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 stationar y backlog distribution in a single server queue with constant service capac ity c, fed by the so-called M/G/infinity input process or Cox input process . Asymptotic lower bounds are obtained for any distribution G and asymptoti c upper bounds are derived when G is a subexponential distribution. We find the bounds to be tight in some instances, e.g. when G corresponds to eithe r the Pareto or lognormal distribution and c - rho < 1, where rho is the ar rival rate at the buffer.