Scaling and memory in recurrence intervals of Internet traffic

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 obeys the same stretching exponential form, $f(x)=A\text{exp}(-B{x}^{\beta })$, 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.

4 pages, 8 figures

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