Scaling and memory in recurrence intervals of Internet trafficShi-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, , between volatilities of Internet traffic rate changes exceeding a certain threshold q, we find that the probability distribution functions, , for both byte and packet flows, show scaling property as . The scaling functions for both byte and packet flows obey the same stretching exponential form, , with 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