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On the Tail of the Waiting Time in a Markov-Modulated M/G/1 Queue

Author

Listed:
  • Søren Asmussen

    (Department of Mathematical Statistics, University of Lund, Box 118, S-221 00, Lund, Sweden)

  • Colm O'cinneide

    (8 Warfield Street, Montclair, New Jersey 07043)

Abstract

We show that the “exponential decay parameter” of the waiting time in a Markov-modulated M/G /1 queue is no larger than that of the corresponding M/G /1 queue with “averaged” parameters, and we give a necessary and sufficient condition for equality. We also explore the effect of speeding up the modulation process. A key tool is a Markov-modulated fluid model.

Suggested Citation

  • Søren Asmussen & Colm O'cinneide, 2002. "On the Tail of the Waiting Time in a Markov-Modulated M/G/1 Queue," Operations Research, INFORMS, vol. 50(3), pages 559-565, June.
    • Handle: RePEc:inm:oropre:v:50:y:2002:i:3:p:559-565
    DOI: 10.1287/opre.50.3.559.7742
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    References listed on IDEAS

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    1. Asmussen, Søren & Frey, Andreas & Rolski, Tomasz & Schmidt, Volker, 1995. "Does Markov-Modulation Increase the Risk?," ASTIN Bulletin, Cambridge University Press, vol. 25(1), pages 49-66, May.
    2. Antony Svoronos & Linda Green, 1987. "The N‐seasons S‐servers loss system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(4), pages 579-591, August.
    3. Joseph Abate & Gagan L. Choudhury & Ward Whitt, 1995. "Exponential Approximations for Tail Probabilities in Queues, I: Waiting Times," Operations Research, INFORMS, vol. 43(5), pages 885-901, October.
    4. Joseph Abate & Gagan L. Choudhury & Ward Whitt, 1996. "Exponential Approximations for Tail Probabilities in Queues II: Sojourn Time and Workload," Operations Research, INFORMS, vol. 44(5), pages 758-763, October.
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    Cited by:

    1. Pang, Guodong & Zheng, Yi, 2017. "On the functional and local limit theorems for Markov modulated compound Poisson processes," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 131-140.

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