Volume 87, Number 6, September 2009
Article Number 68001
Number of page(s) 5
Section Interdisciplinary Physics and Related Areas of Science and Technology
Published online 01 October 2009
EPL, 87 (2009) 68001
DOI: 10.1209/0295-5075/87/68001

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

received 4 June 2009; accepted in final form 3 September 2009; published September 2009
published online 1 October 2009

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 $\beta$ $\approx$ 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.

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

© EPLA 2009