Recent Bellcore studies have shown that high-speed data traffic exhibits ‘long-range dependence’, characterized by H > 0.5, where H is the Hurst parameter of the traffic. In the wake of those studies, there has been much interest in developing tractable analytical models for traffic with long-range dependence, for use in performance evaluation and traffic engineering. Norros has used a traffic model known as Fractional Brownian Motion (FBM) to derive several analytical results on the behavior of a queue subject to such an arrival process. In this paper, we derive a new class of results, also based on the FBM model, which reveal rather curious and unexpected ‘crossover’ properties of the Hurst parameter of the traffic, as regards its effect on the behavior of queues. These results, together with those of Norros, serve to enhance our understanding of the significance of the Hurst parameter H for traffic engineering. In particular, Krishnan and Meempat have used the crossover property derived here to explain, in part, a gap that existed between the results of two sets of Bellcore studies, one casting doubt on the usefulness of Markovian traffic models and methods when H > 0.5, and the other furnishing an example of successful traffic engineering with Markovian methods for traffic known to have H > 0.5. The results derived here can be used to obtain conservative estimates of the multiplexing gains achieved when independent traffic sources with the same Hurst parameter H are multiplexed for combined transmission. In turn, such estimates yield guidelines for the engineering of ATM links that are subject to traffic with long-range dependence.
