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Self-organized criticality in asymmetric exclusion model with noise for freeway traffic

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  • Nagatani, Takashi

Abstract

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′).

Suggested Citation

  • Nagatani, Takashi, 1995. "Self-organized criticality in asymmetric exclusion model with noise for freeway traffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 218(1), pages 145-154.
  • Handle: RePEc:eee:phsmap:v:218:y:1995:i:1:p:145-154
    DOI: 10.1016/0378-4371(95)00093-M
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    References listed on IDEAS

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    1. Derrida, B. & Evans, M.R. & Hakim, V. & Pasquier, V., 1993. "Exact results for the one dimensional asymmetric exclusion model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 200(1), pages 25-33.
    2. Lebowitz, M.A., 1992. "Analytical Marxism and the Marxian Theory of Crisis," Discussion Papers dp92-05, Department of Economics, Simon Fraser University.
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    1. Mier, J.A. & Sánchez, R. & Newman, D.E., 2020. "Tracer particle transport dynamics in the diffusive sandpile cellular automaton," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).

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