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Reduction Methods for Tandem Queuing Systems

Author

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  • Henry D. Friedman

    (Sylvania Electronic Systems, Waltham, Massachusetts)

Abstract

A tandem stage queuing system has n stages A 1 , A 2 , …, A n in series, where stage A i consists of m i parallel channels each having the same constant service time s i . In addition, one of the stages may be a single-channel stage A j having variable service times that are always ≧ s i / m i for i ≠ j . Customers arrive at the first stage and proceed through the stages, in order, on a first-come, first-served, unlimited queuing basis. For any sequence of customer arrival times, the time spent in the system by each customer is independent of the order of the stages. It follows that certain steady-state and time- and customer-dependent problems for the system and for its stages, involving waiting time, queue length, and busy period, can for any interarrival distribution be reduced to corresponding problems for a system of fewer stages, possibly a single stage.

Suggested Citation

  • Henry D. Friedman, 1965. "Reduction Methods for Tandem Queuing Systems," Operations Research, INFORMS, vol. 13(1), pages 121-131, February.
    • Handle: RePEc:inm:oropre:v:13:y:1965:i:1:p:121-131
    DOI: 10.1287/opre.13.1.121
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    Cited by:

    1. Michael Vidalis & Stelios Koukoumialos & Alexandros Diamantidis & George Blanas, 2022. "Analysis of a two echelon supply chain with merging suppliers, a storage area and a distribution center with parallel channels," Operational Research, Springer, vol. 22(1), pages 703-740, March.
    2. Papadopoulos, H. T. & Heavey, C., 1996. "Queueing theory in manufacturing systems analysis and design: A classification of models for production and transfer lines," European Journal of Operational Research, Elsevier, vol. 92(1), pages 1-27, July.
    3. Benjamin Avi-Itzhak & Hanoch Levy, 2001. "Buffer Requirements and Server Ordering in a Tandem Queue with Correlated Service Times," Mathematics of Operations Research, INFORMS, vol. 26(2), pages 358-374, May.
    4. 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.
    5. Wu, Kan & McGinnis, Leon, 2012. "Performance evaluation for general queueing networks in manufacturing systems: Characterizing the trade-off between queue time and utilization," European Journal of Operational Research, Elsevier, vol. 221(2), pages 328-339.
    6. Xiuli Chao & Michael Pinedo, 1992. "On reversibility of tandem queues with blocking," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(7), pages 957-974, December.

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