Scaling and memory in recurrence intervals of Internet traffic

Abstract

By studying the statistics of recurrence intervals, $\ddot{I}„$, between volatilities of Internet traffic rate changes exceeding a certain threshold $q$, we find that the probability distribution functions, $P_q(\ddot{I}„)$, for both byte and packet flows, show scaling property as $P_q(\ddot{I}„)=\frac{1}{\overline{\ddot{I}}„}f(\frac{\ddot{I}}{„}\overline{\ddot{I}}„)$. The scaling functions for both byte and packet flows obeys the same stretching exponential form, $f(x)=A\text{exp}(-B{x}^2)$, with ${\hat{I}}^2\approx 0.45$. 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