First Order Models and Closure of Mass Conservation Equation in Mathematical Theory of Vehicular Traffic Flow

This paper deals with a review and critical analysis of first order hydrodynamic models of vehicular traffic flow obtained by the closure of the mass conservation equation. The closure being obtained by phenomenological models suitable to relate the local mean velocity to local density and density gradients. Various models are described and critically analyzed in the deterministic and stochastic case. The analysis is developed in view of applications of the models to traffic flow simulations for networks of roads. Some research perspectives are derived from the above analysis and proposed in the last part of the paper.