Viability Constraints for Computing Solutions to the Lighthill-Whitham-Richards Model Involving Partial Autonomous Vehicle Flow

Abstract

This article proposes a new algorithm for computing solutions to mixed flow problems involving the classical Lighthill-Whitham-Richards (LWR) flow model. We show that the behavior of autonomous vehicles can be described by viability constrained solutions to an alternate Hamilton-Jacobi formulation of the same model, for appropriate upper constraint functions. We also provide the physical interpretation of viability constrained solutions to the model. This results in a viability-based framework that can be used to incorporate the effect of autonomous vehicles in traffic, even when these vehicles are allowed to switch between modes (autonomous/non autonomous). We then illustrate this algorithm on realistic traffic simulation examples involving partial switched autonomous vehicle flows.