Mean-field limit of a hybrid system for multi-lane multi-class traffic
arXiv:2007.14655
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.
References in corpus (6)
- Dissipation of stop-and-go waves via control of autonomous vehicles: Field experiments
- A well-posedness theory in measures for some kinetic models of collective motion
- Multiscale modeling of granular flows with application to crowd dynamics
- Generalized Wasserstein distance and its application to transport equations with source
- Mean-Field Optimal Control
- Model-based assessment of the impact of driver-assist vehicles using kinetic theory