Abstract

The queue length distribution at a random point in time in the stationary BMAP/G/1 queue is shown to be identical to the stationary distribution of a certain imbedded Markov chain related to the corresponding BMAP/G/1 queue with multiple vacations and exhaustive services. This observation leads to an alternative recursion formula to compute the queue length distribution at a random point in time in the stationary BMAP/G/1 queue, which is simpler than the known formula yet numerically stable

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