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Article Dans Une Revue Discrete and Continuous Dynamical Systems - Series S Année : 2014

Discussion about traffic junction modelling: conservation laws vs Hamilton-jacobi equations

Résumé

In this paper, we consider a numerical scheme to solve first order Hamilton-Jacobi (HJ) equations posed on a junction. The main mathematical properties of the scheme are first recalled and then we give a traffic flow interpretation of the key elements. The scheme formulation is also adapted to compute the vehicles densities on a junction. The equivalent scheme for densities recovers the well-known Godunov scheme outside the junction point. We give two numerical illustrations for a merge and a diverge which are the two main types of traffic junctions. Some extensions to the junction model are finally discussed.

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Autre

Dates et versions

hal-01214831 , version 1 (13-10-2015)

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Guillaume Costeseque, Jean Patrick Lebacque. Discussion about traffic junction modelling: conservation laws vs Hamilton-jacobi equations. Discrete and Continuous Dynamical Systems - Series S, 2014, 7 (3), p 411-433. ⟨10.3934/dcdss.2014.7.411⟩. ⟨hal-01214831⟩
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