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Extension of Cluster Dynamics to Cellular Automata with Shuffle Update

In: Traffic and Granular Flow’05

Author

Listed:
  • David A. Smith

    (University of Bristol, Bristol Centre for Applied Nonlinear Mathematics, Department of Engineering Mathematics)

  • R. Eddie Wilson

    (University of Bristol, Bristol Centre for Applied Nonlinear Mathematics, Department of Engineering Mathematics)

Abstract

Summary The random shuffle update method for the asymmetric exclusion process (ASEP) is introduced and the cluster dynamics technique is extended in order to analyse its dynamics. A sequence of approximate models is introduced, the first element of which corresponds to the classical parallel update rule whose two-cluster dynamics is reviewed. It is then shown how the argument may be extended inductively to solve for the two-cluster probabilities for each element of the sequence of approximate models. A formal limit is then taken, and macroscopic velocities and flow rates are derived.

Suggested Citation

  • David A. Smith & R. Eddie Wilson, 2007. "Extension of Cluster Dynamics to Cellular Automata with Shuffle Update," Springer Books, in: Andreas Schadschneider & Thorsten Pöschel & Reinhart Kühne & Michael Schreckenberg & Dietrich E. Wol (ed.), Traffic and Granular Flow’05, pages 467-472, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-47641-2_43
    DOI: 10.1007/978-3-540-47641-2_43
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