Multiscale continuum-velocity kinetic model for vehicular traffic with local and mean field interactions

TL;DR

This paper develops a multiscale kinetic model for vehicular traffic incorporating local and mean field interactions, using game theory to describe driver-vehicle micro-system dynamics and analyzing solution methods.

Contribution

It introduces a novel kinetic model that integrates microscopic driver behavior with macroscopic traffic phenomena through game theory and multiscale analysis.

Findings

Model captures passing and clustering phenomena effectively

Provides a constructive method for solving the kinetic equations

Bridges microscopic driver activity with macroscopic traffic flow

Abstract

This paper deals with the modeling and mathematical analysis of vehicular traffic phenomena according to a kinetic theory approach, where the microscopic state of vehicles is described by: (i) position, (ii) velocity, as a continuous variable, and also (iii) activity, namely a variable suited to model the quality of the driver-vehicle micro-system. Interactions at the microscopic scale are modeled by methods of game theory with continuous velocity variable, thus leading to the derivation of mathematical models within the framework of the kinetic theory of active particles. Short-range interactions and mean field interactions are modeled to depict velocity changes related to passing and clustering phenomena. Finally, we perform an analysis of a constructive method to solve the model.