Investigation of the dynamical structure factor of the Nagel-Schreckenberg traffic flow model

Abstract

The Nagel-Schreckenberg traffic flow model shows a transition from a free flow regime to a jammed regime for increasing car density. The measurement of the dynamical structure factor offers the chance to observe the evolution of jams without the necessity to define a car to be jammed or not. Above the jamming transition the dynamical structure factor $S(k,\omega)$ exhibits for a given $k$-value two maxima corresponding to the separation of the system into the free flow phase and jammed phase. Analyzing the $k$-dependence of these maxima the backward velocity of the jams is measured. We find that the jam velocity neither depends on the global density of the cars nor the maximal velocity of the model.