Tail probabilities for a multiplexer with self-similar traffic

We consider the large buffer asymptotics of a multiplexer under two different self-similar traffic input models, viz., the infinite server model of Cox and the fractional Gaussian noise input model. In the former case the tail probabilities for the buffer content (in steady state) are shown to decay at most hyperbolically, while in the latter they are asymptotically Weibullian. Therefore, for given input rate and Hurst parameter, these dissimilar asymptotics result in vastly differing buffer engineering practices, thereby pointing to the inadequacy of the Hurst parameter as the sole parameter to characterize long-range dependence in traffic input models