FARIMA(p,d,q) Self-similar Model Based On α-Stable Distribution

Network-flow model is the foundation of researches and applications on networks, such as flow-analysis, flow-prediction, flow-control and comments on networks' prefermance. Only good network-flow model, which is able to describe the accurate characteristics of the real flow in the network, can predict the future flow state accurately in the same network. But in recent years it is discovered that the real-flow in the network is self-similar and heavy-tail distributed, which shows flow's statistical consistency under different time scales and tells us the non- index decays of probability distribution function (PDF) in flow. The traditional network-flow models, which can't well describe the network's nature, are based on the index decays of flow's PDF, so people begin to adopt the self-similar models to do it. Different from the traditional short-range dependent models (SRD) such as Possion model, self-similar models can simulate the real-network's new characteristics and provide more accurate data for controlling, predicting and queuing. FARIMA(p,d,q) is one of the self-similar models and origins from ARMA(p, q) which is one of the short-range dependent models, so it can not only analysis short-range dependence, but also long-range dependence. In 1990s, Taqqu^[51] improved the efficiency of FARIMA(p,d,q) by using FFT algorithm and FARIMA(p,d,q) became to be one of the most used models. But it didn't work well innovated by gaussian distribution. α -stable distribution is heavy-tailed and its burst can be controlled by changing the parameter of α (0<α≤2).As a result, it is reasonable to innovate FARIMA(p,d,q) by α-stable distribution.In this present study, how self-similar phenomena is realized, how it affect thenetwork's performance and why it takes place will be summarized firstly; secondly, definition characteristics ^ analysis method and models of self-similarity will be discussed; then a -stable distribution and FARIMA{p,d,q) innovated by gaussian distribution (old model) will be introduced; last, a new FARIMA(p,d,q) model innovated by a -stable distribution (new model) will be put forward. We use both models to simulate the bellcore's data and compare two results. Through Aggregated-Variance plot and autocorrelation plot, we can see the series from new model is more close to original data than that from old model and the result shows the new model's validity.