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Interpolation approximations for queues in series

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  • Kan Wu
  • Leon McGinnis

Abstract

Tandem queues constitute a fundamental structure of queueing networks. However, exact queue times in tandem queues are notoriously difficult to compute except for some special cases. Several approximation schemes that are based on mathematical assumptions that enable approximate analyses of tandem queues have been reported in the literature. This article proposes an approximation approach that is based on observed properties of the behavior of tandem queues: the intrinsic gap and intrinsic ratio. The approach exploits the nearly linear and heavy-traffic properties of the intrinsic ratio, which appear to hold in realistic production situations. The proposed approach outperforms existing approximation methods across a broad range of examined cases. It is also demonstrated that the proposed approach has the potential when applied to historical data to achieve accurate mean queue time estimates in practical production environments.[Supplemental materials are available for this article. Go to the publisher's online edition of IIE Transactions to view the supplemental file.]

Suggested Citation

  • Kan Wu & Leon McGinnis, 2013. "Interpolation approximations for queues in series," IISE Transactions, Taylor & Francis Journals, vol. 45(3), pages 273-290.
    • Handle: RePEc:taf:uiiexx:v:45:y:2013:i:3:p:273-290
    DOI: 10.1080/0740817X.2012.682699
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    Citations

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    Cited by:

    1. Maddah, Bacel & Nasr, Walid W. & Charanek, Ali, 2017. "A multi-station system for reducing congestion in high-variability queues," European Journal of Operational Research, Elsevier, vol. 262(2), pages 602-619.
    2. Wu, Kan, 2014. "Taxonomy of batch queueing models in manufacturing systems," European Journal of Operational Research, Elsevier, vol. 237(1), pages 129-135.
    3. Morabito, Reinaldo & de Souza, Mauricio C. & Vazquez, Mariana, 2014. "Approximate decomposition methods for the analysis of multicommodity flow routing in generalized queuing networks," European Journal of Operational Research, Elsevier, vol. 232(3), pages 618-629.
    4. Kurz, Julian, 2016. "Capacity planning for a maintenance service provider with advanced information," European Journal of Operational Research, Elsevier, vol. 251(2), pages 466-477.
    5. Kan Wu & Sandeep Srivathsan & Yichi Shen, 2018. "Three-moment approximation for the mean queue time of a GI/G/1 queue," IISE Transactions, Taylor & Francis Journals, vol. 50(2), pages 63-73, February.
    6. Wu, Kan & Zhao, Ning, 2015. "Dependence among single stations in series and its applications in productivity improvement," European Journal of Operational Research, Elsevier, vol. 247(1), pages 245-258.

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