Effects of the design of waiting areas on the dynamic behavior of queues at signalized intersections

The explicit measurement of the evolution process of queues during a cycle has a special significance for evaluating the control scheme at signalized intersections, especially when a certain unconventional operation or intervention is conducted. In order to measure the dynamic behavior of queues at signalized intersections with waiting areas, this paper develops a stochastic queueing model to analytically simulate the evolution process of queues. The key queueing performance indices such as the statistical distributions of queue length and mean values of queue length along the time are derived. Using these indices, the queueing process of vehicles at the intersection with waiting areas can be explicitly formulated, in particular, the dynamic behavior of queues along the time during a cycle can be captured, and the formation of maximum queue length during a cycle can also be measured. Model validation shows that the proposed queueing model can provide an accurate estimation of queueing performance of signalized intersections with waiting areas. In addition, the effects of the use of waiting areas on the evolution process of queue length during a cycle are also tested by numerical simulations under different conditions.