Modeling Back-of-Queue Uncertainty at Signalized Intersections

Abstract

The queue percentile formulation adopted in the 2010 Highway Capacity Manual (HCM) is empirically based. It contains an overly simplified functional form and parameters such that the accuracy of the back-of-queue percentile estimates is compromised. In view of this, the author applies the Delta method to derive the uncertainty formulation of back-of-queue through the first-order Taylor expansion approximation, assuming that the source of uncertainty comes from arrival flow, saturation flow and, for actuated controller, green time variability from vehicle actuation. As multiplication of the independent, positive random variables results in a lognormal distributed outcome, the back-of-queue percentile is quantified as a lognormal predictive interval function. The simulation study shows that the proposed back-of-queue predictive interval is much more accurate than the HCM counterpart in most of the cases evaluated based on the Kolmogorov–Smirnov goodness-of-fit test. The proposed formulations can be used to quantify the back-of-queue predictive interval for both pre-timed and actuated control, whereas HCM is indifferent to the type of control. As expected, the variability of back-of-queue from the actuated control is less than the pre-timed control in unsaturated condition. The predictive interval profiles become identical when the degree of saturation approaches to unity and maxes out the green time.