Critical behavior of a cellular automaton highway traffic model

TL;DR

This paper analyzes the critical behavior of a cellular automaton traffic model, identifying phase transition properties and critical exponents through theoretical and simulation methods.

Contribution

It introduces a novel analysis of the phase transition in a CA traffic model, deriving critical exponents and scaling relations.

Findings

Critical exponents $eta$, $ ext{gamma}$, $ ext{delta}$ determined for $v_{max}=2$

Scaling relation for the order parameter established

Symmetry-breaking field identified as random braking

Abstract

We derive the critical behavior of a CA traffic flow model using an order parameter breaking the symmetry of the jam-free phase. Random braking appears to be the symmetry-breaking field conjugate to the order parameter. For $v_{\max}=2$, we determine the values of the critical exponents $\beta$, $\gamma$ and $\delta$ using an order-3 cluster approximation and computer simulations. These critical exponents satisfy a scaling relation, which can be derived assuming that the order parameter is a generalized homogeneous function of $|\rho-\rho_c|$ and p in the vicinity of the phase transition point.