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

Felisia Angela Chiarello (Dipartimento di Ingegneria e Scienze dell’Informazione e Matematica (DISIM), University of L’Aquila, Italy)

Simone Göttlich (School of Business Informatics and Mathematics, University of Mannheim, Germany)

Thomas Schillinger (School of Business Informatics and Mathematics, University of Mannheim, Germany)

Andrea Tosin (Department of Mathematical Sciences, Politecnico di Torino, Italy)

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

Full Text (PDF format)

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