Scale-free property of optimal network for packet flow by a packet routing control

We investigate an optimal network structure for packet flow on large-scale networks. For this aim, we introduce a cost function which represents efficiency of the packet flow. Our strategy for obtaining an optimal network is to reconnect links in the network so as to minimize the defined cost function. We apply this strategy to a packet communication network in which a packet routing is controlled by using neural networks. We found that the optimal network shows a scale-free property for large degree k when the buffer-size distribution has a power-law form and the probability with which a node is chosen as a destination of a packet is proportional to the buffer size of the node.