Traffic Queue Length Estimation at Permissive Left-Turn Signalized Intersections with Probabilistic Priority

Abstract

Probabilistic yielding behaviors are often observed at permissive left-turn signalized intersections in some countries, which tend to affect the operational performance of intersections such as queue length of left-turn traffic. Based on queuing theory, this research developed an analytical queue length estimation model that took into account the probabilistic priority phenomenon at permitted left-turn signals. The service time distributions for both queued and nonqueued left-turn vehicles were derived, and the M/G2/1 queuing model was applied to determine the queue length of left-turn traffic. To validate the developed queue length model, stochastic simulations with different combinations of left-turn yielding rates, left-turn traffic saturation ratios, and through traffic flow rates were performed. It was found that the left-turn traffic saturation ratio is the most critical factor for the estimation of left-turn traffic queue length. In addition, for permitted intersections with a single through lane and a single left-turn lane, when the opposite through traffic flow rate is greater than 0.3 veh/s, the impact of left-turn yielding rate on left-turn queue length tends to be more significant.