A Robust Mean-field Game of Boltzmann-Vlasov-like Traffic Flow

TL;DR

This paper develops a robust mean-field game framework for traffic flow modeling, bridging microscopic and macroscopic approaches, and demonstrates its effectiveness in optimizing traffic speed and reducing congestion.

Contribution

It introduces a novel robust mean-field game model for traffic flow that accounts for disturbances and noise, providing a rigorous link between particle-based and continuum models.

Findings

Optimal control increases traffic velocity

Reduces traffic congestion

Numerical solutions validate the model's effectiveness

Abstract

Historically, traffic modelling approaches have taken either a particle-like (microscopic) approach, or a gas-like (meso- or macroscopic) approach. Until recently with the introduction of mean-field games to the controls community, there has not been a rigorous framework to facilitate passage between controls for the microscopic models and the macroscopic models. We begin this work with a particle-based model of autonomous vehicles subject to drag and unknown disturbances, noise, and a speed limit in addition to the control. We formulate a robust stochastic differential game on the particles. We pass formally to the infinite-particle limit to obtain a robust mean-field game PDE system. We solve the mean-field game PDE system numerically and discuss the results. In particular, we obtain an optimal control which increases the bulk velocity of the traffic flow while reducing congestion.