Predicting Quality of Service for Traffic with Long-Range Fluctuations

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