Nonlinear hydrodynamic models of traffic flow in the presence of tollgates

A nonlinear hydrodynamic model of traffic flow is here proposed in order to refine the modeling of driverʹs behaviour. This model is able to describe the car density and flow evolution in the presence of tollgates too. In any case, the associate evolution problem is a classical Dirichlet problem related to the flow measurement. Numerical simulations related to the solution of initial-boundary value problems are obtained by employing a scientific program written by the software Mathematica.