The problem of road traffic, and its effects on pollution, time-consumption and their social and economical consequences, requires an accurate policy and planning of road networks. The recent advances in technology and Internet can provide low-cost and reliable solutions to the collection of traffic data. GPS-equipped mobile devices can contribute to reduce traffic and the amount of time spent on the road by providing more accurate sources of travel information. Traffic management via GPS data requires the construction of traffic models capable of integrating measurements from GPS enabled smart-phones and the creation of phase transition models capable of handling the dispersion of traffic behavior in congested regimes.

Finally, the creation of the corresponding Godunov schemes to compute numerical solutions allows monitoring traffic evolution and solving traffic flow optimization problems. Together, the two teams will tackle a problem that has become fundamental in congested areas: flow reroutes. The problem formulation is as follows: "what is an optimal reroute strategy for some of the highway traffic flow into the secondary network, to decongest the freeways, without congesting the arterials?" This problem is extremely hard to solve in a continuous setting (it will involve optimal control strategies for networks of hyperbolic partial differential equations networked by weak boundary conditions, for which existence and uniqueness of solutions is still an open problem). Therefore, the Associated Team will approach the problem from a discrete (numerical) standpoint, to provide constructive results (in a discrete setting), which can be implemented in practice.