Optimal Resource Allocation in Random Networks with Transportation Bandwidths

TL;DR

This paper uses statistical physics to analyze resource allocation in sparse random networks with limited bandwidths, revealing phase transitions and the impact of connectivity on efficiency.

Contribution

It introduces algorithms based on recursive relations for resource allocation and uncovers phase transitions related to network connectivity and bandwidth.

Findings

Bottlenecks cause increased idle links at low bandwidths.

Higher connectivity improves allocation efficiency.

A phase transition occurs at a critical bandwidth, forming balanced node clusters.

Abstract

We apply statistical physics to study the task of resource allocation in random sparse networks with limited bandwidths for the transportation of resources along the links. Useful algorithms are obtained from recursive relations. Bottlenecks emerge when the bandwidths are small, causing an increase in the fraction of idle links. For a given total bandwidth per node, the efficiency of allocation increases with the network connectivity. In the high connectivity limit, we find a phase transition at a critical bandwidth, above which clusters of balanced nodes appear, characterised by a profile of homogenized resource allocation similar to the Maxwell's construction.