Contribution à l'étude du trafic routier sur réseaux à l'aide des équations d'Hamilton-Jacobi

Abstract : This work focuses on modeling and simulation of traffic flows on a network. Modeling road traffic on a homogeneous section takes its roots in the middle of XXth century and it has generated a substantial literature since then. However, taking into account discontinuities of the network such as junctions, has attracted the attention of the scientific circle more recently. However, these discontinuities are the major sources of traffic congestion, recurring or not, that basically degrades the level of service of road infrastructure. This work therefore aims to provide a unique perspective on this issue, while focusing on scale problems and more precisely on microscopic-macroscopic passage in existing models. The first part of this thesis is devoted to the relationship between microscopic car-following models and macroscopic continuous flow models. The asymptotic passage is based on a homogenization technique for Hamilton-Jacobi equations. In a second part, we focus on the modeling and simulation of vehicular traffic flow through a junction. The considered macroscopic model is built on Hamilton-Jacobi equations as well. Finally, the third part focuses on finding analytical or semi-analytical solutions, through representation formulas aiming to solve Hamilton-Jacobi equations under adequate assumptions. In this thesis, we are also interested in a generic class of second order macroscopic traffic flow models, the so-called GSOM models
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Guillaume Costeseque. Contribution à l'étude du trafic routier sur réseaux à l'aide des équations d'Hamilton-Jacobi. Mathématiques [math]. Université Paris-Est, 2014. Français. ⟨NNT : 2014PEST1081⟩. ⟨tel-01119173v2⟩

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