On the occurrence and predictability of overloads in telecommunication networks

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: 28 May 2009

Abstract

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 with increasing of the preceeding interval r₀ and iii) to a “hazard function” 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.