Phase Diagram Of The Biham-Middleton-Levine Traffic Model In Three Dimensions

TL;DR

This study explores the three-dimensional Biham-Middleton-Levine traffic model, revealing a complex phase diagram with a new low-speed phase caused by percolating clusters, differing significantly from lower-dimensional cases.

Contribution

The paper provides the first detailed numerical analysis of the 3D Biham-Middleton-Levine model, identifying a novel low-speed phase and characterizing the phase transitions.

Findings

Distinct phase diagram in 3D compared to 1D and 2D

Existence of a low-speed phase with non-zero average speed

Transition to jamming is at least second order

Abstract

We study numerically the behavior of the Biham-Middleton-Levine traffic model in three dimensions. Our extensive numerical simulations show that the phase diagram for this model in three dimensions is markedly different from that in one and two dimensions. In addition to the full speed moving as well as the completely jamming phases, whose respective average asymptotic car speeds $<v>$ equal one and zero, we observe an extensive region of car densities $\rho$ with a low but non-zero average asymptotic car speed. The transition from this extensive low average asymptotic car speed region to the completely jamming region is at least second order. We argue that this low speed region is a result of the formation of a spatially-limited-extended percolating cluster. Thus, this low speed phase is present in $n > 3$ dimensional Biham-Middleton-Levine model as well.