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The M / M /1 Queue in a Markovian Environment

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  • Peter Purdue

    (University of Kentucky, Lexington, Kentucky)

Abstract

This paper discusses the M / M /1 queue embedded in a Markovian environment (or, subject to extraneous phase changes). It studies the busy period, equilibrium conditions, and emptiness probabilities by using analytic matric functions, and makes comparisons with the work of Neuts and of Naor and Yechiali.

Suggested Citation

  • Peter Purdue, 1974. "The M / M /1 Queue in a Markovian Environment," Operations Research, INFORMS, vol. 22(3), pages 562-569, June.
    • Handle: RePEc:inm:oropre:v:22:y:1974:i:3:p:562-569
    DOI: 10.1287/opre.22.3.562
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    Cited by:

    1. 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.
    2. Kuban Altinel, I. & Ozekici, Suleyman, 1998. "Optimum component test plans for systems with dependent components," European Journal of Operational Research, Elsevier, vol. 111(1), pages 175-186, November.
    3. H. Thorsdottir & I. M. Verloop, 2016. "Markov-modulated M/G/1-type queue in heavy traffic and its application to time-sharing disciplines," Queueing Systems: Theory and Applications, Springer, vol. 83(1), pages 29-55, June.
    4. Gabriel Zayas‐Cabán & Emmett J. Lodree & David L. Kaufman, 2020. "Optimal Control of Parallel Queues for Managing Volunteer Convergence," Production and Operations Management, Production and Operations Management Society, vol. 29(10), pages 2268-2288, October.

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