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

TL;DR

This study analyzes the dynamical structure factor of the Nagel-Schreckenberg traffic model to observe jam formation and measure jam velocities without defining jams explicitly, revealing jam velocity independence from density and maximal velocity.

Contribution

It introduces the use of the dynamical structure factor to analyze traffic jams and measures jam velocities, providing new insights into traffic flow dynamics.

Findings

Dynamical structure factor shows two maxima indicating free flow and jammed phases.

Jam velocity is independent of global car density.

Jam velocity does not depend on the maximal velocity of the 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.