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We address a multi-class traffic model, for which we computationally assessthe ability of mean-field games (MFG) to yield approximate Nash equilibria fortraffic flow games of intractable large finite-players. We introduce atwo-class traffic framework, following and extending the single-class lines of\cite{huang_game-theoretic_2020}. We extend the numerical methodologies, withrecourse to techniques such as HPC and regularization of LGMRES solvers. Thedeveloped apparatus allows us to perform simulations at significantly largerspace and time discretization scales. For three generic scenarios of cars andtrucks, and three cost functionals, we provide numerous numerical resultsrelated to the autonomous vehicles (AVs) traffic dynamics, which corroboratefor the multi-class case the effectiveness of the approach emphasized in\cite{huang_game-theoretic_2020}. We additionally provide several originalcomparisons of macroscopic Nash mean-field speeds with their microscopicversions, allowing us to computationally validate the so-called $\epsilon-$Nashapproximation, with a rate slightly better than theoretically expected.

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