High-performance distribution of limited resources via a dynamical reallocation scheme

Using the context of routing efficiency in a complex scale-free network, we study the problem of how a limited amount of resources should be distributed to the nodes in a network so as to achieve a better performance, without imposing a certain pre-determined distribution. A dynamical reallocation scheme, based on the willingness of sharing resources with a busy neighboring node, is proposed as a tool for allowing an initially uniform distribution of resource to evolve to a high-performance distribution. The resulting distribution gives a critical packet generation rate Rc that is significantly enhanced when compared with evenly distributing the same amount of resources on the nodes. There emerges a relation between the resource allocated to a node and the degree of the node in the form of Ci=a+bkiγ. The exponent γ is found to vary with the packet generation rate R. For R<Rc, γ takes on a high value and shows a weak dependence on R; for R>Rc, γ drops with R; and for R≫Rc, γ saturates. For good performance, the values of γ indicate a behavior different from that linear in k, as often assumed in previous studies. The resource distribution is also analyzed in terms of the betweenness of the nodes.