Coarse-grained cellular automaton for traffic systems

TL;DR

This paper introduces a coarse-grained cellular automaton model for traffic systems, capturing phase transitions between passable and jammed states, with computational techniques to analyze large state spaces.

Contribution

It presents a novel cellular automaton framework for traffic simulation that includes phase transition analysis and state space reduction methods.

Findings

Identifies phase transition between passable and jammed traffic states.

Demonstrates the model on a city map and lattice structures.

Uses symmetry-based reduction to improve computational efficiency.

Abstract

A coarse-grained cellular automaton is proposed to simulate traffic systems. There, cells represent road sections. A cell can be in two states: jammed or passable. Numerical calculations are performed for a piece of square lattice with open boundary conditions, for the same piece with some cells removed and for a map of a small city. The results indicate the presence of a phase transition in the parameter space, between two macroscopic phases: passable and jammed. The results are supplemented by exact calculations of the stationary probabilities of states for the related Kripke structure constructed for the traffic system. There, the symmetry-based reduction of the state space allows to partially reduce the computational limitations of the numerical method.