Analysis of a Markovian Queuing Model for High-Speed Signal-Free Intersections

Signal-free intersections for connected and autonomous vehicles (CAVs) is an emerging technology with significant efficiency and safety benefits. However, models for macroscopic performance evaluation and decision making have not been well developed. To address this, we consider a novel, analytical queuing model for CAV coordination at signal-free intersections. CAVs arrive at the intersection according to Poisson processes, and the service times are heterogeneous and sequencing-dependent. We use this model to quantitatively relate key operational parameters (vehicle speed/acceleration, inter-vehicle headway) to key performance metrics (throughput and delay). We apply the Foster-Lyapunov drift condition to obtain stability criteria, which leads to a lower bound for mean capacity and an upper bound for mean delay. We validate our model and results on a realistic microscopic simulation testbed. We also quantitatively estimate the performance improvement due to CAVs with respect to non-CAV intersections. Keywords: Connected and autonomous vehicles, signalfree intersections, piecewise-deterministic Markov processes, Lyapunov function.