Global solution to the Cauchy problem for discrete velocity models of vehicular traffic

This paper offers the proof of the existence for large times of the Cauchy problem for a class of vehicular traffic models with discrete velocities derived from the mathematical tools of the kinetic theory for active particles. This approach has the ability to capture some basic aspects concerning the complexity of the systems under consideration through an appropriate modeling, via stochastic games, of the interactions at the microscopic scale. The proof is related to specific aspects of the real system and hopefully can contribute towards improving the modeling approach.