Communications in Mathematical Sciences

Volume 19 (2021)

Number 6

Microscopic and macroscopic traffic flow models including random accidents

Pages: 1579 – 1609



Simone Göttlich (Department of Mathematics, University of Mannheim, Germany)

Thomas Schillinger (Department of Mathematics, University of Mannheim, Germany)


We introduce microscopic and macroscopic stochastic traffic models including traffic accidents. The microscopic model is based on a Follow-the-Leader approach whereas the macroscopic model is described by a scalar conservation law with space-dependent flux function. Accidents are introduced as interruptions of a deterministic evolution and are directly linked to the traffic situation. Based on a Lax–Friedrichs discretization, convergence of the microscopic model to the macroscopic model is shown. Numerical simulations are presented to compare the above models and show their convergence behaviour.


microscopic and macroscopic traffic flow models, random accidents, numerical convergence analysis, discretization schemes

2010 Mathematics Subject Classification

35L65, 65M06, 90B20

Received 19 August 2020

Accepted 6 February 2021

Published 2 August 2021