Web traffic demand forecasting using wavelet‐based multiscale decomposition

In this paper we propose an experimental forecasting strategy taking into account the long‐range dependence of aggregate network traffic, and we apply it to provide one‐minute‐ahead World‐Wide Web (Web) traffic demand forecasts in terms of average number of bytes transferred. Recently, statistical examination of Web traces have shown evidence that Web traffic arising from file transfers exhibits a behavior that is consistent with the notion of self‐similarity. Essentially, self‐similarity indicates that significant burstiness is present on a wide range of time scales (i.e., the process is long‐range dependent). Hence the idea of exploiting this multiscale property with a view towards discovering and capturing regularities underlying the time series which may prove useful for short‐term traffic load forecasting. We carry out a wavelet transform decomposition of the original series to decompose the traffic time series into varying scales of temporal resolution, with the aim of making the underlying temporal structures more tractable. In a second step, each individual wavelet series—supposed to capture some features of the series—is fitted with a dynamical recurrent neural network (DRNN) model to output the wavelet forecast. The latter are afterwards recombined to form the next‐minute Web Traffic demand. The method is applied on a large set of HTTP logs and is shown to yield good results. © 2001 John Wiley & Sons, Inc.

[1]  Fionn Murtagh,et al.  Multiresolution in astronomical image processing: A general framework , 1995, Int. J. Imaging Syst. Technol..

[2]  David E. Rumelhart,et al.  Predicting the Future: a Connectionist Approach , 1990, Int. J. Neural Syst..

[3]  Virgílio A. F. Almeida,et al.  Characterizing reference locality in the WWW , 1996, Fourth International Conference on Parallel and Distributed Information Systems.

[4]  Fionn Murtagh,et al.  Dynamical recurrent neural networks -- towards environmental time series prediction , 1995, Int. J. Neural Syst..

[5]  Kihong Park,et al.  On the relationship between file sizes, transport protocols, and self-similar network traffic , 1996, Proceedings of 1996 International Conference on Network Protocols (ICNP-96).

[6]  Fionn Murtagh,et al.  Multiresolution Support Applied to Image Filtering and Restoration , 1995, CVGIP Graph. Model. Image Process..

[7]  F. Murtagh,et al.  The Wavelet Transform in Multivariate Data Analysis , 1996 .

[8]  Jean-Luc Starck,et al.  Filtering and deconvolution by the wavelet transform , 1994, Signal Process..

[9]  Walter Willinger,et al.  Proof of a fundamental result in self-similar traffic modeling , 1997, CCRV.

[10]  Peter Tiño,et al.  Learning long-term dependencies in NARX recurrent neural networks , 1996, IEEE Trans. Neural Networks.

[11]  Kumpati S. Narendra,et al.  Identification Using Feedforward Networks , 1995, Neural Computation.

[12]  Mark J. Shensa,et al.  The discrete wavelet transform: wedding the a trous and Mallat algorithms , 1992, IEEE Trans. Signal Process..

[13]  Azer Bestavros,et al.  Self-similarity in World Wide Web traffic: evidence and possible causes , 1996, SIGMETRICS '96.

[14]  B. Silverman,et al.  The Stationary Wavelet Transform and some Statistical Applications , 1995 .

[15]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[16]  P.R.J. Asveld,et al.  Review of J.G.Brookshear: Theory of computation - Formal languages, automata and complexity (1989), Benjamin/Cummings, Redwood city, CA , 1991 .

[17]  C. Lee Giles,et al.  An experimental comparison of recurrent neural networks , 1994, NIPS.

[18]  Walter Willinger,et al.  Self-Similarity in High-Speed Packet Traffic: Analysis and Modeling of Ethernet Traffic Measurements , 1995 .

[19]  Eric A. Wan,et al.  Finite impulse response neural networks with applications in time series prediction , 1994 .

[20]  Fionn Murtagh,et al.  Combining Neural Network Forecasts on Wavelet-transformed Time Series , 1997, Connect. Sci..