# American Institute of Mathematical Sciences

June  2014, 7(3): 411-433. doi: 10.3934/dcdss.2014.7.411

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

 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, France 2 Ifsttar, COSYS-GRETTIA, 14-20 boulevard Newton, Cité Descartes Champs sur Marne, 77447 Marne la Vallée Cedex 2

Received  June 2013 Revised  October 2013 Published  January 2014

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.
Citation: Guillaume Costeseque, Jean-Patrick Lebacque. Discussion about traffic junction modelling: Conservation laws VS Hamilton-Jacobi equations. Discrete & Continuous Dynamical Systems - S, 2014, 7 (3) : 411-433. doi: 10.3934/dcdss.2014.7.411
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