Exploring highly-efficient routing strategy on scale-free networks with limited and diverse node capacity

Since the delivery capacity of each node is neither uniform nor strictly proportional to the degree in many real networked systems such as the Internet, we consider the node capacity is composed of a small uniform fraction and a large degree dependent proportion. By comparing the optimal routing strategy [B. Danila, Y. Yu, J. A. Marsh and K. E. Bassler, Phys. Rev. E 74 (2006) 046106; B. Danila, Y. Yu, J. A. Marsh and K. E. Bassler, Chaos 17 (2007) 026102] with the shortest path routing (SPR), the results show that the OR appears to be not efficient enough to enhance network traffic capacity. Then the efficient betweenness defined as the average betweenness for per delivery capacity is employed, and a so-called highly-efficient routing (HER) strategy is proposed. By iteratively minimizing the maximum efficient betweenness of any node in the network, the highest traffic capacity is achieved at the cost of a little average path lengthening. This work is very useful for network service providers to optimize the weight of each link incrementally to improve whole network transport ability.