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A Single-Server Queue with Markov Modulated Service Times

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  • Yong-Pin Zhou
  • Noah Gans

Abstract

We study an M/MMPP/1 queuing system, where the arrival process is Poisson and service requirements are Markov modulated. When the Markov Chain modulating service times has two states, we show that the distribution of the number-in-system is a superposition of two matrix-geometric series and provide a simple algorithm for computing the rate and coefficient matrices. These results hold for both finite and infinite waiting space systems and extend results obtained in Neuts [5] and Naoumov [4]. Numerical comparisons between the performance of the M/MMPP/1 system and its M/G/1 analogue lead us to make the conjecture that the M/MMPP/1 system performs better if and only if the total switching probabilities between the two states satisfy a simple condition. We give an intuitive argument to support this conjecture.

Suggested Citation

  • Yong-Pin Zhou & Noah Gans, 1999. "A Single-Server Queue with Markov Modulated Service Times," Center for Financial Institutions Working Papers 99-40, Wharton School Center for Financial Institutions, University of Pennsylvania.
    • Handle: RePEc:wop:pennin:99-40
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    File URL: http://fic.wharton.upenn.edu/fic/papers/99/9940.pdf
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    Cited by:

    1. Legros, Benjamin, 2022. "The principal-agent problem for service rate event-dependency," European Journal of Operational Research, Elsevier, vol. 297(3), pages 949-963.
    2. Benjamin Legros, 2022. "The principal-agent problem for service rate event-dependency," Post-Print hal-03605421, HAL.
    3. Dhingra, Vibhuti & Kumawat, Govind Lal & Roy, Debjit & Koster, René de, 2018. "Solving semi-open queuing networks with time-varying arrivals: An application in container terminal landside operations," European Journal of Operational Research, Elsevier, vol. 267(3), pages 855-876.

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