Accurate Estimation of the Hurst Parameter of Long-Range Dependent Traffic Using Modified Allan and Hadamard Variances

Internet traffic exhibits self-similarity and long-range dependence (LRD) on various time scales. In this paper, we propose to use the Modified Allan Variance (MAVAR) and a Modified Hadamard Variance (MHVAR) to estimate the Hurst parameter H of LRD traffic series or, more generally, the exponent a of data with fa (a < 0) power-law spectrum. MHVAR generalizes the principle of MAVAR, a time-domain quantity widely used for frequency stability characterization, to higher-order differences of input data. In our knowledge, this MHVAR has been mentioned in literature only few times and with little detail so far. The behaviour of MAVAR and MHVAR with power-law random processes and some common deterministic signals (viz. drifts, sine waves, steps) is studied by analysis and simulation. The MAVAR and MHVAR accuracy in estimating H is evaluated and compared to that of wavelet Logscale Diagram (LD). Extensive simulations show that MAVAR and MHVAR achieve significantly better confidence and no bias in H estimation. Moreover, MAVAR and MHVAR feature a number of other advantages, which make them valuable to complement other established techniques such as LD. Finally, MHVAR and LD are also applied to a real IP traffic trace.