Garden of Eden states in traffic models

TL;DR

This paper explores the impact of Garden of Eden states in cellular automaton traffic models, showing how their elimination improves the accuracy of flux predictions, especially for higher maximum velocities.

Contribution

It introduces the concept of Garden of Eden states in traffic models and demonstrates how removing them yields more accurate flux estimates, matching simulations.

Findings

Elimination of GoE states improves flux predictions.

Exact solution for v_max=1 is recovered.

Higher flux values are achieved for v_max=2 after removing GoE states.

Abstract

We investigate the allowed configurations in the stationary state of the cellular automaton model for single-lane traffic. It is found that certain states in the configuration space can not be reached if one uses parallel dynamics. These so-called Garden of Eden (GoE) states do not exist for random-sequential dynamics and are responsible for the strong short-ranged correlations found in parallel dynamics. By eliminating the GoE states we obtain a simple and effective approximative description of the model. For $v_{max}=1$ the exact solution is recovered. For $v_{max}=2$ this elimination leads to much higher values of the flux compared to the mean-field result which are in good agreement with Monte Carlo simulations.