Mean-field limit of a hybrid system for multi-lane multi-class traffic
Abstract
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 the autonomous vehicles possibly influenced by external policy makers. 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 generates a source term to the mean-field PDE. This leads to an infinite-dimensional hybrid system, which is described by coupled Vlasov-type PDE, ODEs and discrete events.
Keywords
Cite
@article{arxiv.2007.14655,
title = {Mean-field limit of a hybrid system for multi-lane multi-class traffic},
author = {Xiaoqian Gong and Benedetto Piccoli and Giuseppe Visconti},
journal= {arXiv preprint arXiv:2007.14655},
year = {2021}
}