Abstract
Based on the integral relationship between Brownian motion and fractional Brownian motion, we model a process with long-range dependence, Y, as the output of a time-invariant linear filter applied to a more familiar process X — one that does not have long-range dependence. We develop a general criterion for a broad class of X to satisfy a moderate deviations principle (MDP). Based on the MDP of X, we then establish the MDP for Y. Using this framework, we develop both transient and steady-state results, in terms of the MDP, regarding the asymptotic behavior of queues fed with the long-range dependent input process Y. We study two types of filter models, with bounded and unbounded time intervals, respectively.
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