Scaling and memory in recurrence intervals of Internet traffic

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

doi:10.1209/0295-5075/87/68001

All issues

Volume 87 / No 6 (September 2009)

EPL, 87 6 (2009) 68001

Abstract

Issue		EPL Volume 87, Number 6, September 2009


Article Number		68001
Number of page(s)		5
Section		Interdisciplinary Physics and Related Areas of Science and Technology
DOI		https://doi.org/10.1209/0295-5075/87/68001
Published online		01 October 2009

EPL, 87 (2009) 68001

Scaling and memory in recurrence intervals of Internet traffic

Shi-Min Cai¹^,2, Zhong-Qian Fu¹, Tao Zhou²^,3, Jun Gu¹ and Pei-Ling Zhou¹

¹ Department of Electronic Science and Technology, University of Science and Technology of China Hefei Anhui, 230026, PRC
² Department of Physics, University of Fribourg - Chemin du Musée 3, 1700 Fribourg, Switzerland
³ Department of Modern Physics, University of Science and Technology of China - Hefei Anhui, 230026, PRC

Corresponding author: zhutou@ustc.edu

Received: 4 June 2009
Accepted: 3 September 2009

Abstract

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.

PACS: 89.75.-k – Complex systems / 89.75.Da – Systems obeying scaling laws / 89.20.Hh – World Wide Web, Internet

© EPLA, 2009

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