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Arranging Queues in Series: A Simulation Experiment

Author

Listed:
  • S. Suresh

    (AT&T Bell Laboratories, Murray Hill, New Jersey 07974)

  • W. Whitt

    (AT&T Bell Laboratories, Murray Hill, New Jersey 07974)

Abstract

For given external arrival process and given service-time distributions, the object is to determine the order of infinite-capacity single-server queues in series that minimizes the long-run average sojourn time per customer. We gain additional insight into this queueing design problem, and congestion in non-Markov open queueing networks more generally, by performing simulations for the case of two queues. For this design problem, we conclude that the key issue is variability: The order tends to matter more when the service-time distributions have significantly different variability, and less otherwise. Arranging the queues in order of increasing service-time variability, using the squared coefficient of variation as a partial characterization of variability, seems to be an effective simple design heuristic. Parametric-decomposition approximations seem to provide relatively good quantitative estimates of how much the order matters.

Suggested Citation

  • S. Suresh & W. Whitt, 1990. "Arranging Queues in Series: A Simulation Experiment," Management Science, INFORMS, vol. 36(9), pages 1080-1091, September.
    • Handle: RePEc:inm:ormnsc:v:36:y:1990:i:9:p:1080-1091
    DOI: 10.1287/mnsc.36.9.1080
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    Cited by:

    1. van den Hout, W.B., 1996. "The power-series algorithm : A numerical approach to Markov processes," Other publications TiSEM ad00ca29-7daf-4bdb-b994-c, Tilburg University, School of Economics and Management.
    2. Dasu, Sriram, 1998. "Class dependent departure process from multiclass phase queues: Exact and approximate analyses," European Journal of Operational Research, Elsevier, vol. 108(2), pages 379-404, July.
    3. Romero-Silva, Rodrigo & Shaaban, Sabry & Marsillac, Erika & Laarraf, Zouhair, 2021. "The impact of unequal processing time variability on reliable and unreliable merging line performance," International Journal of Production Economics, Elsevier, vol. 235(C).
    4. Kim, Sunkyo, 2004. "The heavy-traffic bottleneck phenomenon under splitting and superposition," European Journal of Operational Research, Elsevier, vol. 157(3), pages 736-745, September.

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