Modelling the queues of connected and autonomous vehicles at signal-free intersections considering the correlated vehicle arrivals

Advances in connected and autonomous vehicle (CAV) technologies have made signal-free intersections a viable option for enhancing traffic performance. In the absence of traffic signal control, sequencing control strategies become crucial to ensuring the safety and efficiency of conflicting traffic flows at these intersections. The First-Come-First-Serve (FCFS) and Longest-Queue-First (LQF) strategies have received significant attention as fundamental approaches to managing connected and automated vehicles at signal-free intersections, serving as baselines for evaluating innovative strategies. However, the impact of varying traffic demand in conflicting directions on the volatility of CAV queues at signal-free intersections remains unclear, and there is a lack of analytical quantitative estimates on how these two fundamental sequencing strategies affect fairness within CAV queues. Furthermore, in urban road networks, CAVs entering a downstream intersection typically originate from an upstream intersection, and thus CAVs typically move in bunching and correlation. However, this phenomenon has received little attention in the modelling of CAV queues. To this end, in this paper, by virtue of the salient advantage of the Markovian Arrival Process (MAP) in describing the bunching and correlated arrival properties, an MAP-based double-input queueing model and its computational framework are developed to estimate the queueing process of CAVs at signal-free intersections. Some basic statistical metrics, such as queue length, delay, conditional queue length, and queue length variance, are derived. Additionally, numerical experiments are conducted to examine the queueing performance of FCFS and LQF strategies under different traffic conditions. The results suggest that the effectiveness of FCFS and LQF strategies varies depending on the level of traffic demand in the conflicting directions.