Kinetic models for traffic flow resulting in a reduced space of microscopic velocities
Abstract
The purpose of this paper is to study the properties of kinetic models for traffic flow described by a Boltzmann-type approach and based on a continuous space of microscopic velocities. In our models, the particular structure of the collision kernel allows one to find the analytical expression of a class of steady-state distributions, which are characterized by being supported on a quantized space of microscopic speeds. The number of these velocities is determined by a physical parameter describing the typical acceleration of a vehicle and the uniqueness of this class of solutions is supported by numerical investigations. This shows that it is possible to have the full richness of a kinetic approach with the simplicity of a space of microscopic velocities characterized by a small number of modes. Moreover, the explicit expression of the asymptotic distribution paves the way to deriving new macroscopic equations using the closure provided by the kinetic model.
Keywords
Cite
@article{arxiv.1507.08961,
title = {Kinetic models for traffic flow resulting in a reduced space of microscopic velocities},
author = {Gabriella Puppo and Matteo Semplice and Andrea Tosin and Giuseppe Visconti},
journal= {arXiv preprint arXiv:1507.08961},
year = {2016}
}
Comments
Replaced with revised version