Internet traffic exhibits self-similarity and longrange 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 the LRD traffic series or, more generally, the exponent α of data with 1/fα(α ≥ 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 deter-ministic 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.

Internet traffic exhibits self-similarity and long-range dependence (LRD) on various time scales. In this paper, we propose the use of modified allan variance (MAVAR) and modified Hadamard variance (MHVAR) for the estimation of the Hurst parameterHof LRD traffic series, or more generally, the exponent$\alpha$of data with$1/f^\alpha$$(\alpha \ge 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 a few times and with little detail so far.

Internet traffic exhibits self-similarity and long-range dependence (LRD) on various time scales. In this paper, we propose to use the Modified Hadamard Variance (MHVAR), a time-domain measure for high-resolution spectral analysis, to estimate the Hurst parameter H of LRD traffic data series or, more generally, the exponent α of traffic series with 1/fα power-law spectrum. MHVAR generalizes the principle of the Modified Allan Variance (MAVAR), a well-known tool widely used since 1981 for frequency stability characterization, to higher-order differences of input data; in our knowledge, it has been mentioned in literature only few times and with little detail so far. The behaviour of MHVAR with power-law random processes and some common deterministic signals (viz. drifts, sine waves, steps) is studied. The MHVAR performance in estimating H is evaluated by analysis and simulation, comparing it to the wavelet Logscale Diagram (LD) and to MAVAR. Extensive simulations show that MHVAR has highest accuracy and confidence in fractional-noise parameter estimation, even slightly better than MAVAR. Moreover, MHVAR features a number of other advantages, which make it useful to complement other established techniques such as MAVAR and LD. Finally, MHVAR and LD are also applied to a real IP traffic trace.