Analysis and synthesis of self-similar network traffic

For simulation-based studies, the use of long-range dependent models gives rise to new and challenging problems for statistical inference, stochastic modeling, and synthetic traffic generation. The degree of long-range dependence is captured by the Hurst parameter. Practical network traffic modeling requires generating synthetic sequences. These data sequences must have similar features as the measured traffic. Exact methods for generating synthetic sequences from Fractional Gaussian Noise (FGN) and Fractional Autoregressive Integrated Moving-Average models are not appropriate for long traces.; A fast method to generate self-similar sequences is developed. This method uses a linear function of the frequency to compute the power spectrum of FGN. The algorithm is based on synthesizing sample paths that have the same power spectrum as FGN. The amplitude spectrum is obtained from a synthetic series of the power spectrum. On the other hand, an artificial phase is added accordingly. An inverse-Fast Fourier Transform (FFT) is used to get the corresponding time sequence. Because the Discrete Time Fourier Transform and its inverse can be rapidly computed using the FFT algorithm, this method is known as the FFT method of synthesizing FGN.; It is shown that a linear approximation can be used to determine the power spectrum of FGN. This linear approximation reduces the complexity of the calculation without compromising the accuracy. A statistical analysis of the synthesized sequences is performed to evaluate the quality of the generated series. A fast method to estimate the Hurst parameter, based on an iterative procedure, is proposed and evaluated.; The multiplexing of self-similar traffic using superposition is discussed and analyzed. Additionally, an algorithm to detect the change points in the value of the Hurst parameter is developed.; Finally, queueing simulations, using real and synthetic traffic, are performed and discussed.