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An MX/GI/1/N finite capacity queue with close-down time, vacation time and exhaustive service discipline is considered under the partial batch acceptance strategy as well as under the whole batch acceptance strategy. Applying the supplementary variable technique the queue length distribution at an arbitrary instant and at a departure epoch is obtained under both strategies, where no assumption on the batch size distribution is made. The loss probabilities and the Laplace-Stieltjes transforms of the waiting time distribution of the first customer and of an arbitrary customer of a batch are also given. Numerical examples give some insight into the behavior of the system

journal of applied mathematics and stochastic analysis

An <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$M^X /GI/1/N$" id="E1"><mml:mrow><mml:msup><mml:mi>M</mml:mi><mml:mi>X</mml:mi></mml:msup><mml:mo>/</mml:mo><mml:mi>G</mml:mi><mml:mi>I</mml:mi><mml:mo>/</mml:mo><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mi>N</mml:mi></mml:mrow></mml:math> queue with close-down and vacation times

An MX/GI/1/N queue with close-down and vacation times