A novel flux-fluctuation law for network with self-similar traffic

The actual network traffic can show self-similar and long-range dependent features, however, the revealed flux-fluctuation laws are only applicable to networks with short-range dependent traffic. In this paper, we propose an improved theoretical flux-fluctuation law of the self-similar traffic based on Pareto ON/OFF model. The proposed law shows that (i) the greater the self-similarity is, the stronger the influence of the internal factor is; (ii) the influence of the external factor is only determined by a single parameter characterizing the external network load. Numerical simulations illustrate the validity of the proposed flux-fluctuation law under diverse network scales and topologies with various self-similarity of traffic and time windows. We also demonstrate the effectiveness of the proposed law on the actual traffic data in the real GEANT network. As compared to the existing laws, the flux-fluctuation law proposed in this paper can better fit the actual variation of self-similar traffic and facilitate the detection of nodes with abnormal traffic.