Scaling and memory in recurrence intervals of Internet traffic

TL;DR

This paper investigates the statistical properties of recurrence intervals in Internet traffic, revealing scaling laws, a universal stretching exponential distribution, and long-term memory effects in traffic volatility.

Contribution

It uncovers universal scaling behavior and long-term correlations in recurrence intervals of Internet traffic fluctuations, advancing understanding of traffic dynamics.

Findings

Recurrence interval distributions follow a universal stretching exponential form.

Strong memory effects exist, with short intervals tending to follow short ones.

Long-term correlations are demonstrated through detrended fluctuation analysis.

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, $f(x)=A\texttt{exp}(-Bx^{\beta})$, 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.