Fast Self-Similar Teletraffic Generation Based on FGN and Inverse DWT∗

It is generally accepted that self-similar (or fractal) processes may provide better models of teletraffic in modern computer networks than Poisson processes. Thus, an important requirement for conducting simulation studies of telecommunication networks is the ability to generate long synthetic stochastic selfsimilar sequences. A new generator of pseudo-random self-similar sequences, based on the fractional Gaussian noise (FGN) and wavelet transform is proposed and analysed in this paper. Specifically, this generator uses Daubechies wavelets. The motivation behind this selection of wavelets is that Daubechies wavelets lead to more accurate results, by matching the self-similar structure of long range dependent processes. The statistical accuracy and time required to produce sequences of a given (long) length are experimentally studied. This generator shows a high level of accuracy of the output data (in the sense of the Hurst parameter) and is fast. Its theoretical algorithmic complexity is O(n).