Applied Mathematics Seminar | Khai T. Nguyen, Conservation laws and some applications to traffic flows

  In this talk, I will introduce a new class of models of traffic flow on a network of roads. In these models, the percentage of drivers who travel along an incoming road and wish to turn into an outgoing road is not a constant. Moreover, the drivers who enter a congested road are placed in a buffer of limited capacity, waiting their turn in line. The main goal is to describe traffic flow at intersections and study an optimization problem on a network of roads. 

 

I will present our results on well-posedness and robustness of the equations for a large class of initial data, and the existence of globally optimal solutions, Nash equilibrium solutions for a decision problem involving a continuum of drivers on the network.