Exact Relation between Loss Probability and Queue Length in an Atm Multiplexer with Correlated Arrivals and Periodic Vacations

This paper considers discrete-time single-server queueing systems where the arrivals of cells are a timecorrelated arrival process and the service for cells is done every R slots. In particular, the arrivals is governed by a stationary Markov chain, where no arrivals are assumed to occur only when the Markov chain is in a particular state. A typical example of the arrival processes satisfying the above assumption is a superposed arrival process of heterogeneous on-o sources and Bernoulli sources, where the on-periods of the on-o sources have arbitrary distributions and the o -periods of the on-o sources are geometrically distributed. For such queueing systems, we develop two new numerical methods to estimate the loss probability. The numerical methods exploit an exact relation between the loss probability in a nite-bu er queue and the queue length distribution in the corresponding in nite-bu er queue. The exact relation enable us to e ciently compute the loss probability with su cient accuracy, since the asymptotic or exact queue length distribution in the in nite-bu er queue can be e ciently estimated by stable formulas.