A Simple Example of a Two-Dimensional Model for Traffic: Discussion about Assumptions and Numerical Methods

This article presents a two-dimensional (2D) macroscopic model for traffic flow on a network. We considered a 2D conservation law in which we suggested a new method to estimate the direction of the velocity using only information and properties of the network. We present an algorithm for the computation of the 2D velocity on the network and present numerical simulations. Moreover, the numerical approximation of the 2D equation was carried out using an operator and splitting method and we present the results of some simulations on realistic networks. Lastly, we propose a comparison with the well-known cell transmission model method.