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

Experimental measurements show that Internet traffic exhibits self-similarity and long-range dependence (LRD). A delicate issue is the estimation of traffic statistical quantities that characterize self-similarity and LRD, such as the Hurst parameter H. In this paper, we propose to use the modified Allan variance (MAVAR), a well-known time-domain tool originally studied for frequency stability characterization, for estimating the power-law spectrum and thus the H parameter of LRD traffic time series. This novel method is validated by comparison with one of the most widely adopted algorithms for analyzing LRD traffic: the log-scale diagram technique, based on wavelet analysis. Both methods are applied to a pseudo-random data series, generated with known values of H. MAVAR exhibits outstanding accuracy in estimating H, better than the classical log-scale method. Finally, both techniques are applied to a real IP traffic trace, providing a further example of the capabilities of MAVAR.