On Cellular Automata Models of Traffic Flow with Look-Ahead Potential

TL;DR

This paper investigates a cellular automata traffic flow model with look-ahead potential, analyzing statistical assumptions, spatial correlations, and proposing an improved coarse-grained ODE model with empirical corrections.

Contribution

It introduces a refined coarse-grained ODE model for traffic flow that accounts for spatial correlations and relaxes previous statistical assumptions.

Findings

Spatial correlations are crucial in models with look-ahead potential.

Relaxing statistical assumptions improves the coarse-grained model.

Empirical correction effectively captures spatial dependence.

Abstract

We study the statistical properties of a cellular automata model of traffic flow with the look-ahead potential. The model defines stochastic rules for the movement of cars on a lattice. We analyze the underlying statistical assumptions needed for the derivation of the coarse-grained model and demonstrate that it is possible to relax some of them to obtain an improved coarse-grained ODE model. We also demonstrate that spatial correlations play a crucial role in the presence of the look-ahead potential and propose a simple empirical correction to account for the spatial dependence between neighboring cells.