A Fluid-Dynamic Traffic Model on Road Networks

We consider a mathematical model for fluid-dynamic flows on networks which is based on conservation laws. Road networks are studied as graphs composed by arcs that meet at some nodes, corresponding to junctions, which play a key-role. Indeed interactions occur at junctions and there the problem is underdetermined. The approximation of scalar conservation laws along arcs is carried out by using conservative methods, such as the classical Godunov scheme and the more recent discrete velocities kinetic schemes with the use of suitable boundary conditions at junctions. Riemann problems are solved by means of a simulation algorithm which processes each junction. We present the algorithm and its application to some simple test cases and to portions of urban network.