Numerical Investigation of a Mesoscopic Vehicular Traffic Flow Model Based on a Stochastic Acceleration Process

TL;DR

This paper numerically analyzes a mesoscopic vehicular traffic flow model based on stochastic acceleration processes, revealing detailed velocity and acceleration distributions and their dependencies on traffic density.

Contribution

It introduces a novel numerical solution for a stochastic master equation in traffic flow using a modified DSMC method, providing new insights into traffic dynamics.

Findings

Velocity and acceleration distributions in stochastic equilibrium

Dependence of mean velocity and scattering on traffic density

Correlations between traffic variables and car density

Abstract

In this paper a spatial homogeneous vehicular traffic flow model based on a stochastic master equation of Boltzmann type in the acceleration variable is solved numerically for a special driver interaction model. The solution is done by a modified direct simulation Monte Carlo method (DSMC) well known in non equilibrium gas kinetic. The velocity and acceleration distribution functions in stochastic equilibrium, mean velocity, traffic density, ACN, velocity scattering and correlations between some of these variables and their car density dependences are discussed.