The Kasteleyn model and a cellular automaton approach to traffic flow
Condensed Matter
2009-10-28 v2
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.
Keywords
Cite
@article{arxiv.cond-mat/9512062,
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},
journal= {arXiv preprint arXiv:cond-mat/9512062},
year = {2009}
}
Comments
Latex, 13 pages including 3 ps-figures