SELF-ORGANIZED CRITICALITY AND SCALING IN LIFETIME OF TRAFFIC JAMS

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 [m] of traffic jams scales as [m] approximate to L(v) with v = 0.65 +/- 0.04. It is shown that the cumulative distribution N-m(L) of life-times satisfies the finite-size scaling form N-m(L) approximate to L(-1)f(m/L(v)).