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

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 $0.3\mathrm{veh}/\mathrm{s}$, the impact of left-turn yielding rate on left-turn queue length tends to be more significant.

Left-turn movements are considered the most dangerous maneuverer, and traffic engineers have to balance a trade-off between traffic safety and operational efficiency when determining an appropriate left-turn traffic control strategy at signalized intersections. So, the permissive left-turn control strategy has been commonly applied at intersections with low to medium traffic demands. This paper established the relationship between left-turn traffic queue length and left-turn yielding rate, through traffic flow rate, and left-turn saturation ratio. Among these factors, the left-turn saturation ratio was found to be the primary factor that needs to be considered when determining left-turn queue length. In practice, preemptive left-turn behavior could, to some extent, improve traffic operations of the permissive left-turn traffic, while traffic management authorities should reasonably guide such behavior to minimize its impacts on traffic safety. Findings from this study could be used to evaluate the operational efficiency of permissive left-turn intersections under nonstrict priority conditions, and the estimated left-turn queue lengths have the potential of assisting in the optimal design of the storage of the left-turn lane.