Boundary conditions for first order macroscopic models of vehicular traffic in the presence of tollgates

This paper presents a new approach to the modeling of boundary conditions for first order models of vehicular traffic in highways. The first step consists in deriving a model for the dynamics of the flow of vehicles. Simulations of the parameters lead to a detailed analysis of the qualitative properties of the model. Subsequently, for such model, the statement of initial-boundary value problems is deduced, with domain decomposition, for a tract of highway between tollgates.