LETTER TO THE EDITOR: 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 appropriate way, the dimer configurations of the Kasteleyn model on a hexagonal lattice can be interpreted as spacetime 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.
- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- May 1996
- DOI:
- 10.1088/0305-4470/29/10/002
- arXiv:
- arXiv:cond-mat/9512062
- Bibcode:
- 1996JPhA...29L.229B
- Keywords:
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- Condensed Matter
- E-Print:
- Latex, 13 pages including 3 ps-figures