The evolution process of queues at signalized intersections under batch arrivals

The randomness of queue formation and dissipation at signalized intersections is a very important feature of traffic phenomenon, which can be directly reflected by the dynamics and randomness of queue length during a signal cycle. Focusing on the dynamic nature and uncertainty of queues at signalized intersections, a random queueing model with vacations for queues on the multilane is constructed. In particular, the periodic unavailability of signalized intersection and the queue length transitions during a cycle are explicitly taken into account under batch arrival pattern. The steady-state distributions of the queue length along with the time within one cycle on multilane are derived. With it, the effects of batch arrival characteristics of vehicles on the evolution of queue formation and dissipation at signalized intersections are fully captured. The analytical model is compared with Webster's formula and is further validated with field data, which show that the proposed queueing model is capable of providing a reliable estimation on the queue length In addition, numerical experiments are also conducted to clarify how the queueing process along with the time is affected by different batch arrival patterns, traffic demands, and signal timing, etc.