Nonlocal reaction traffic flow model with on-off ramps

We present a non-local version of a scalar balance law modeling traffic flow with on-ramps and off-ramps. The source term is used to describe the inflow and output flow over the on-ramp and off-ramps respectively. We approximate the problem using an upwind-type numerical scheme and we provide ${\mathbf{L}}^{\mathrm{\infty }}$ and $\mathbf{B}\mathbf{V}$ estimates for the sequence of approximate solutions. Together with a discrete entropy inequality, we also show the well-posedness of the considered class of scalar balance laws. Some numerical simulations illustrate the behaviour of solutions in sample cases.