Contents Online
Communications in Mathematical Sciences
Volume 22 (2024)
Number 3
Hydrodynamic traffic flow models including random accidents: A kinetic derivation
Pages: 845 – 870
DOI: https://dx.doi.org/10.4310/CMS.2024.v22.n3.a10
Authors
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.
Keywords
particle models, Follow-the-Leader, macroscopic traffic models, random accidents, uncertainty quantification
2010 Mathematics Subject Classification
35Q20, 35Q70, 90B20
F.A.C. is member of Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). F.A.C. was partially supported by the Ministry of University and Research (MUR), Italy, under the grant PRIN 2020 - Project N. 20204NT8W4, “Nonlinear evolution PDEs, fluid dynamics and transport equations: theoretical foundations and applications”. F.A.C. would like to thank Debora Amadori for useful discussions about the analytical properties. S. G. was supported by the German Research Foundation (DFG) under grant GO 1920/10-1, 11-1 and 12-1. A.T. is member of Gruppo Nazionale per la Fisica Matematica (GNFM) of INdAM, Italy.
Received 11 May 2023
Received revised 6 November 2023
Accepted 8 November 2023
Published 4 March 2024