Discrete and Continuous Dynamical Systems - Series S (DCDS-S)

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

Pages: 411 - 433, Volume 7, Issue 3, June 2014      doi:10.3934/dcdss.2014.7.411

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Guillaume Costeseque - 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, France (email)
Jean-Patrick Lebacque - Ifsttar, COSYS-GRETTIA, 14-20 boulevard Newton, Cité Descartes Champs sur Marne, 77447 Marne la Vallée Cedex 2, France (email)

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.

Keywords:  Junction, numerical scheme, traffic, Hamilton-Jacobi equations.
Mathematics Subject Classification:  Primary: 65M06, 35F21; Secondary: 90B20.

Received: June 2013;      Revised: October 2013;      Available Online: January 2014.