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arXiv · 0905.3878

Scaling and memory in recurrence intervals of Internet traffic

Shi-Min Cai·Zhong-Qian Fu·Tao Zhou·Jun Gu·Pei-Ling Zhou
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Abstract

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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Shi-Min Cai, Zhong-Qian Fu, Tao Zhou, Jun Gu, Pei-Ling Zhou. 2009-08-23. Scaling and memory in recurrence intervals of Internet traffic. https://doi.org/10.1209/0295-5075/87/68001

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