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Queues in Which Customers Receive Simultaneous Service from a Random Number of Servers: A System Point Approach

Author

Listed:
  • Percy H. Brill

    (University of Waterloo)

  • Linda Green

    (Columbia University)

Abstract

We examine a multi-server queueing system with Poisson arrivals in which customers require simultaneous service from a random number of servers. Servers assigned to the same customer begin and end service concurrently. Service times are, in general, assumed to be exponentially distributed. A system point approach is presented as a framework for obtaining the waiting time distribution for each customer type. Explicit solutions are derived for the two-server system.

Suggested Citation

  • Percy H. Brill & Linda Green, 1984. "Queues in Which Customers Receive Simultaneous Service from a Random Number of Servers: A System Point Approach," Management Science, INFORMS, vol. 30(1), pages 51-68, January.
    • Handle: RePEc:inm:ormnsc:v:30:y:1984:i:1:p:51-68
    DOI: 10.1287/mnsc.30.1.51
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    Citations

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    Cited by:

    1. Isaac Grosof & Mor Harchol-Balter & Alan Scheller-Wolf, 2022. "WCFS: a new framework for analyzing multiserver systems," Queueing Systems: Theory and Applications, Springer, vol. 102(1), pages 143-174, October.
    2. Michael Dreyfuss & Yair Y. Shaki & Uri Yechiali, 2022. "The double-space parking problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(4), pages 1131-1147, December.
    3. Mor Harchol-Balter, 2022. "The multiserver job queueing model," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 201-203, April.
    4. Alexander Rumyantsev & Evsey Morozov, 2017. "Stability criterion of a multiserver model with simultaneous service," Annals of Operations Research, Springer, vol. 252(1), pages 29-39, May.
    5. Larisa Afanaseva & Elena Bashtova & Svetlana Grishunina, 2020. "Stability Analysis of a Multi-server Model with Simultaneous Service and a Regenerative Input Flow," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1439-1455, December.
    6. Gregory Dobson & Hsiao-Hui Lee & Arvind Sainathan & Vera Tilson, 2012. "A Queueing Model to Evaluate the Impact of Patient "Batching" on Throughput and Flow Time in a Medical Teaching Facility," Manufacturing & Service Operations Management, INFORMS, vol. 14(4), pages 584-599, October.
    7. Ansari, Sardar & Yoon, Soovin & Albert, Laura A., 2017. "An approximate hypercube model for public service systems with co-located servers and multiple response," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 103(C), pages 143-157.
    8. Mor Harchol-Balter, 2021. "Open problems in queueing theory inspired by datacenter computing," Queueing Systems: Theory and Applications, Springer, vol. 97(1), pages 3-37, February.

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