Predicting quality of service for traffic with long-range fluctuations

We discuss the implications of self similar models for the problem of estimating loss probabilities in networks, and their validity. We present the tail asymptotics in a queue serviced at constant rate and whose input process has long-range dependence, for example, fractional Brownian motion (FBM) with Hurst parameter H>1/2. Some heterogeneous superpositions of such sources are also treated. We examine the experimental basis for self-similar modelling. If fluctuations in traffic levels can be accounted for by variations in time-dependent external parameters, rather than statistically through parsimonious modelling by FBM, then quality of service predictions may be achieved by applications of techniques familiar for short-range dependent traffic.