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.

In this paper I will review and illustrate some large deviation results for queues with interacting traffic, both for shared buffer and shared capacity models. These results are examples of a general scheme which can be applied to an endless variety of network problems where the goal is to establish probability approximations for aspects of a system (such as queue lengths) under very general ergodicity and mixing assumptions about the network inputs. 1 To appear in the Proceedings of the Royal Statistical Society Research Workshop on Stochastic Networks, Edinburgh, 1995. 1 Introduction In this paper I will review and illustrate some large deviation results for queues with interacting traffic, both for shared buffer and shared capacity models. These results are examples of a general scheme which can be applied to an endless variety of network problems where the goal is to establish probability approximations for aspects of a system (such as queue lengths) under very general ergodici...

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