Phase transition behavior in a cellular automaton model with different initial configurations

TL;DR

This paper studies phase transition behaviors in a cellular automaton traffic model, revealing how different initial configurations lead to distinct types of phase transitions and analyzing their dynamic properties.

Contribution

It introduces the impact of initial configurations on phase transition types in the Nagel-Schreckenberg model and characterizes their dynamic exponents.

Findings

Deterministic initial configurations cause first-order transitions.

Random initial configurations cause second-order transitions.

Energy dissipation rate and relaxation time follow power-law behavior.

Abstract

We investigate the dynamical transition from free-flow to jammed traffic, which is related to the divergence of the relaxation time and susceptibility of the energy dissipation rate $E_d$, in the Nagel-Schreckenberg (NS) model with two different initial configurations. Different initial configurations give rise to distinct phase transition. We argue that the phase transition of the deterministic NS model with megajam and random initial configuration is first- and second-order phase transition, respectively. The energy dissipation rate $E_d$ and relaxation time follow power-law behavior in some cases. The associated dynamic exponents have also been presented.