Unraveling the puzzling intermediate states in the Biham-Middleton-Levine traffic model

Traffic gridlock on a honeycomb city

Inspired by an old and almost in oblivion urban plan, we report the behavior of the Biham-Middleton-Levine (BML) model-a paradigm for studying phase transitions of traffic flow-on a hypothetical city with a perfect honeycomb street network. In contrast with the original BML model on a square lattice, the same model on a honeycomb does not show any anisotropy or intermediate states, but a single continuous phase transition between free and totally congested flow, a transition that can be completely characterized by the tools of classical percolation. Although the transition occurs at a lower density than for the conventional BML, simple modifications, like randomly stopping the cars with a very small probability or increasing the traffic light periods, drives the model to perform better on honeycomb lattices. As traffic lights and disordered perturbations are inherent in real traffic, these results question the actual role of the square gridlike designs and suggest the honeycomb topology as an interesting alternative for urban planning in real cities.