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

Xiangchen Cheng, Wei Tang, Ming Yang, Li Jin

TL;DR

The paper addresses macroscopic performance guarantees for sequencing at signal-free intersections by modeling traffic as a two-OD piecewise-deterministic Markov process (PDMP). It develops policy-specific Lyapunov analyses to derive stability criteria and delay bounds, showing that min-switchover (MS) maximizes capacity while longer-queue-first (LQF) minimizes capacity and increases delay, with FIFO occupying an intermediate position. The authors provide closed-form capacity regions and delay upper bounds for FIFO and MS, and a sufficient bound for LQF, validated through SUMO micro-simulations that corroborate theoretical predictions. Practical PDMP-based sequencing algorithms are presented and demonstrated to translate into implementable vehicle instructions, offering a principled framework to compare sequencing policies in signal-free intersections.

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.

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

TL;DR

The paper addresses macroscopic performance guarantees for sequencing at signal-free intersections by modeling traffic as a two-OD piecewise-deterministic Markov process (PDMP). It develops policy-specific Lyapunov analyses to derive stability criteria and delay bounds, showing that min-switchover (MS) maximizes capacity while longer-queue-first (LQF) minimizes capacity and increases delay, with FIFO occupying an intermediate position. The authors provide closed-form capacity regions and delay upper bounds for FIFO and MS, and a sufficient bound for LQF, validated through SUMO micro-simulations that corroborate theoretical predictions. Practical PDMP-based sequencing algorithms are presented and demonstrated to translate into implementable vehicle instructions, offering a principled framework to compare sequencing policies in signal-free intersections.

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.
Paper Structure (20 sections, 1 theorem, 44 equations, 13 figures, 2 tables, 1 algorithm)

This paper contains 20 sections, 1 theorem, 44 equations, 13 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Modeling and Formulation
  3. Piecewise-deterministic Markov model
  4. Sequencing policies
  5. Performance metrics
  6. Analytical performance guarantees
  7. Numerical example
  8. Proof of Theorem \ref{['thm_two']}
  9. FIFO
  10. MS
  11. LQF
  12. Implementation and Validation
  13. Implementation of PDMP-based policies
  14. FIFO
  15. MS
  16. ...and 5 more sections

Key Result

Theorem 1

Suppose an intersection with arrival rates $\lambda\in\mathbb R_{\ge0}^2$ and headway matrix $\Theta$. Let $\bar{R}$ and $\sigma_R^2$ be the mean and variance of the crossing time.

Figures (13)

  • Figure 1: A two-OD intersection for CAVs and the hierarchy for decision making. This paper focuses on vehicle sequencing.
  • Figure 2: Modeling intersection as PDMP.
  • Figure 3: Minimal headway depends on the sequence.
  • Figure 5: Two representations for PDMP.
  • Figure 6: Stability regimes under various policies. MS stabilizes the white, light gray, dark gray regimes, FIFO stabilizes the white and light gray regimes, and LQF stabilizes the white regime only.
  • ...and 8 more figures

Theorems & Definitions (1)

  • Theorem 1