On the continuum limit of the Follow-the-Leader model and its stability

We consider the Follow-the-Leader (FtL) model and study which properties of the initial positioning of the vehicles ensure its convergence to the classical Lighthill-Whitham-Richards (LWR) model for traffic flow. Robustness properties of both FtL and LWR models with respect to the initial discretization schemes are investigated. Some numerical simulations are also discussed.