ATM Traffic Prediction Methods using Wavelet Analysis

This work introduces the wavelet transform as an important element for ATM traffic prediction. Two methods are proposed. The first method proposes data fittings by the fGn model of parameter H, adequate for long dependence stationary processes. The estimated H is accomplished by a method based on Wavelet analysis. A small order Wiener filter is projected to implement the prediction and the final proposal results in a filter coefficient correction method that improves the prediction quality. The second method proposes a combination of wavelet transforms to feed forward artificial neural networks. Wavelet transforms are used to preprocess the nonlinear time-series in order to provide a step-closer phase learning paradigm to the artificial neural network. The network uses a variable length time window on approximation coefficients over all scales. This approach improves the generalization ability as well as the accuracy of the artificial neural network for ATM traffic prediction. Both prediction methods are evaluated on traffic data files from Bellcore. ATM traffic has the self-similarity property that establishes the preservation of the statistical properties in different time scales. The fractal geometry and the fractal process offer facilities for the understanding, modeling and analysis of self-similarity processes [4][10]. A stochastic process x(t) defined in the time interval (-f,f) for any real number a>0, is statistically self similar with Hurst parameter H if follows the relation : DW [ D W [ + G (1) 182