Computational investigations of a multi-class traffic flow model: mean-field and microscopic dynamics

TL;DR

This paper computationally investigates a multi-class traffic flow model, assessing mean-field game approximations for large-scale traffic scenarios involving cars and trucks, and validating the epsilon-Nash approximation through extensive simulations.

Contribution

It introduces novel numerical methodologies combining HPC and regularization techniques to simulate large-scale multi-class traffic models and validates mean-field game approaches against microscopic dynamics.

Findings

Mean-field approximations closely match microscopic speeds.

The epsilon-Nash approximation rate exceeds theoretical expectations.

Simulations demonstrate the effectiveness of the approach for large-scale traffic scenarios.

Abstract

We address a multi-class traffic model, for which we computationally assess the ability of mean-field games (MFGs) to yield approximate Nash equilibria for traffic flow games of intractable large finite-players. We introduce ad hoc numerical methodologies, with recourse to techniques such as High-Performance Computing (HPC) and regularization of Loose Generalized Minimal Residual (LGMRES) solvers. The developed apparatus allows us to perform simulations at significantly larger space and time discretization scales. For three generic scenarios of cars and trucks, and three cost functionals, we provide numerous numerical results related to the autonomous vehicles (AVs) traffic dynamics, which corroborate for the multi-class case the effectiveness of the approach emphasized in [22]. We additionally provide several original comparisons of macroscopic Nash mean-field speeds with their microscopic versions, allowing us to computationally validate the so-called $\epsilon-$Nash approximation, with a rate slightly better than theoretically expected.