On the Packet Delay Distribution in Power-law Networks

Measurement studies of the Internet topology have revealed that the degree distribution exhibits a power-law attribute. That is, the probability P(k) that a node has k outgoing links follows P(k) similar to k. However, it is known that the power-law degree distribution alone does not determine traffic-level behaviors in Internet topologies. In this paper, we investigate packet-level delay behavior of topologies having power-law degree distribution. Our results show that the packet delay distribution of the actual ISP topology also follows the power-law, while the delay distribution of model-based topology does not. We then investigate the structural differences between the topologies, and show that the modularity structure of ISP's router-level topologies makes the packet delay distribution being long-tail.