The modified allan variance as time-domain analysis tool for estimating the hurst parameter of long-range dependent traffic

Abstract

Internet traffic exhibits self-similarity and long-range dependence (LRD) on various timescales. A well studied issue is the estimation of statistical parameters characterizing traffic selfsimilarity and LRD, such as the Hurst parameter H. In this paper, we propose to adapt the Modified Allan Variance (MAVAR), a time-domain quantity originally conceived to discriminate fractional noise in frequency stability measurement, to estimate the Hurst parameter of LRD traffic traces and, more generally, to identify fractional noise components in network traffic. This novel method is validated by comparison to one of the best techniques for analyzing self-similar and LRD traffic: the logscale diagram based on wavelet analysis. Both methods are applied to pseudo-random LRD data series, generated with assigned values of H. The superior spectral sensitivity of MAVAR achieves outstanding accuracy in estimating H, even better than the logscale method. The behaviour of MAVAR with most common deterministic signals that yield nonstationarity in data under analysis is also studied. Finally, both techniques are applied to a real IP traffic trace, providing a sound example of the usefulness of MAVAR also in traffic characterization, to complement other established techniques as the logscale method. NoteThis paper is based in part on ideas presented in the preliminary version "The Modified Allan Variance as Time-Domain Analysis Tool for Estimating the Hurst Parameter of Long-Range Dependent Traffic", by S. Bregni and L.

Improved Estimation of the Hurst Parameter of Long-Range Dependent Traffic Using the Modified Hadamard Variance

“…Although MAVAR proved very sensitive and robust in fractional-noise parameter estimation [6] [7], yet requiring lightweight computational effort, we extended our scope of research studying other variances with even higher spectral resolution, aiming at further improving the accuracy of estimation of H and γ, but still with reasonable complexity. In this section, the most interesting variances considered in our study, by analysis and simulation, are overviewed.…”

“…In this work, we extended the scope of research [6], investigating the properties of other time-domain variances designed after AVAR, with the aim at further improving the accuracy of estimation of H and γ. Then, a Modified Hadamard Variance (MHVAR) is studied by analysis and simulation.…”

“…MAVAR was designed with the goal of discriminating noise types with power-law spectrum (i.e., in broad terms, fractional noise) recognized very commonly in frequency sources. MAVAR has been demonstrated to feature superior spectral sensitivity and accuracy in fractional-noise parameter estimation, coupled with robustness against nonstationarity in data analyzed [6] [7]. MAVAR was successfully applied to real network traffic analysis, allowing to identify fractional noise in experimental results [6][7] [13].…”

“…The MHVAR method has been applied to pseudo-random LRD data series and evaluated by comparison to the well-established logscale diagram (LD) technique based on wavelet analysis [2][4] and to the MAVAR method previously proposed in [6] [7]. Moreover, the behaviour of MHVAR with some deterministic signals that yield nonstationarity in data under analysis is addressed.…”

“…In previous papers [6] [7], the Modified Allan Variance (MAVAR) was introduced as traffic analysis tool for accurate estimation of H and γ. MAVAR is a well-known time-domain quantity, originally conceived in 1981 for frequency stability characterization of precision oscillators [8] [11] by modifying the definition of the Allan Variance (AVAR) recommended by IEEE in 1971 [12]. MAVAR was designed with the goal of discriminating noise types with power-law spectrum (i.e., in broad terms, fractional noise) recognized very commonly in frequency sources.…”