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. Recursive relations from the Bethe approximation are converted into useful algorithms. 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, characterized by a profile of homogenized resource allocation similar to the Maxwell construction. Copyright © 2009 IOP Publishing Ltd.
|Journal of Statistical Mechanics: Theory and Experiment
|Published - 2009