Vehicle Sequencing at Signal-Free Intersections: Analytical Performance Guarantees Based on PDMP Formulation

TL;DR

This paper models vehicle sequencing at signal-free intersections using PDMPs, providing analytical capacity and delay bounds for common policies, validated through micro-simulations, advancing theoretical understanding of intersection performance.

Contribution

It introduces a PDMP-based framework to analytically evaluate intersection capacity and delay for typical sequencing policies, a novel approach in this context.

Findings

Capacity regions are explicitly characterized.

Upper bounds on travel delay are derived.

Results are validated through micro-simulation experiments.

Abstract

Signal-free intersections are a representative application of smart and connected vehicle technologies. Although extensive results have been developed for trajectory planning and autonomous driving, the formulation and evaluation of vehicle sequencing have not been well understood.In this paper, we consider theoretical guarantees of macroscopic performance (i.e., capacity and delay) of typical sequencing policies at signal-free intersections. We model intersection traffic as a piecewise-deterministic Markov process (PDMP). We analytically characterize the intersection capacity regions and provide upper bounds on travel delay under three typical policies, viz. first-in-first-out, min-switchover, and longer-queue-first. We obtain these results by constructing policy-specific Lyapunov functions and computing mean drift of the PDMP. We also validate the results via a series of micro-simulation-based experiments.