Synchronized Traffic Flow from a Modified Lighthill-whitman Model

A simple macroscopic argument leading to a diffusively corrected form of the classical kinematic-wave (Lighthill-Whitham) model of the flow of vehicular traffic is described. An example of a diffusively corrected kinematic-wave model displays a diffusion coefficient that is negative, for sufficiently large densities. It is shown that such a diffusively corrected kinematic-wave model is capable of reproducing elements of the synchronized flow reported by Kerner and Rehborn.