Fokker-Planck Asymptotics for Traffic Flow Models

TL;DR

This paper derives new Fokker-Planck kinetic models for traffic flow from microscopic rules, connecting them to existing models and validating through numerical experiments.

Contribution

It introduces novel Fokker-Planck models for traffic flow derived from microscopic interactions and asymptotic limits, expanding the modeling framework.

Findings

Derived new Fokker-Planck models from microscopic rules.

Connected existing models within a unified framework.

Validated models with numerical experiments.

Abstract

Starting from microscopic interaction rules we derive kinetic models of Fokker--Planck type for vehicular traffic flow. The derivation is based on taking a suitable asymptotic limit of the corresponding Boltzmann model. As particular cases, the derived models comprise existing models. New Fokker--Planck models are also given and their differences to existing models are highlighted. Finally, we report on numerical experiments.