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 $\beta$, $\gamma$ 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.

6 pages, 12 figures

References in corpus (4)

• The Nagel-Schreckenberg model revisited
• Cellular automaton rules conserving the number of active sites
• Exact results for deterministic cellular automata traffic models
• Density Fluctuations and Phase Transition in the Nagel-Schreckenberg Traffic Flow Model

Cited by in corpus (8)

• Cellular Automata Models of Road Traffic
• Probabilistic cellular automata with conserved quantities
• Criticality in Dynamic Arrest: Correspondence between Glasses and Traffic
• A slow-to-start traffic model related to a M/M/1 queue
• On the existence of a variational principle for deterministic cellular automaton models of highway traffic flow
• Critical behavior of number-conserving cellular automata with nonlinear fundamental diagrams
• A criterion for condensation in kinetically constrained one-dimensional transport models
• Evidence of Non-Equilibrium Critical Phenomena in a Simple Model of Traffic