Lane formation in a microscopic model and the corresponding partial differential equation

We study the lane formation capabilities of a cellular automaton model introduced by [A. Kirchner and A. Schadschneider: Simulation of evacuation processes using a bionics-inspired cellular automaton model for pedestrian dynamics. Physica A: Statistical Mechanics and its Applications, 312(1-2):260 276, 2002]. We present numerical examples demonstrating the formation of lanes in the microscopic setting. Using the link to a macroscopic partial differential equation, we are able to give conditions on the stability of perturbations corresponding to the formation of lanes in the microscopic case.