SELF-ORGANIZED CRITICALITY IN ASYMMETRIC EXCLUSION MODEL WITH NOISE FOR FREEWAY TRAFFIC

The one-dimensional asymmetric simple-exclusion model with open boundaries for parallel update is extended to take into account temporary stopping of particles. The model presents the traffic flow on a highway with temporary deceleration of cars. Introducing temporary stopping into the asymmetric simple-exclusion model drives the system asymptotically into a steady state exhibiting a self-organized criticality. In the self-organized critical state, start-stop waves (or traffic jams) appear with various sizes (or lifetimes). The typical interval [s] between consecutive jams scales as [s] approximate to L(v) with v = 0.51 +/- 0.05 where L is the system size. It is shown that the cumulative jam-interval distribution N-s(L) satisfies the finite-size scaling form N-s(L) approximate to L(-v)f(s/L(v)). Also, the typical lifetime [m] of traffic jams scales as [m]approximate to L(v) with v' = 0.52 +/- 0.05. The cumulative distribution N-m(L) of lifetimes satisfies the finite-size scaling form N-m(L)approximate to L(-1)g(m/L(v')).