Analysis of a Markovian Queuing Model for Autonomous Signal-Free Intersection

TL;DR

This paper develops an analytical Markovian queuing model to evaluate vehicle flow and delay at autonomous, signal-free intersections, providing insights into operational efficiency and stability.

Contribution

It introduces a novel queuing model for autonomous intersections, linking operational parameters to performance metrics and validating results through simulation.

Findings

Model accurately predicts throughput and delay.

Connected autonomous vehicles improve intersection efficiency.

Stability conditions are derived using Foster-Lyapunov criteria.

Abstract

We consider a novel, analytical queuing model for vehicle coordination at signal-free intersections. Vehicles arrive at an intersection according to Poisson processes, and the crossing times are constants dependent of vehicle types. We use this model to quantitatively relate key operational parameters (vehicle speed/acceleration, inter-vehicle headway) to key performance metrics (throughput and delay) under the first-come-first-serve rule. We use the Foster-Lyapunov drift condition to obtain stability criteria and an upper bound for average time delay. Based on these results, we compare the efficiency of signal free intersections with conventional vehicles and with connected and autonomous vehicles. We also validate our results in Simulation of Urban Mobility (SUMO).