Self-Organization of Balanced Nodes in Random Networks with Transportation Bandwidths

TL;DR

This paper uses statistical physics to analyze resource allocation in random networks with limited bandwidths, revealing how nodes self-organize to balance shortages and form clusters, with implications for different network topologies.

Contribution

It introduces a mean-field approach to model resource shortages and demonstrates self-organization phenomena in both homogeneous and scale-free networks.

Findings

Nodes self-organize to balance shortages

Clusters of interconnected nodes form with unsaturated links

Hubs sacrifice to improve overall network balance

Abstract

We apply statistical physics to study the task of resource allocation in random networks with limited bandwidths along the transportation links. The mean-field approach is applicable when the connectivity is sufficiently high. It allows us to derive the resource shortage of a node as a well-defined function of its capacity. For networks with uniformly high connectivity, an efficient profile of the allocated resources is obtained, which exhibits features similar to the Maxwell construction. These results have good agreements with simulations, where nodes self-organize to balance their shortages, forming extensive clusters of nodes interconnected by unsaturated links. The deviations from the mean-field analyses show that nodes are likely to be rich in the locality of gifted neighbors. In scale-free networks, hubs make sacrifice for enhanced balancing of nodes with low connectivity.