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This paper analyzes a finite buffer size discrete-time Geo/G/1/N queue with multiple working vacations and different input rate. Using supplementary variable technique and embedded Markov chain method, the queue-length distribution solution in the form of formula at arbitrary epoch is obtained. Some performance measures associated with operating cost are also discussed based on the obtained queue-length distribution. Then, several numerical experiments follow to demonstrate the effectiveness of the obtained formulae. Finally, a state-dependent operating cost function is constructed to model an express logistics service center. Regarding the service rate during working vacation as a control variable, the optimization analysis on the cost function is carried out by using parabolic method

discrete dynamics in nature and society

Study on the Queue-Length Distribution in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>G</mml:mi><mml:mi>e</mml:mi><mml:mi>o</mml:mi><mml:mo>/</mml:mo><mml:mi>G</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>M</mml:mi><mml:mi>W</mml:mi><mml:mi>V</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>/</mml:mo><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mi>N</mml:mi></mml:math>Queue with Working Vacations

Study on the Queue-Length Distribution inGeo/G(MWV)/1/NQueue with Working Vacations