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arXiv · cond-mat/9512062

The Kasteleyn model and a cellular automaton approach to traffic flow

J. G. Brankov·V. B. Priezzhev·A. Schadschneider·M. Schreckenberg
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Abstract

We propose a bridge between the theory of exactly solvable models and the investigation of traffic flow. By choosing the activities in an apropriate way the dimer configurations of the Kasteleyn model on a hexagonal lattice can be interpreted as space-time trajectories of cars. This then allows for a calculation of the flow-density relationship (fundamental diagram). We further introduce a closely-related cellular automaton model. This model can be viewed as a variant of the Nagel-Schreckenberg model in which the cars do not have a velocity memory. It is also exactly solvable and the fundamental diagram is calculated.

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J. G. Brankov, V. B. Priezzhev, A. Schadschneider, M. Schreckenberg. 1995-12-12. The Kasteleyn model and a cellular automaton approach to traffic flow. https://doi.org/10.1088/0305-4470%2F29%2F10%2F002

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