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Viability constraints for computing solutions to the Lighthill-Whitham-Richards model involving partial autonomous vehicle flow. (English) Zbl 1502.35046

Summary: 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.

MSC:

35F21 Hamilton-Jacobi equations
76A30 Traffic and pedestrian flow models
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