Periodic states, local effects and coexistence in the BML traffic jam model

Abstract

The Biham–Middleton–Levine (BML) model is simple lattice model of traffic flow, self-organization and jamming. Rather than a sharp phase transition between free-flow and jammed, it was recently shown that there is a region where stable intermediate states exist, with details dependent on the aspect ratio of the underlying lattice. Here we investigate square aspect ratios, focusing on the region where random, disordered intermediate (DI) states and conventional global jam (GJ) states coexist, and show that DI states dominate for some densities and timescales. Moreover, we show that periodic intermediate (PI) states can also coexist. PI states converge to periodic limit cycles with short recurrence times and were previously conjectured to arise from idiosyncrasies of relatively prime aspect ratios. The observed coexistence of DI, PI and GJ states shows that global parameters, density together with aspect ratio, are not sufficient to determine the full jamming outcome. We investigate additional features that lead towards jamming and show that a strategic perturbation of a few selected bits can change the nature of the flow, nucleating a global jam.