Periodic States, Local Effects and Coexistence in the BML Traffic Jam Model

The Biham-Middleton-Levine model (BML) is simple lattice model of traffic flow, self-organization and jamming. Recently, the conventional understanding was shown to be incomplete: rather than a sharp phase transition between free-flow and jammed, there is an additional region where convergence to intermediate states is observed, with details dependent on the aspect ratio of the underlying lattice. For aspect ratios formed by two subsequent Fibonacci numbers, intermediate states converge to ordered, periodic limit cycles (i.e., periodic intermediate (PI) states). In contrast, for square aspect ratios, intermediate states typically converge to random, disordered intermediate (DI) states. We show these DI states are very robust to perturbation and occur more frequently than the conventional states for some densities. Furthermore, we report here on the discovery of PI states on square aspect ratios, showing PI states are not just an idiosyncrasy of particular aspect ratios. Finally, we investigate features that lead towards jamming and identify that local effects can dominate. A strategic perturbation of a few selected bits can change the nature of the flow, nucleating a global jam. The global parameters, density together with aspect ratio, are not sufficient to determine the full jamming outcome.