Self-Organized Criticality and Scaling in Lifetime of Traffic Jams

Abstract

The deterministic cellular automaton 184 (the one-dimensional asymmetric simple-exclusion model with parallel dynamics) is extended to take into account injection or extraction of particles. The model presents the traffic flow on a highway with inflow or outflow of cars. Introducing injection or extraction of particles into the asymmetric simple-exclusion model drives the system asymptotically into a steady state exhibiting a self-organized criticality. The typical lifetime of traffic jams scales as ≅ L^ν with ν =0.65± 0.04. It is shown that the cumulative distribution N_m (L) of lifetimes satisfies the finite-size scaling form N_m (L) ≅ L^-1 f(m/L^ν).