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A Queueing System in Which Customers Require a Random Number of Servers

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  • Linda Green

    (Columbia University, New York, New York)

Abstract

We consider a multiserver queueing system in which customers request service from a random number of identical servers. In contrast to batch arrival queues, customers cannot begin service until all required servers are available. Servers assigned to the same customer may free separately. For this model, we derive the steady-state distribution for waiting time, the distribution of busy servers, and other important measures. Sufficient conditions for the existence of a steady-state distribution are also obtained.

Suggested Citation

  • Linda Green, 1980. "A Queueing System in Which Customers Require a Random Number of Servers," Operations Research, INFORMS, vol. 28(6), pages 1335-1346, December.
    • Handle: RePEc:inm:oropre:v:28:y:1980:i:6:p:1335-1346
    DOI: 10.1287/opre.28.6.1335
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    Cited by:

    1. 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.
    2. Alexander Dudin & Olga Dudina & Sergei Dudin & Konstantin Samouylov, 2021. "Analysis of Multi-Server Queue with Self-Sustained Servers," Mathematics, MDPI, vol. 9(17), pages 1-18, September.
    3. L. G. Afanaseva & S. A. Grishunina, 2020. "Stability conditions for a multiserver queueing system with a regenerative input flow and simultaneous service of a customer by a random number of servers," Queueing Systems: Theory and Applications, Springer, vol. 94(3), pages 213-241, April.
    4. Linda V. Green & Peter J. Kolesar, 2004. "ANNIVERSARY ARTICLE: Improving Emergency Responsiveness with Management Science," Management Science, INFORMS, vol. 50(8), pages 1001-1014, August.
    5. 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.
    6. Mariana Olvera-Cravioto & Octavio Ruiz-Lacedelli, 2021. "Stationary Waiting Time in Parallel Queues with Synchronization," Mathematics of Operations Research, INFORMS, vol. 46(1), pages 1-27, February.
    7. 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.
    8. Dijk, N.M. van & Smeitink, E., 1988. "A non-exponential queueing system with batch servicing," Serie Research Memoranda 0013, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.

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