Effects of Probabilistic Priority on Delay at Permissive Left-Turn Signalized Intersections

Probabilistic yielding is a commonly observed behavior at permissive left-turn signalized intersections in some developing countries, which has been studied in the past to reveal its effect on traffic capacity. However, the effect on left-turn traffic delay is still unrevealed and requires further investigation. Different from the method established for investigating traffic capacity, the most challenging issue in studying traffic delay is the recognition of queued and non-queued left-turn vehicles. Based on queuing theory, an analytical delay estimation model was developed in this paper, wherein the probabilistic yielding behavior at a permissive left-turn intersection was put into consideration. To estimate left-turn traffic delay by the M/G2/1 queuing model, the service time distributions for both queued and non-queued left-turn vehicles were derived. Then, stochastic simulations were performed to validate the established analytical model in case of various combinations of left-turn yielding rates, volume-to-capacity ratios (v/c ratios) of left-turn traffic, and through traffic flow rates. Considering that the traffic scenario is consistent with the traffic situation of a permissive left-turn signalized intersection described in HCM when the yielding rate equals 1, the proposed estimation model and simulation results were also validated by the HCM method. It was found that the proposed left-turn traffic delay estimation model is a cost-effective alternative to the microscopic simulation and HCM method. Through sensitivity tests, this research found that left-turn traffic delay increased rapidly with the left-turn yielding rate, the through traffic flow rate, and the left-turn v/c ratio, among which the through traffic flow rate is the most critical factor. Furthermore, it was found that the effect of the left-turn yielding rate on left-turn traffic delay appeared to be more prominent when the left-turn yielding rate was between 0 and 0.2. The results of this study can contribute to the guidance of traffic signal warrants for permissive left-turn phases.