506 IGPM506.pdf        July 2020
TITLE Mean_field limit of a hybrid system for multi-lane multi-class traffic
AUTHORS Xiaoqian Gong, Benedetto Piccoli, Giuseppe Visconti
ABSTRACT This article aims to study coupled mean-field equation and ODEs with discrete events motivated by vehicular traffic flow. 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 changing. The mean-field limit of the finite-dimensional hybrid system is rigorously derived by letting the number of human-driven vehicles go to infinity, and it consists of an infinite-dimensional hybrid system. The latter is described by coupled Vlasov-type PDE, ODEs and discrete events. In particular, the microscopic lane changing maneuver of the human-driven vehicles generates a source term to a Vlasov-type PDE.
KEYWORDS multi-lane traffic, autonomous vehicles, mean-field limit, hybrid systems, generalized Wasserstain distance