A multi-class kinetic traffic flow model: discrete-velocity formulation and diffusively-corrected macroscopic limits
Abstract
This paper introduces a multi-class extension of a discrete-velocity kinetic traffic flow model based on a non-local Prigogine-Herman framework. We derive a hyperbolically scaled system of equations from a continuous kinetic formulation describing interactions between different vehicle classes through braking and relaxation terms. The model is then discretized with respect to the velocity variable for an arbitrary number of vehicle classes, and the structural properties of the resulting formulation are analyzed. In particular, we prove hyperbolicity and total linear degeneracy. Due to the non-conservative structure of the model, we employ a path-conservative finite volume scheme for the numerical approximation of the system. Finally, we derive the corresponding diffusively-corrected macroscopic multi-class model, investigate its stability and present numerical simulations on a single-lane road to illustrate the theoretical findings.
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BibTeX
@misc{mezquitanieto2026multiclass,
title = {{A multi-class kinetic traffic flow model: discrete-velocity formulation and diffusively-corrected macroscopic limits}},
author = {Carmen Mezquita-Nieto and Paola Goatin and Axel Klar},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.27159},
eprint = {2608.27159},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.27159},
}
RIS
TY - UNPB
TI - A multi-class kinetic traffic flow model: discrete-velocity formulation and diffusively-corrected macroscopic limits
AU - Carmen Mezquita-Nieto
AU - Paola Goatin
AU - Axel Klar
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.27159
UR - https://arxiv.org/abs/2608.27159
AB - This paper introduces a multi-class extension of a discrete-velocity kinetic traffic flow model based on a non-local Prigogine-Herman framework. We derive a hyperbolically scaled system of equations from a continuous kinetic formulation describing interactions between different vehicle classes through braking and relaxation terms. The model is then discretized with respect to the velocity variable for an arbitrary number of vehicle classes, and the structural properties of the resulting formulation are analyzed. In particular, we prove hyperbolicity and total linear degeneracy. Due to the non-conservative structure of the model, we employ a path-conservative finite volume scheme for the numerical approximation of the system. Finally, we derive the corresponding diffusively-corrected macroscopic multi-class model, investigate its stability and present numerical simulations on a single-lane road to illustrate the theoretical findings.
ER -