Asymptotic Behavior of a Multiplexer Fed by a Long-range Dependent Process

In this paper we study the asymptotic behavior of the tail of the stationary backlog distribution in a single server queue with constant service capacity c, fed by the so-called M=G=1 input processs or Cox input processs. Asymptotic lower bounds are obtained for any distribution G and asymptotic upper bounds are derived when G is a subexponential distribution. We nd the bounds to be tight in some instances, e.g., G corresponding to either the Pareto or lognormal distribution and c ? < 1, where is the arrival rate to the buuer. Any opinions, ndings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reeect the views of the National Science Foundation.