Mathematical modeling of multilane vehicular traffic by discrete kinetic theory approach

TL;DR

This paper develops a discrete kinetic theory-based model for multilane vehicular traffic, incorporating interactions and external factors, with proofs of well-posedness and numerical validation for both homogeneous and inhomogeneous cases.

Contribution

It introduces a novel discrete kinetic model for multilane traffic that accounts for interactions and external influences, with theoretical and numerical validation.

Findings

Model accurately captures multilane traffic dynamics.

Proved well-posedness of the model's Cauchy problem.

Numerical simulations validate the model's effectiveness.

Abstract

This paper deals with the modeling and numerical simulations of multilane vehicular traffic according to the discrete kinetic theory approach. The nonlinear additive interactions and external actions such as tollgates as well traffic signs are considered and modeled. The well-posedness of the related Cauchy problem for the spatially homogeneous case has been proved by using Banach fixed-point theory. Numerical simulations are carried out to validate the improved model in the cases of spatially homogeneous and inhomogeneous problems.