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We consider the discrete-time GeoX/G/1 queue under N-policy with single and multiple vacations. In this queueing system, the server takes multiple vacations and a single vacation whenever the system becomes empty and begins to serve customers only if the queue length is at least a predetermined threshold value N. Using the well-known property of stochastic decomposition, we derive the stationary queue-length distributions for both vacation models in a simple and unified manner. In addition, we derive their busy as well as idle-period distributions. Some classical vacation models are considered as special cases

journal of applied mathematics

On the Discrete-Time<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:msup><mml:mrow><mml:mtext>Geo</mml:mtext></mml:mrow><mml:mrow><mml:mi>X</mml:mi></mml:mrow></mml:msup><mml:mo>/</mml:mo><mml:mi>G</mml:mi><mml:mo>/</mml:mo><mml:mn>1</mml:mn></mml:math>Queues under<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:math>-Policy with Single and Multiple Vacations

On the Discrete-TimeGeoX/G/1Queues underN-Policy with Single and Multiple Vacations