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A Transform-Free Approximation for the Finite Capacity M / G / s Queue

Author

Listed:
  • Toshikazu Kimura

    (Hokkaido University, Sapporo, Japan)

Abstract

This paper develops a transform-free approximation for the steady-state queue-length distribution in an M / G / s queue with finite waiting spaces. The approximation is obtained by using a conservation law and some heuristics. It is shown that the approximation is exact for the cases with either no extra waiting space, exponential service-time distribution, or a certain two-parameter family of service-time distributions. It is also shown that the approximation has the same light-traffic properties as the known light-traffic limit theorem for the infinite capacity case when the number of waiting spaces is not less than one.

Suggested Citation

  • Toshikazu Kimura, 1996. "A Transform-Free Approximation for the Finite Capacity M / G / s Queue," Operations Research, INFORMS, vol. 44(6), pages 984-988, December.
    • Handle: RePEc:inm:oropre:v:44:y:1996:i:6:p:984-988
    DOI: 10.1287/opre.44.6.984
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    Cited by:

    1. Dae W. Choi & Nam K. Kim & Kyung C. Chae, 2005. "A Two-Moment Approximation for the GI / G / c Queue with Finite Capacity," INFORMS Journal on Computing, INFORMS, vol. 17(1), pages 75-81, February.
    2. F. R. B. Cruz & A. R. Duarte & G. L. Souza, 2018. "Multi-objective performance improvements of general finite single-server queueing networks," Journal of Heuristics, Springer, vol. 24(5), pages 757-781, October.
    3. Smith, J. MacGregor & Cruz, F.R.B. & van Woensel, T., 2010. "Topological network design of general, finite, multi-server queueing networks," European Journal of Operational Research, Elsevier, vol. 201(2), pages 427-441, March.
    4. Hui-Yu Zhang & Qing-Xin Chen & James MacGregor Smith & Ning Mao & Ai-Lin Yu & Zhan-Tao Li, 2017. "Performance analysis of open general queuing networks with blocking and feedback," International Journal of Production Research, Taylor & Francis Journals, vol. 55(19), pages 5760-5781, October.

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