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Evaluating the Overflow Probability Using the Infinite Queue

Author

Listed:
  • Hirotaka Sakasegawa

    (School of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169, Japan)

  • Masakiyo Miyazawa

    (Department of Information Sciences, Science University of Tokyo, Noda City, Chiba 278, Japan)

  • Genji Yamazaki

    (Department of Engineering Management, Tokyo Metropolitan Institute of Technology, Hino City, Tokyo 191, Japan)

Abstract

This paper presents an approximation formula for the overflow probability for GI/GI/c(N) queues in terms of a queue-length distribution for the corresponding GI/GI/c(\infty ) queues, where N is the total capacity of the system. The approximation is based on the conservation law, and on assumptions which might be acceptable if N \gg c. The authors' approximation formula is numerically examined for various phase-type GI/GI/c(N) queues and the results show that the approximation is very good for practical parameter settings. The authors' approximation stands merely on a stationarity assumption. Therefore, it is also expected to be good for G/G/c(N) queues with a large N.

Suggested Citation

  • Hirotaka Sakasegawa & Masakiyo Miyazawa & Genji Yamazaki, 1993. "Evaluating the Overflow Probability Using the Infinite Queue," Management Science, INFORMS, vol. 39(10), pages 1238-1245, October.
    • Handle: RePEc:inm:ormnsc:v:39:y:1993:i:10:p:1238-1245
    DOI: 10.1287/mnsc.39.10.1238
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    Cited by:

    1. 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.

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