Abstract: | *This talk will review some basic models describing traffic flow on a network of roads. Microscopic (ODE) and macroscopic (PDE) models of vehicle flow will be presented, together with boundary conditions to be imposed at road intersections. Here a key issue is to identify suitable Riemann solvers, which yield existence and uniqueness of solutions to the Cauchy problem, continuously depending on parameters. The existence and stability of Nash equilibria, where each driver chooses an optimal departure time and route to destination in order to minimize his own cost, will be also discussed. A large portion of the talk will be devoted to open problems and research directions.* |