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A macroscopic traffic flow model accounting for bounded acceleration

Abstract : This paper details a new macroscopic traffic flow model accounting for the boundedness of traffic acceleration, which is required for physical realism. Our approach relies on the coupling between a scalar conservation law, which refers to the seminal LWR model, and a system of Ordinary Differential Equations describing the trajectory of accelerating vehicles, which we treat as moving constraints. We propose a Wave Front Tracking Algorithm to construct approximate solutions. We use this algorithm to prove the existence of solutions to the associated Cauchy Problem, and provide some numerical examples illustrating the solution behaviour.
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Contributor : Nicolas Laurent-Brouty <>
Submitted on : Thursday, November 26, 2020 - 4:41:43 PM
Last modification on : Friday, November 27, 2020 - 3:30:59 AM


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  • HAL Id : hal-02155131, version 4


Nicolas Laurent-Brouty, Guillaume Costeseque, Paola Goatin. A macroscopic traffic flow model accounting for bounded acceleration. SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, In press. ⟨hal-02155131v4⟩



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