互联网流量递归区间的标度和记忆
Scaling and memory in recurrence intervals of Internet traffic
摘要：
通过研究互联网流量速率变化的波动性超过某个阈值$q$之间的递归间隔$τ$的统计特性，我们发现字节流和分组流的概率分布函数$P_{q}(τ)$都表现出$P_{q}(τ)=\frac{1}{\overlineτ}f(\fracτ{\overlineτ})$的标度特性。字节流和数据包流的缩放函数都遵循相同的拉伸指数形式，即$f(x)=A\texttt{exp}(-Bx^β)$和$β\approx 0.45$。此外，我们检测到一个强大的记忆效应，即一个短（或长）的复发间隔往往是由另一个短（或长）。去趋势波动分析进一步证明了复发间隔中存在长期相关性。
英文摘要：
By studying the statistics of recurrence intervals, $τ$, between volatilities of Internet traffic rate changes exceeding a certain threshold $q$, we find that the probability distribution functions, $P_{q}(τ)$, for both byte and packet flows, show scaling property as $P_{q}(τ)=\frac{1}{\overlineτ}f(\fracτ{\overlineτ})$. The scaling functions for both byte and packet flows obeys the same stretching exponential form, $f(x)=A\texttt{exp}(-Bx^β)$, with $β\approx 0.45$. In addition, we detect a strong memory effect that a short (or long) recurrence interval tends to be followed by another short (or long) one. The detrended fluctuation analysis further demonstrates the presence of long-term correlation in recurrence intervals.
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