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A duality relation for busy cycles inGI/G/1 queues

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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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Authors and Affiliations

  1. School of Management, The University of Texas at Dallas, P.O. Box 830688, 75083-0688, Richardson, TX, USA

    Shun-Chen Niu

  2. Department of Computer Science, Florida Atlantic University, P.O. Box 3091, 33431-0991, Boca Raton, FL, USA

    Robert B. Cooper

Authors
  1. Shun-Chen Niu
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  2. Robert B. Cooper
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Niu, SC., Cooper, R.B. A duality relation for busy cycles inGI/G/1 queues. Queueing Syst 8, 203–209 (1991). https://doi.org/10.1007/BF02412250

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  • DOI: https://doi.org/10.1007/BF02412250

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