The green and red lights of a traffic signal can be viewed as the up and down states of an Ising spin. Moreover, traffic signals in a city interact with each other, if they are controlled in a decentralised way. In this paper, a simple model of such interacting signals on a finite-size two-dimensional lattice is shown to have Ising-like dynamics that undergoes a ferromagnetic phase transition. Probabilistic behaviour of the model is realised by chaotic billiard dynamics that arises from coupled non-chaotic elements. This purely deterministic model is expected to serve as a starting point for considering statistical mechanics of traffic signals.
Chaotic Ising-like dynamics in traffic signals
Hideyuki Suzuki, Jun-ichi Imura & Kazuyuki Aihara
Scientific Reports 3, Article number: 1127 http://dx.doi.org/10.1038/srep01127