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 the use of modified allan variance (MAVAR) and modified Hadamard variance (MHVAR) for the estimation of the Hurst parameter H of 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.