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Research Article | Open Access

Mean-field limit of a hybrid system for multi-lane car-truck traffic

Department of Mathematics and Statistics, Queen's University, Kingston, ON K7L 3N6, Canada
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, USA
Department of Mathematical Sciences and Center for Computational and Integrative Biology, Rutgers University, Camden, NJ, USA
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Abstract

In the present work we model multi-lane traffic flow in presence of two population of vehicles: cars and trucks. We first develop a finite-dimensional hybrid system which rely on continuous Bando-Follow-the-Leader dynamics coupled with discrete events motivated by the lane-change maneuvers. Then we rigorously prove that the mean-field limit is given by a system of Vlasov-type PDE with source terms generated by the lane-change maneuvers of the human-driven vehicles.

Keywords

Heterogeneous trafficcar-following modelsmesoscopic traffic modelsmulti-lane traffichybrid systemmean-field limit

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Networks and Heterogeneous Media
Volume 18 Issue 2,
June 2023
Pages 723-752
DOI: 10.3934/nhm.2023031

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Cite this article:
Chiri MT, Gong X, Piccoli B. Mean-field limit of a hybrid system for multi-lane car-truck traffic. Networks and Heterogeneous Media, 2023, 18(2): 723-752. https://doi.org/10.3934/nhm.2023031

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Received: 01 September 2021
Revised: 30 May 2022
Accepted: 11 January 2023
Published: 15 June 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)