Real-time estimation of the parameters of long-range dependence

An on-line version of the Abry-Veitch (see IEEE GLOBECOM'98, Sydney, Australia,p.3716-21, 1998) wavelet-based estimator of the Hurst parameter is presented. It has very low memory and computational requirements and scales naturally to arbitrarily high data rates, enabling its use in real-time applications such as admission control, and avoiding the need to store huge data sets for off-line analysis. The performance of the estimator as a function of the length of data processed is demonstrated using simulated data. An implementation for 10-Mb/s Ethernet based on standard hardware supporting sampling rates of 1 data point per millisecond is described, and results of its operation presented, as is an implementation for 155-Mb/s asynchronous transfer mode networks. Finally we illustrate the power of on-line measurements by collecting measurements over a period of five months, and using them to look for diurnal trends in scaling properties of the data.