Strengths and Limitations of the Wavelet Spectrum Method in the Analysis of Internet Traffic

The fluctuations of Internet traffic possess an intricate structure which cannot be simply explained by long-range dependence and self-similarity. In this work, we explore the use of the wavelet spectrum, whose slope is commonly used to estimate the Hurst parameter of long-range dependence. We show that much more than simple slope estimates are needed for detecting important traffic features. In particular, the multi-scale nature of the traffic does not admit simple description of the type attempted by the Hurst parameter. We also demonstrate some practical limitations of the wavelet spectrum. We explore the causes of these limitations using simulated data. This analysis leads us to a better understanding of a number of challenging phenomena observed in real network traffic.

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