Numerical modeling of queues at multi-lane signalized intersections with a versatile arrival process

In urban environments, vehicles typically travel in platoons due to periodic releases from upstream traffic signals. Consequently, the inter-arrival times of vehicles within a platoon exhibit significant correlations at downstream signalized intersections. To investigate the impact of these correlated arrival characteristics of headways on the queueing process at signalized intersections, this paper proposes a multi-lane stochastic queueing model with periodic vacations based on a continuous-time Markovian arrival process (MAP). We derive the joint probability distribution of queue length, arrival phase, and signal state. This formulation provides an explicit characterization of the randomness and dynamic behavior of the queueing process at signalized intersections. Additionally, we compute performance metrics such as the mean queue length over time in a signal cycle, providing insights into the dynamic evolution of queues under conditions of correlated vehicle arrivals. Furthermore, by the unique structural properties of the MAP, we numerically assess how correlations in the inter-arrival times influence queueing performance at signalized intersections.