On the occurrence and predictability of overloads in telecommunication networks

摘要

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 R_Q (r_0) with increasing of the preceeding interval ro and iii) to a "hazard function" W_Q(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.