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A factorization property for BMAP/G/1 vacation queues under variable service speed

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  • Jung Baek
  • Ho Lee
  • Se Lee
  • Soohan Ahn

Abstract

This paper proposes a simple factorization principle that can be used efficiently and effectively to derive the vector generating function of the queue length at an arbitrary time of the BMAP/G/1/ queueing systems under variable service speed. We first prove the factorization property. Then we provide moments formula. Lastly we present some applications of the factorization principle. Copyright Springer Science+Business Media, LLC 2008

Suggested Citation

  • Jung Baek & Ho Lee & Se Lee & Soohan Ahn, 2008. "A factorization property for BMAP/G/1 vacation queues under variable service speed," Annals of Operations Research, Springer, vol. 160(1), pages 19-29, April.
    • Handle: RePEc:spr:annopr:v:160:y:2008:i:1:p:19-29:10.1007/s10479-007-0292-z
    DOI: 10.1007/s10479-007-0292-z
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    References listed on IDEAS

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    1. Uri Yechiali, 1973. "A Queuing-Type Birth-and-Death Process Defined on a Continuous-Time Markov Chain," Operations Research, INFORMS, vol. 21(2), pages 604-609, April.
    2. M. Eisen & M. Tainiter, 1963. "Stochastic Variations in Queuing Processes," Operations Research, INFORMS, vol. 11(6), pages 922-927, December.
    3. Peter Purdue, 1974. "The M / M /1 Queue in a Markovian Environment," Operations Research, INFORMS, vol. 22(3), pages 562-569, June.
    4. Ho Woo Lee & Boo Yong Ahn, 2002. "Operational behavior of the MAP / G / 1 queue under N -policy with a single vacation and set-up," International Journal of Stochastic Analysis, Hindawi, vol. 15, pages 1-30, January.
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    Citations

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    Cited by:

    1. Jung Baek & Ho Lee & Se Lee & Soohan Ahn, 2013. "A MAP-modulated fluid flow model with multiple vacations," Annals of Operations Research, Springer, vol. 202(1), pages 19-34, January.
    2. Souvik Ghosh & A. D. Banik, 2018. "Computing conditional sojourn time of a randomly chosen tagged customer in a $$\textit{BMAP/MSP/}1$$ BMAP / MSP / 1 queue under random order service discipline," Annals of Operations Research, Springer, vol. 261(1), pages 185-206, February.
    3. Wojciech M. Kempa, 2016. "Transient workload distribution in the $$M/G/1$$ M / G / 1 finite-buffer queue with single and multiple vacations," Annals of Operations Research, Springer, vol. 239(2), pages 381-400, April.

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