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On the Optimal Allocation of Servers and Workloads in Closed Queueing Networks

Author

Listed:
  • Yves Dallery

    (Université Pierre et Marie Curie, Paris, France)

  • Kathryn E. Stecke

    (University of Michigan, Ann Arbor, Michigan)

Abstract

In this paper, properties are derived that are useful for characterizing optimal allocations of servers and workloads in single-class, multiserver closed queueing networks (CQNs). The problem is as follows: Suppose a particular workload is allocated to a set of servers within a subnetwork of a CQN. This set of servers is to be partitioned into several multiserver stations. The number of stations, the number of servers, and the workload allocation to each station define a configuration of this subnetwork. Thus, the problem is to determine the best configuration of each subnetwork to maximize the throughput in the original CQN. Decomposition is used to address this problem. Results are obtained for subnetworks in isolation. These results are used to solve the optimal-configuration problem. Applications of the results to design and planning problems of flexible manufacturing are also described.

Suggested Citation

  • Yves Dallery & Kathryn E. Stecke, 1990. "On the Optimal Allocation of Servers and Workloads in Closed Queueing Networks," Operations Research, INFORMS, vol. 38(4), pages 694-703, August.
    • Handle: RePEc:inm:oropre:v:38:y:1990:i:4:p:694-703
    DOI: 10.1287/opre.38.4.694
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    Citations

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    Cited by:

    1. Frenk, J.B.G. & Labbé, M. & van Vliet, M. & Zhang, S., 1994. "Improved algorithms for machine allocation in manufacturing systems," Econometric Institute Research Papers 11742, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    2. Aksin, O. Zeynep & Harker, Patrick T., 2003. "Capacity sizing in the presence of a common shared resource: Dimensioning an inbound call center," European Journal of Operational Research, Elsevier, vol. 147(3), pages 464-483, June.
    3. Xiuli Chao & Liming Liu & Shaohui Zheng, 2003. "Resource Allocation in Multisite Service Systems with Intersite Customer Flows," Management Science, INFORMS, vol. 49(12), pages 1739-1752, December.
    4. H. S. R. Martins & F. R. B. Cruz & A. R. Duarte & F. L. P. Oliveira, 2019. "Modeling and optimization of buffers and servers in finite queueing networks," OPSEARCH, Springer;Operational Research Society of India, vol. 56(1), pages 123-150, March.
    5. Subba Rao, S. & Gunasekaran, A. & Goyal, S. K. & Martikainen, T., 1998. "Waiting line model applications in manufacturing," International Journal of Production Economics, Elsevier, vol. 54(1), pages 1-28, January.
    6. Refael Hassin & Yair Y. Shaki & Uri Yovel, 2015. "Optimal service‐capacity allocation in a loss system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(2), pages 81-97, March.
    7. Bitran, Gabriel R. & Morabito, Reinaldo., 1994. "Open queueing networks : optimization and performance evaluation models for discrete manufacturing systems," Working papers 3743-94., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    8. J. Smith, 2015. "Optimal workload allocation in closed queueing networks with state dependent queues," Annals of Operations Research, Springer, vol. 231(1), pages 157-183, August.

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