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A new proof of finite moment conditions for GI/G/1 busy periods

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Abstract

A generalization of the GI/G/1 queue is considered where the service time of the nth customer and the inter-arrival time between arrivalsn andn+1 may be dependent random variables. New proofs are obtained of finite moment conditions for busy periods and the ladder epochs of a corresponding random walk. The method of proof, which is much different from the usual ones, directly relates busy period moments to virtual and actual delay moments.

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Authors and Affiliations

  1. Department of Mathematics, Towson State University, 21204, Towson, MD, USA

    Saeed Ghahramani

  2. Department of Industrial Engineering and Operations Research, University of California, 94720, Berkeley, CA, USA

    Ronald W. Wolff

Authors
  1. Saeed Ghahramani
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  2. Ronald W. Wolff
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Ghahramani, S., Wolff, R.W. A new proof of finite moment conditions for GI/G/1 busy periods. Queueing Syst 4, 171–178 (1989). https://doi.org/10.1007/BF01158551

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  • DOI: https://doi.org/10.1007/BF01158551

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