The Kasteleyn model and a cellular automaton approach to traffic flow

TL;DR

This paper connects exactly solvable models with traffic flow analysis by interpreting dimer configurations as car trajectories and introduces an exactly solvable cellular automaton model to study flow-density relationships.

Contribution

It establishes a novel link between the Kasteleyn model and traffic flow, and introduces a new cellular automaton variant that is exactly solvable.

Findings

Calculated the flow-density relationship (fundamental diagram) for the Kasteleyn model.

Developed an exactly solvable cellular automaton model related to traffic flow.

Provided analytical results for the fundamental diagram of the new automaton.

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.