## Scaling and memory in recurrence intervals of Internet traffic

### Cai, Shi-Min ; Fu, Zhong-Qian ; Zhou, Tao ; Gu, Jun ; Zhou, Pei-Ling

### In: Europhysics Letters, 2009, vol. 87, p. 68001

By studying the statistics of recurrence intervals, τ, between volatilities of Internet traffic rate changes exceeding a certain threshold q, we find that the probability distribution functions, Pq(τ), 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... More

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- By studying the statistics of recurrence intervals, τ, between volatilities of Internet traffic rate changes exceeding a certain threshold q, we find that the probability distribution functions, Pq(τ), 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*exp (-*Bx*^{β}), with β≈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.