Using the Modified Allan Variance for Accurate Estimation of the Hurst Parameter of Long-Range Dependent Traffic

Internet traffic exhibits self-similarity and long-range dependence (LRD) on various time scales. 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. Note This paper is based in part on ideas presented in the preliminary version “The Modified Allan Variance as TimeDomain Analysis Tool for Estimating the Hurst Parameter of Long-Range Dependent Traffic“, by S. Bregni and L. Primerano, appeared in Proc. of IEEE GLOBECOM 2004, Dallas, TX, USA, Dec. 2004. This work was supported in part by the Italian Ministry of Education, University and Research (MIUR) under the research FIRB project TANGO. February 21, 2005 Ver. I – Submitted to IEEE Transactions on Information Theory 1 S. Bregni Using the Modified Allan Variance for Accurate Estimation of the Hurst Parameter of Long-Range Dependent Traffic