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

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.

BML model on non-orientable surfaces

“…[11] for the torus case, we also report the existence of intermediate states in the Klein bottle that coexist with global jam states and almost free flow states for values of p close to the critical zone. In Fig.…”

“…In Ref. [11] authors report that in 45 experiments they carried out no correlation between these two facts was found.…”

“…[11] several factors that can help in the appearance of jams for p being fixed are investigated. One of these factors is the disparity among the number of red and blue particles.…”

“…Also, we investigate the influence that the ratio between the number of red and blue particles has over the speed of the system, a question considered in Ref. [11].…”

Consensus in noisy environments with switching topology and time-varying delays

“…Recent studies have considered several dynamics such as synchronization of coupled oscillators [1,2], traffic and congestion [3][4][5][6][7], and evolution of cooperation games [8][9][10][11][12][13][14][15][16][17][18]. In this paper, we study the consensus problem on networks, which is not only theoretically interesting but also practically important.…”