The continuum limit of non-local follow-the-leader models

We study a generalized Follow-the-Leader model where the driver considers the position of an arbitrary but finite number of vehicles ahead, as well as the position of the vehicle directly behind the driver. It is proved that this model converges to the classical Lighthill–Whitham–Richards model for traffic flow when traffic becomes dense. This also underscores the robustness of the Lighthill–Whitham–Richards model.