Critical behavior of a traffic flow model

TL;DR

This paper investigates the critical transition in a traffic flow model, revealing how jams form and evolve through analysis of the dynamical structure factor and finite-size scaling, highlighting long-range correlations near the transition.

Contribution

It introduces a novel approach using the dynamical structure factor to observe jam evolution without predefined jam criteria, and analyzes critical behavior at the transition.

Findings

Dynamical structure factor shows two maxima above the jamming transition.

Finite-size scaling reveals long-range correlations near the transition.

Jams exhibit critical behavior with long-range correlations approaching the transition.

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 exhibits for a given k-value two maxima corresponding to the separation of the system into the free flow phase and jammed phase. We obtain from a finite-size scaling analysis of the smallest jam mode that approaching the transition long range correlations of the jams occur.