Discussion about traffic junction modelling: Conservation laws VS Hamilton-Jacobi equations

Guillaume Costeseque; Jean-Patrick Lebacque

doi:10.3934/dcdss.2014.7.411

Article Contents

2014, Volume 7, Issue 3: 411-433. Doi: 10.3934/dcdss.2014.7.411

This issue Previous Article Pattern formation in 2D traffic flows Next Article A front tracking method for a strongly coupled PDE-ODE system with moving density constraints in traffic flow

Discussion about traffic junction modelling: Conservation laws VS Hamilton-Jacobi equations

Guillaume Costeseque^1, and
Jean-Patrick Lebacque^2,

1.
Université Paris-Est, Ecole des Ponts ParisTech, CERMICS & IFSTTAR, GRETTIA, 6 & 8 avenue Blaise Pascal, Cité Descartes, Champs sur Marne, 77455 Marne la Vallée Cedex 2
2.
Ifsttar, COSYS-GRETTIA, 14-20 boulevard Newton, Cité Descartes Champs sur Marne, 77447 Marne la Vallée Cedex 2

Received: May 31, 2013

Revised: September 30, 2013

Published: May 2014

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Abstract

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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Mathematics Subject Classification: Primary: 65M06, 35F21; Secondary: 90B20.

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