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Stabilizing Traffic via Autonomous Vehicles: A Continuum Mean Field Game Approach

Kuang Huang, Xuan Di, Qiang Du, Xi Chen

TL;DR

It is shown from linear stability analysis and numerical experiments that AVs help stabilize the traffic and the impact of AV’s penetration rate and controller design on the traffic stability is quantified.

Abstract

This paper presents scalable traffic stability analysis for both pure autonomous vehicle (AV) traffic and mixed traffic based on continuum traffic flow models. Human vehicles are modeled by a non-equilibrium traffic flow model, i.e., Aw-Rascle-Zhang (ARZ), which is unstable. AVs are modeled by the mean field game which assumes AVs are rational agents with anticipation capacities. It is shown from linear stability analysis and numerical experiments that AVs help stabilize the traffic. Further, we quantify the impact of AV's penetration rate and controller design on the traffic stability. The results may provide insights for AV manufacturers and city planners.

Stabilizing Traffic via Autonomous Vehicles: A Continuum Mean Field Game Approach

TL;DR

It is shown from linear stability analysis and numerical experiments that AVs help stabilize the traffic and the impact of AV’s penetration rate and controller design on the traffic stability is quantified.

Abstract

This paper presents scalable traffic stability analysis for both pure autonomous vehicle (AV) traffic and mixed traffic based on continuum traffic flow models. Human vehicles are modeled by a non-equilibrium traffic flow model, i.e., Aw-Rascle-Zhang (ARZ), which is unstable. AVs are modeled by the mean field game which assumes AVs are rational agents with anticipation capacities. It is shown from linear stability analysis and numerical experiments that AVs help stabilize the traffic. Further, we quantify the impact of AV's penetration rate and controller design on the traffic stability. The results may provide insights for AV manufacturers and city planners.

Paper Structure

This paper contains 13 sections, 3 theorems, 25 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Mean Field Game
  4. Aw-Rascle-Zhang Model
  5. Model Formulation
  6. Pure AV Traffic: Mean Field Game
  7. Mixed Traffic: Coupled MFG-ARZ System
  8. Pure AV Traffic: Linear Stability Analysis
  9. Mixed Traffic: Numerical Experiments
  10. Experimental Settings
  11. Numerical Method
  12. Numerical Results
  13. Conclusion

Key Result

Theorem II.1

The ARZ model eq:arz1eq:arz2 is linearly stable around the uniform flow $(\bar{\rho},\bar{u})$ where $\bar{u}=U(\bar{\rho})$ if and only if $h'(\bar{\rho})>-U'(\bar{\rho})$.

Figures (3)

  • Figure 1: Stability regions for the first and second groups of experiments
  • Figure 2: Evolution of normalized total density when $\beta=0$, $\bar{\rho}^{\text{TOT}}=0.4\rho_{\text{jam}}$, 0% AV (left) and 30% AVs (right)
  • Figure 3: Stability region for the third group of experiments

Theorems & Definitions (6)

  • Definition II.1
  • Theorem II.1
  • Definition III.1
  • Definition III.2
  • Proposition IV.1
  • Corollary IV.2