M.I. Bogachev, D.V. Gaivoronsky, O.A. Markelov

The paper discusses the predictability of traffic bursts on the world wide web exemplified using the data from four different HTTP servers, among them three servers with quasi-stationary dynamics and one server with significantly non-stationary behavior. Traffic on global networks is known to be characterized by heavy-tailed distributions and to exhibit pronounced bursts well above the average traffic levels, due to simultaneously accessing the same resources by multiple users as the outcome of the erratic human behavior. In dynamical network resource management, predicting heavy traffic bursts is one of the essential challenges. Network traffic is known to contain several superimposed cycles related to human activity (daily, weekly etc.), and its fluctuation component around the typical quasi-cyclic trend is also known to exhibit both linear and nonlinear long-range dependence. In addition, there is usually some extra short-term memory involved. By comparing three variant of predicting techniques, namely (i) the optimal linear predictor using the Hurst exponent that characterizes the traffic records, (ii) the precursory pattern recognition technique which uses short-term memory to obtain the probability of a burst, and (iii) the return interval approach that exploits information about previous bursts, the predictability of the traffic bursts is studied here. The results indicate that all three methods provide comparable efficiency, and thus the selection of the method should be rather based on the available information about the previous activity on the server and/or its typical patterns that allow estimation of the parameters required by the techniques involved. It is also shown that, due to rather weak nonlinear dependence, nonlinear methods can hardly outperform linear ones.