Modeling and numerical simulation of variability in traffic queues at traffic signals using a queueing model approach

Vehicle queues are commonly observed at signalized intersections in urban areas. The stochastic nature of time-dependent traffic demand may have a substantial impact on traffic performance at intersections; in particular, at high traffic loads, a sudden surge in traffic demand can have a considerable impact on the traffic queueing process. The goal of this study is to explicitly characterize the queues of vehicles at signalized intersections with respect to time-varying traffic demand, thus allowing us to quantitatively analyze how fluctuations in vehicle arrivals affect the uncertainty and variability of the queueing process of vehicles. To this end, we propose a novel queueing model that accounts for dynamic changes in traffic demand over time. This model is able to capture not only how peak hours affect the system performance from a long-term perspective, but also explains how the queues accumulated during peak hours gradually dissipate over time. Our work establishes fundamental queueing metrics, and we also validate the proposed model by comparing the estimated queue length from the analytical model with simulation results across multiple cases, demonstrating a good approximation of the queue length. In addition, we perform a series of numerical experiments to investigate the impact of traffic flow fluctuations on the queueing dynamics of vehicles in some typical traffic environments.