Extension of Cluster Dynamics to Cellular Automata with Shuffle Update

David A. Smith and R. Eddie Wilson
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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

A chapter in Traffic and Granular Flow’05, 2007, pp 467-472 from Springer

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.

Keywords: Cellular Automaton; Approximate Model; Classical Parallel; Cluster Dynamics; Cellular Automaton Model (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-47641-2_43

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DOI: 10.1007/978-3-540-47641-2_43

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