Abstract
We apply the factorization principle to derive the generating function of the queue length and the vector Laplace–Stieltjes transform of the waiting time of a BMAP/G/1 queue. The mean performance measures are provided with a computational experience. Scope and purpose The classical method of obtaining the queue length and waiting time distributions of BMAP/G/1 queues starts with the analysis of the imbedded Markov renewal process at departure epochs. This method is intricate and time consuming when the idle period process is complicated. In this paper, we demonstrate that the factorization property can be applied efficiently and effectively to derive the queue length distributions of BMAP/G/1 queueing systems by avoiding the conventional standard procedures. The approach demonstrated in this paper can be applied to the analysis of many other BMAP/G/1 queueing systems with higher behavioral complexities.
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