Scaling and memory in recurrence intervals of Internet traffic

By studying the statistics of recurrence intervals, $\tau $, between volatilities of Internet traffic rate changes exceeding a certain threshold q, we find that the probability distribution functions, $P_{q}(\tau)$, for both byte and packet flows, show scaling property as $P_{q}(\tau)=\frac{1}{\over...

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Bibliographic Details
Published in:Europhysics letters 2009-09, Vol.87 (6), p.68001
Main Authors: Cai, Shi-Min, Fu, Zhong-Qian, Zhou, Tao, Gu, Jun, Zhou, Pei-Ling
Format: Article
Language:English
Subjects:
89.20.Hh
89.75.-k
89.75.Da
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Summary:By studying the statistics of recurrence intervals, $\tau $, between volatilities of Internet traffic rate changes exceeding a certain threshold q, we find that the probability distribution functions, $P_{q}(\tau)$, for both byte and packet flows, show scaling property as $P_{q}(\tau)=\frac{1}{\overline{\tau}}f(\frac{\tau}{\overline{\tau}}) $. The scaling functions for both byte and packet flows obey the same stretching exponential form, $f(x)=A{\rm exp}\,(-Bx^{\beta})$, with β ≈ 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.
ISSN:0295-5075
1286-4854
DOI:10.1209/0295-5075/87/68001