A Mean Field Games approach for multi-lane traffic management

TL;DR

This paper introduces a novel mean field games framework for multi-lane traffic management, modeling self-driven vehicles with perfect information, leading to a unique PDE system involving continuity equations and variational inequalities.

Contribution

It presents a new mathematical model using mean field games for multi-lane traffic, incorporating hybrid control and non-standard PDE systems.

Findings

Develops a PDE system with two continuity equations and a variational inequality.

Provides a theoretical foundation for traffic modeling with self-driven vehicles.

Highlights the mathematical complexity of hybrid control in traffic systems.

Abstract

In this work we discuss an Mean Field Games approach to traffic management on multi-lane roads. Such approach is particularly indicated to model self driven vehicles with perfect information of the domain. The mathematical interest of the problem is related to the fact that the system of partial differential equations obtained in this case is not in the classic form, but it consists of two continuity equations (one for each lane) and a variational inequality, coming from the Hamilton-Jacobi theory of the hybrid control.