Compared accuracy evaluation of estimators of traffic long-range dependence

Internet traffic exhibits self-similarity and long-range dependence (LRD). Accurate estimation of statistical parameters characterizing self-similarity and LRD is an important issue, aiming at best modelling traffic e.g. to the purpose of network simulation. Major attention has been devoted to designing algorithms for estimating the Hurst parameter H of LRD traffic series or, more generally, the exponent γ ≥ 0 of data with 1/f^γ power-law spectrum. In this paper, by evaluation on thousands of pseudo-random LRD data series, we compare the H and γ estimation accuracy attained by some of the most widely used methods mentioned above: variance-time plot, R/S statistic, lag-1 autocorrelation, wavelet logscale diagram, Modified Allan and Hadamard Variances. In literature, there are almost no detailed comparison studies on the actual accuracy attained by various methods. Thus, our detailed results will be valuable for those interested to the analysis of traffic or, in general, of power-law data.