A duality relation for busy cycles inGI/G/1 queues |
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Authors: | Shun-Chen Niu Robert B. Cooper |
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Affiliation: | (1) School of Management, The University of Texas at Dallas, P.O. Box 830688, 75083-0688 Richardson, TX, USA;(2) Department of Computer Science, Florida Atlantic University, P.O. Box 3091, 33431-0991 Boca Raton, FL, USA |
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Abstract: | Using a generalization of the classical ballot theorem, Niu and Cooper [7] established a duality relation between the joint distribution of several variables associated with the busy cycle inM/G/1 (with a modified first service) and the corresponding joint distribution of several related variables in its dualGI/M/1. In this note, we generalize this duality relation toGI/G/1 queues with modified first services; this clarifies the original result, and shows that the generalized ballot theorem is superfluous for the duality relation. |
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Keywords: | GI/G/1 queue duality busy cycle modified first service |
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