In this talk we present a new simple model for traffic flow on networks based on the LWR model.
Starting from the model proposed in , we derive a system of conservation laws with space-dependent and discontinuous flux, each of which describes the evolution of a population of drivers with a unique origin-destination pair. The main advantage of this formulation is that junctions actually disappear, so that a unique mathematical theory can be applied for the whole network, i.e., there is no need to manage junctions separately as in the classical theory . To avoid the excessive increase of the equations of the system, a modified version of the model is also proposed, in order to deal with large networks.
Surprisingly, if the equations are numerically approximate by means of the Godunov scheme, the resulting algorithm *automatically* maximizes the flux at junctions, thus selecting a reasonable solution of the problem.
Numerical examples for small- and medium-scale networks are provided, aiming at showing the simplicity of the algorithm.
 M. Mercier, Traffic flow modelling with junctions, J. Math. Anal. Appl., 350 (2009), 369-383.
 M. Garavello and B. Piccoli, Traffic flow on networks, AIMS, 2006.
Maya Briani, Emiliano Cristiani (http://www.iac.rm.cnr.it/ cristiani/)