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

TL;DR

This study explores the complex coexistence of different traffic flow states in the BML model, revealing how aspect ratio and density influence the emergence of stable intermediate and jammed states, with implications for controlling traffic jams.

Contribution

It uncovers the coexistence of disordered, periodic, and global jam states in the BML model for square lattices and shows how small perturbations can induce jamming.

Findings

Disordered intermediate states dominate at certain densities.

Periodic intermediate states can coexist with other states.

Small perturbations can trigger global jamming.

Abstract

The Biham-Middleton-Levine model (BML) 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.