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DCDS-S

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.

NHM

This Special Issue gathers contributions, most of which were presented at
the Workshop ``Mathematics of Traffic Flow Modeling, Estimation and Control", organized at the Institute for Pure and Applied Mathematics
of the University of California Los Angeles on December 7--9 2011.

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keywords:

NHM

The aim of this paper is to build a dynamical traffic model in a dense urban area. The main contribution of this article is to take into account the four possible directions of traffic flows with flow vectors of dimension $4$ and not $2$ as in fluid mechanic on a plan. Traffic flows are viewed as confrontation results between users demands and a travel supply of the network. The model gathers elements of intersection theory and two-dimensional continuum networks.

keywords:
partial differential equations
,
dynamical model.
,
users' demand
,
network supply
,
Traffic network

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