Using relaxational dynamics to reduce network congestion

TL;DR

This paper demonstrates that relaxational dynamics, modeled via the Family surface-growth model, significantly reduce congestion in scale-free networks by inducing a structural transition in gradient network clusters, especially as connectivity decreases.

Contribution

It introduces the use of relaxational dynamics from surface-growth physics to improve load balancing and reduce congestion in scale-free networks.

Findings

Congestion pressure drops significantly with relaxational dynamics.

Structural transition in gradient network clusters reduces congestion.

Lowering the connectivity exponent enhances congestion reduction.

Abstract

We study the effects of relaxational dynamics on congestion pressure in scale free networks by analyzing the properties of the corresponding gradient networks (Z. Toroczkai, K. E. Bassler, Nature {\bf 428}, 716 (2004)). Using the Family model (F. Family, J. Phys. A, {\bf 19}, L441 (1986)) from surface-growth physics as single-step load-balancing dynamics, we show that the congestion pressure considerably drops on scale-free networks when compared with the same dynamics on random graphs. This is due to a structural transition of the corresponding gradient network clusters, which self-organize such as to reduce the congestion pressure. This reduction is enhanced when lowering the value of the connectivity exponent $\lambda$ towards 2.