On the occurrence and predictability of overloads in telecommunication networksM. I. Bogachev1, 2 and A. Bunde1
1 Institut für Theoretische Physik III, Justus-Liebig-Universität Giessen - Heinrich-Buff-Ring 16, 35392, Giessen, Germany
2 Radio System Department, St. Petersburg State Electrotechnical University - Professor Popov str. 5, 197376, St. Petersburg, Russia
received 20 March 2009; accepted in final form 28 May 2009; published June 2009
published online 26 June 2009
We study the statistics of return intervals between large events above a certain threshold Q in the total intraday outgoing traffic of three different HTTP servers, with duration ranging from two months up to one year. We find that the nonlinear component of the memory that characterizes the traffic records leads i) to a broad distribution of the return intervals that approximately can be described by a stretched gamma distribution, ii) to a strong increase in the conditional return period RQ(r0) with increasing of the preceeding interval r0 and iii) to a “hazard function” WQ(t; 1) which approximately decreases by a power law with increasing elapsed time t from the last Q-exceeding event. We show that all these quantities depend only slightly on the chosen threshold Q. Using a ROC-analysis we show that the nonlinear memory is essential for the predictability of large traffic events.
64.60.al - Fractal and multifractal systems.
95.75.Wx - Time series analysis, time variability.
05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.
© EPLA 2009