### Abstract

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.

Original language | English |
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Publication status | Published - Oct 2005 |

### Keywords

- traffic
- cellular automata

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## Cite this

Smith, DA., & Wilson, R. E. (2005).

*Extension of cluster dynamics to cellular automata with shuffle update*. http://hdl.handle.net/1983/155