Modeling Multilane Traffic with Moving Obstacles by Nonlocal Balance Laws*

We consider a system of nonlocal balance laws where each balance law is coupled with the remaining balance laws both by a nonlocal velocity function that takes into account the averaged density of all other equations and by a right-hand ``semilinear"" term. We demonstrate existence and uniqueness of weak solutions for a small time horizon and a maximum principle for additional assumptions on the input data. This maximum principle ensures the applicability of the considered system of nonlocal balance laws to real-world problems. In the case of traffic flow, we show how the nonlocal impact and the coupling via the ``semilinear"" term can model multilane traffic flow with lane changing. We also demonstrate the applicability of the model to an on-ramp scenario in which the cars have to move from the on-ramp to the adjacent lane within a finite spatial domain. Moreover, we demonstrate how the problem of having obstacles can be modeled with these equations, introducing an additional ODE for the obstacle's dynamic. Several numerical results are presented and their reasonability is discussed.