ON THE BEHAVIOR OF THE BATCH ARRIVAL QUEUE M(X)/M/1 DURING A BUSY PERIOD

Abstract

The queue size process (Q(t))0 less-than-or-equal-to t less-than-or-equal-to t0 of the batch arrival queue M(x)/M/1 is studied under the condition that the duration of its busy period is larger than t0. Explicit formulas for the transition probabilities are given and the limiting Markov process for t0 --> infinity is investigated. Several properties of this process are considered. Its transition probabilities and moments and the distribution of its minimum are derived and a functional limit theorem for the rescaled process is proved. (C) 1994 John Wiley & Sons, Inc.