Critical behavior of a cellular automaton highway traffic model

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 $β$, $γ$ and $δ$ 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 $|ρ-ρ_c|$ and p in the vicinity of the phase transition point.