Self-similar traffic parameter estimation: a semi-parametric periodogram-based algorithm

Abstract

Recent results from packet measurement analysis have shown that packet traffic exhibits fractal properties such as self-similarity (or its concomitant, long-range dependence) which are fundamentally different from features found in circuit switched voice traffic and captured by commonly used packet traffic models such as batch-Poisson and Markov modulated Poisson process (MMPP). These fractal properties are associated with the well-known burstiness of packet traffic, and self-similar traffic models (e.g., fractional Brownian motion (FBM)) permit parsimonious descriptions of packet traffic. The FBM model requires only 3 parameters: mean rate, peakedness (a measure of the fluctuations about the mean rate), and the Hurst parameter (characterizing long-range dependence). From the viewpoint of applying such models in practice, the estimation of these parameters is of crucial importance. We use a semi-parametric periodogram-based algorithm (SPA) to estimate the Hurst parameter and the peakedness. The algorithm is based on the fact that the power spectral density (PSD) of long-range dependent processes obey a power-law near the origin (i.e., 1/f-noise). We apply SPA to estimate the traffic parameters of both synthetically generated FBM traces as well as real Ethernet traces. Our analysis indicates that, compared with other methods SPA offers several advantages: (i) the marginals of the traffic time series are not required to be Gaussian (ii) it is computationally efficient (iii) it can estimate the peakedness factor as well as the Hurst parameter.