The Kasteleyn Model and a Cellular Automaton Approach to Traffic Flow

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. Permanent address: Institute of Mechanics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria

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Cite this paper

@inproceedings{Brankov1995TheKM, title={The Kasteleyn Model and a Cellular Automaton Approach to Traffic Flow}, author={J G Brankov and V B Priezzhev and A Schadschneider and M Schreckenberg}, year={1995} }