Method to Estimate the Distribution of Average Vehicle Delay at Signalized Intersections

In North America, the Highway Capacity Manual (HCM) is the most widely adopted method for analysis of signalized intersections. The HCM and other analytical methods provide a point estimate of average vehicle delay for a specified lane group over a defined time period (e.g. peak hour) and this delay is used to specify the level of service. The estimated delay is a function of a number of factors including geometry, signal timings, approach volumes, traffic stream composition, etc. Some of these factors, particularly, peak hour volume, can be considered to be random variable and therefore the distribution of intersection delay is a function of the distribution of these random factors. This paper presents the findings of a study that addresses the variability in estimated HCM delay (and therefore level of service) as a function of the variation of intersection peak hour volumes. A numerical method is proposed to find the distribution of delay for permitted movements for which capacity changes as a result of variability in the opposing volume. The proposed method is demonstrated through application to a hypothetical intersection. The results indicate that when the lane group is operating near to capacity the HCM point estimate of delay is not sufficient for evaluating the quality of service of the intersection. Therefore, the distribution of delay should be used (rather than a point estimate) in order to design the intersection signal plan. Finally, a simplified procedure is proposed which approximates the proposed numerical method and can be used by practitioners to determine the probability that the intersection operates at a certain level of service (e.g. operating at level of service E or worse).