Hydrodynamic traffic flow models including random accidents: A kinetic derivation

TL;DR

This paper derives a second order macroscopic traffic flow model incorporating random accidents from a stochastic particle system, and evaluates its performance through numerical simulations and uncertainty analysis.

Contribution

It introduces a novel kinetic derivation of a hyperbolic PDE-based traffic model that accounts for stochastic accidents and discontinuous flux functions.

Findings

The second order model accurately captures traffic dynamics compared to particle simulations.

Numerical analysis of accidents provides insights into traffic flow uncertainties.

The model effectively incorporates stochastic accident effects into macroscopic traffic predictions.

Abstract

We present a formal kinetic derivation of a second order macroscopic traffic model from a stochastic particle model. The macroscopic model is given by a system of hyperbolic partial differential equations (PDEs) with a discontinuous flux function, in which the traffic density and the headway are the averaged quantities. A numerical study illustrates the performance of the second order model compared to the particle approach. We also analyse numerically uncertain traffic accidents by considering statistical measures of the solution to the PDEs.