Optimization of traffic flow conditions by minimization of quadratic functionals

This paper deals with a scalar hydrodynamic model of traffic flow. In this model, the driver adapts his velocity to a fictitious density that he feels in nonequilibrium conditions, and he makes an effort to optimize the comfort and to minimize fuel consumption and gas emission. These optimization problems are here considered and analyzed by introducing and minimizing a quadratic functional. The analysis is developed on the basis of suitable simulations.