Synthesis of fractional gaussian noise using linear approximation for generating self-similar network traffic

Abstract

The present paper focuses on self-similar network traffic generation. Network traffic modeling studies the generation of synthetic sequences. The generated sequences must have similar features to the measured traffic. Exact methods for generating self-similar sequences are not appropriate for long traces. Our main objective in the present paper is to improve the efficiency of Paxson's method for synthesizing self-similar network traffic. Paxson's method uses a fast, approximate synthesis for the power spectrum of the FGN and uses the inverse Fourier transform to obtain the time-domain sequences. We demonstrate that a linear approximation can be used to determine the power spectrum of the FGN. This linear approximation reduces the complexity of the computation without compromising the accuracy in synthesizing the power spectrum of the FGN. Our results show that long traces can be generated in much less time. To compare our method with existing ones, we will measure the rurming time in generating long and short sample paths from the FGN. We will also conduct experiments to show that Our method can generate selfsimilar traffic for specified Hurst parameters with high accuracy.

Two approximation methods to synthesize the power spectrum of fractional Gaussian noise

“…Following the notation of (3), Ledesma and Liu (2000) showed that it is possible to get an accurate approximation by keeping the first two terms in Eq. (2).…”

“…Using Leibnitz's rule to derive under the integral sign (Spiegel and Liu, 1998;Ledesma and Liu, 2000) we obtain…”

“…An expression for G(H ) when H = 0.5 was found by Ledesma and Liu (2000). Despite the complexity of (10) and (11), the FOA method is very efficient due to the fact that the computation of F (H ) and G(H ) is not a function of .…”

“…Applying Leibnitz's rule to (15), using (14), and after some algebra (see Ledesma and Liu, 2000), we get a system of equations for m, p and q as shown:…”

Impact of round trip delay self-similarity on TCP performance

“…We set up the simulation environment as illustrated in Fig.2. We assume that RTT is given by FGN(Fractional Gaussian Noise) [16] with mean and variance of 0.05 sec and 0.0015 sec 2 , respectively. FGN can provide a self-similar process according to Hurst parameter.…”