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Communications in Mathematical Sciences
Volume 19 (2021)
Number 6
Microscopic and macroscopic traffic flow models including random accidents
Pages: 1579 – 1609
DOI: https://dx.doi.org/10.4310/CMS.2021.v19.n6.a6
Authors
Abstract
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.
Keywords
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