Volume 29, 2023
|Number of page(s)||24|
|Published online||22 August 2023|
School of Mathematics and Statistical Sciences, Arizona State Univeristy, Tempe, AZ, USA
2 Department of Mathematical Sciences and Center for Computational and Integrative Biology, Rutgers University, Camden, NJ, USA
3 Department of Mathematics, Sapienza University of Rome, Rome, Italy
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Accepted: 5 May 2023
This article aims to study coupled mean-field equation and ODEs with discrete events motivated by vehicular traffic flow. Precisely, multi-lane traffic flow in presence of human-driven and autonomous vehicles is considered, with autonomous vehicles possibly influenced by external policymakers. First, a finite-dimensional hybrid system is developed based on the continuous Bando-Follow-the-Leader dynamics coupled with discrete events due to lane-change maneuvers. Then the mean-field limit of the finite-dimensional hybrid system is rigorously derived for the dynamics of the human-driven vehicles. The microscopic lane-change maneuvers of the human-driven vehicles generate a source term for the mean-field PDE. This leads to an infinite-dimensional hybrid system described by coupled Vlasov-type PDE, ODEs, and discrete events.
Mathematics Subject Classification: 90B20 / 34A38 / 35Q83
Key words: Multi-lane traffic / autonomous vehicles / mean-field limit / hybrid systems / generalized Wasserstain distance
The research of X.G. was partially supported by the NSF CPS Synergy project “Smoothing Traffic via Energy-efficient Autonomous Driving” (STEAD) CNS 1837481.
The research of B.P. is based upon work supported by the U.S. Department of Energy’s Office of Energy Efficiency and Renewable Energy (EERE) under the Vehicle Technologies Office award number CID DE-EE0008872. The views expressed herein do not necessarily represent the views of the U.S. Department of Energy or the United States Government.
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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