An $n$-populations model for traffic flow

Source abstract

We present an $n$ -population generalization of the Lighthill–Whitham and Richards traffic flow model. This model is analytically interesting because of several non-standard features. For instance, it leads to non-classical shocks and enjoys an unexpected stability in spite of the presence of umbilic points. Furthermore, while satisfying all the minimal ‘common sense’ requirements, it also allows for a description of phenomena often neglected by other models, such as overtaking.