A fully-discrete-state kinetic theory approach to traffic flow on road networks

TL;DR

This paper introduces a novel kinetic theory approach for modeling vehicular traffic on road networks, emphasizing a discrete microscopic state space to incorporate system granularity and address technical complexities.

Contribution

It presents a fully-discrete-state kinetic model for traffic flow on networks, bridging microscopic granularity with mesoscopic statistical mechanics.

Findings

Successfully models traffic flow on complex networks

Addresses technical challenges of kinetic models in interconnected roads

Provides a new framework for microscopic-based traffic analysis

Abstract

This paper presents a new approach to the modeling of vehicular traffic flows on road networks based on kinetic equations. While in the literature the problem has been extensively studied by means of macroscopic hydrodynamic models, to date there are still not, to the authors' knowledge, contributions tackling it from a genuine statistical mechanics point of view. Probably one of the reasons is the higher technical complexity of kinetic traffic models, further increased in case of several interconnected roads. Here such difficulties of the theory are overcome by taking advantage of a discrete structure of the space of microscopic states of the vehicles, which is also significant in view of including the intrinsic microscopic granularity of the system in the mesoscopic representation.