A minimal model for congestion phenomena on complex networks

TL;DR

This paper introduces a minimal yet analytically tractable model of traffic flow on complex networks, revealing rich phase transition phenomena and the impact of traffic control on congestion, with implications for Internet and transportation networks.

Contribution

It presents a new minimal model capturing diverse congestion phenomena and provides analytical insights into phase transitions and traffic control effects on complex networks.

Findings

Traffic control enlarges free-flow regions in heterogeneous networks.

Discontinuous congestion can be triggered by strong traffic control.

Model reproduces empirical traffic fluctuation scaling in the Internet.

Abstract

We study a minimal model of traffic flows in complex networks, simple enough to get analytical results, but with a very rich phenomenology, presenting continuous, discontinuous as well as hybrid phase transitions between a free-flow phase and a congested phase, critical points and different scaling behaviors in the system size. It consists of random walkers on a queueing network with one-range repulsion, where particles can be destroyed only if they can move. We focus on the dependence on the topology as well as on the level of traffic control. We are able to obtain transition curves and phase diagrams at analytical level for the ensemble of uncorrelated networks and numerically for single instances. We find that traffic control improves global performance, enlarging the free-flow region in parameter space only in heterogeneous networks. Traffic control introduces non-linear effects and, beyond a critical strength, may trigger the appearance of a congested phase in a discontinuous manner. The model also reproduces the cross-over in the scaling of traffic fluctuations empirically observed in the Internet, and moreover, a conserved version can reproduce qualitatively some stylized facts of traffic in transportation networks.