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

Abstract

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 ? of traffic series with 1/f? 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.