A fully-discrete-state kinetic theory approach to modeling vehicular traffic

TL;DR

This paper introduces a novel discrete-state kinetic model for vehicular traffic that captures physical granularity and allows for realistic scenario simulation and analytical study of traffic phenomena.

Contribution

It is the first to incorporate all aspects of physical granularity of car flow within a generalized kinetic theory framework.

Findings

Model effectively simulates queue formation and traffic phenomena.

Analytically tractable with rigorous proof of fundamental properties.

Enables realistic scenario analysis in traffic modeling.

Abstract

This paper presents a new mathematical model of vehicular traffic, based on the methods of the generalized kinetic theory, in which the space of microscopic states (position and velocity) of the vehicles is genuinely discrete. While in the recent literature discrete-velocity kinetic models of car traffic have already been successfully proposed, this is, to our knowledge, the first attempt to account for all aspects of the physical granularity of car flow within the formalism of the aforesaid mathematical theory. Thanks to a rich but handy structure, the resulting model allows one to easily implement and simulate various realistic scenarios giving rise to characteristic traffic phenomena of practical interest (e.g., queue formation due to roadworks or to a traffic light). Moreover, it is analytically tractable under quite general assumptions, whereby fundamental properties of the solutions can be rigorously proved.