Self-organized criticality in 1D traffic flow model with inflow or outflow

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Abstract
The asymmetric simple-exclusion model with parallel dynamics (the deterministic cellular automaton 184) is extended to take into account the exchange of cars between different lanes on a multi-lane roadway. The traffic flow model is presented by the one-dimensional asymmetric exclusion model with injection or extraction of particles. The system is driven asymptotically into a steady state exhibiting a self-organized criticality. The typical interval (s) between consecutive jams scales as (s) approximately=Lv with v=0.62+or-0.04 where L is the system size. It is shown that the jam-interval distribution ns(L) satisfies the finite-size scaling form ns(L) approximately=L- beta f(s/Lv) with beta =2v.