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〉 ≃ Lv with v = 0.51 ± 0.05 where L is the system size. It is shown that the cumulative jam-interval distribution Ns(L) satisfies the finite-size scaling form (Ns(L) ≃ L−vf(s/Lv). Also, the typical lifetime 〈m7rang; of traffic jams scales as 〈m〉 ≃ Lv′ with v′ = 0.52 ± 0.05. The cumulative distribution Nm(L) of lifetimes satisfies the finite-size scaling form Nm(L)≃L−1g(m/Lv′).