The Analysis of a Statistical Multiplexer with Nonindependent Arrivals and Errors

Most stochastic models for discrete time statistical multiplexers make the assumption that 1) arrivals are governed by a Bernoulli process and that 2) transmission errors or multiplexer failures are described by an independent error process. We study a multiplexer operating in a two state Markovian environment in which each state is characterized by its own Bernoulli arrival process and independent error process. We derive the probability generating function for the queue length distribution for such a system. We also consider two special cases of this model. One referred to as the saturated arrival model corresponds to a system in which during one of the two states, the saturated state, at least one arrival occurs during each discrete time unit. The other model, the breakdown model, corresponds to a system in which during one of the two states, the breakdown state, the multiplexer is inoperative. For both models, we generalize the analysis to cases in which the durations of the saturated state and breakdown state may take on values described by arbitrary distributions. Finally, we study the effects of different arrival processes and error processes on queue length behavior.