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Self-Similarity of Network Data Analysis
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Self-Similarity of Network Data Analysis : ウィキペディア英語版
Self-Similarity of Network Data Analysis

In computer networks, self-similarity is a feature of network data transfer dynamics. When modeling network data dynamics the traditional time series models, such as an autoregressive moving average model (ARMA(p, q)), are not appropriate. This is because these models only provide a finite number of parameters in the model and thus interaction in a finite time window, but the network data usually have a long-range dependent temporal structure. A self-similar process is one way of modeling network data dynamics with such a long range correlation. This article defines and describes network data transfer dynamics in the context of a self-similar process. Properties of the process are shown and methods are given for graphing and estimating parameters modeling the self-similarity of network data.
== Definition ==

Suppose X be a weakly stationary (2nd-order stationary) process
with mean \mu, variance \sigma^2, and autocorrelation function \gamma(t).
Assume that the autocorrelation function \gamma(t) has the form
\gamma(t)\rightarrow t^L(t) as t\to\infty, where 0<\beta<1
and L(t) is a slowly varying function at infinity, that is \lim_\frac=1 for all x>0.
For example, L(t)=const and L(t)=\log (t) are slowly varying functions.
Let X_k^=\frac(X_+\cdot\cdot\cdot+X_),
where k=1,2,3,\ldots, denote an aggregated point series over non-overlapping blocks of size m, for each m is a positive integer.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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