83-90.