We present a macroscopic and differential traffic model introduced in [1]. It is well-known that navigation systems play an important role in forecasting traffic flows on road networks. In this presentation, we show the possibility of coupling a non-linear transportation process to different strategic choices made by the users to reach their destination. An Hamilton-Jacobi conservation law is employed. Moreover, a multi-class traffic flow model is considered to account for different populations interacting on the same network. Numerical results will be presented to evaluate the efficiency of the model, encompassing both theoretical aspects, such as the Braess' Paradox [2], and practical considerations, such as a real scenario in London's streets. For more details, refer to [1]. 1] Festa, A. and Goatin, P. and F.V. , Navigation System-Based Routing Strategies in Traffic Flows on Networks. J. Optim. Theory Appl., 2023. [2] Colombo, R.M. and Holden, H. , On the Braess paradox with nonlinear dynamics and control theory. J. Optim. Theory Appl., 2016.