Accurate estimation of the Hurst parameter of long-range dependent traffic using modified Allan and Hadamard variances

Abstract--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 of data with 1/f ( 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...

• Type: Journal
• Year: 2008
• Where: TCOM
• Authors: Stefano Bregni, Luca Jmoda
• Keywords: LRD Traffic Series, Modified Allan Variance, Modified Hadamard Variance, TCOM 2008