Fundamental diagrams for kinetic equations of traffic flow

TL;DR

This paper examines how discrete kinetic traffic models can replicate fundamental diagrams of traffic flow, analyzing their long-term behavior, equilibria, and asymptotic properties.

Contribution

It introduces and analyzes discrete kinetic models for traffic flow, demonstrating their ability to reproduce key features of fundamental diagrams.

Findings

Models capture asymptotic trends of traffic flow

Equilibria correspond to fundamental diagram features

Qualitative properties depend on number of microstates

Abstract

In this paper we investigate the ability of some recently introduced discrete kinetic models of vehicular traffic to catch, in their large time behavior, typical features of theoretical fundamental diagrams. Specifically, we address the so-called "spatially homogeneous problem" and, in the representative case of an exploratory model, we study the qualitative properties of its solutions for a generic number of discrete microstates. This includes, in particular, asymptotic trends and equilibria, whence fundamental diagrams originate.