Non-local traffic flow models with time delay: Well-posedness and numerical approximation

We prove the well-posedness of weak entropy solutions of a scalar non-local traffic flow model with time delay. Existence is obtained by convergence of finite volume approximate solutions constructed by Lax-Friedrichs and Hilliges-Weidlich schemes, while the $ \mathbf{L^1} $ stability with respect to the initial data and the delay parameter relies on a Kružkov-type doubling of variable technique.Numerical tests are provided to illustrate the efficiency of the proposed schemes, as well as the solution dependence on the delay and look-ahead parameters.