A nonlocal Lagrangian traffic flow model and the zero-filter limit

2023/02/08 by Coclite, Giuseppe M., Karlsen, Kenneth H., Risebro, Nils Henrik · 1 citation
#35L65 #65M12 #90B20 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2302.03889

Abstract

In this study, we start from a Follow-the-Leaders model for traffic flow that is based on a weighted harmonic mean (in Lagrangian coordinates) of the downstream car density. This results in a nonlocal Lagrangian partial differential equation (PDE) model for traffic flow. We demonstrate the well-posedness of the Lagrangian model in the L¹ sense. Additionally, we rigorously show that our model coincides with the Lagrangian formulation of the local LWR model in the ``zero-filter'' (nonlocal-to-local) limit. We present numerical simulations of the new model. One significant advantage of the proposed model is that it allows for simple proofs of (i) estimates that do not depend on the ``filter size'' and (ii) the dissipation of an arbitrary convex entropy.

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• Coexisting Automated and Human-Driven Vehicles: Well-Posedness of a Mixed Nonlocal-Local Traffic Model

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