This was part of Mean-Field Models for Interacting Agents

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

Xiaoqian Gong, Arizona State University

Wednesday, November 3, 2021

Abstract: We aim 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 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.