A Queuing Model and Capacity Analysis for Reservation-Based Autonomous Intersection

Traffic capacity is an important indicator of traffic supply capability. An accurate portrayal of intersection capacity serves as a foundation for various intersection management studies, supporting the optimization of traffic operational efficiency and resource allocation. However, existing research on autonomous intersections primarily estimates intersection capacity through simulation experiments, which often suffer from low efficiency. Consequently, the challenge lies in developing more convenient methods for capacity analysis in such environments. To address this gap, this paper proposes analytical models for the traffic capacity of autonomous intersections based on queuing theory. Firstly, the analytical model of the traffic capacity in the conflict zones is derived. Based on that, the capacity model for the autonomous intersection is developed by incorporating vehicle interaction modes, varying arrival rates, and distinct turning ratios for each approach. Depending on the settings of safety time headways, two models, referred to as the specific and uniform cases, are considered. Further, the capacity range, queuing length, and queuing time of the two scenarios are derived. Finally, the rationality and accuracy of the proposed models are verified based on numerical simulations. The results show that the proposed models can better estimate the actual operating conditions of autonomous intersections. The average errors of the autonomous intersection model in the one-lane intersection scenario are less than 2%, with a 22% error reduction from the baseline model. Besides, the average errors of the multi-lane autonomous intersection model are less than 4%. The average relative and absolute errors between the model predictions and simulation results for queuing length and queuing time are negligible. The proposed models offer valuable insights for intersection design, level of service determination, and management control strategy selection.