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Optimal Workload Allocation in Open Networks of Multiserver Queues

Author

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  • Joel M. Calabrese

    (Department of Business Analysis and Computing Systems, San Francisco State University, San Francisco, California 94132)

Abstract

In this paper, we examine the general problem of workload allocation in an open Jackson network of multiserver queues. We show that use of the open network model leads to a separable, convex formulation of the problem with relatively simple optimality conditions. Using these conditions, we prove in general that server groups with the same number of servers should be loaded equally and larger groups should be loaded more heavily than smaller groups. It is also shown that server pooling, combining servers into larger groups, will always reduce congestion and/or increase throughput. We discuss the significance of our results for job shop applications and also for the concept of a production bottleneck. In systems with an unbalanced configuration of servers, traditional, deterministic bottleneck analysis is distinctly nonoptimal; our results provide a simple way to locate production bottlenecks in shops with significant queueing effects.

Suggested Citation

  • Joel M. Calabrese, 1992. "Optimal Workload Allocation in Open Networks of Multiserver Queues," Management Science, INFORMS, vol. 38(12), pages 1792-1802, December.
    • Handle: RePEc:inm:ormnsc:v:38:y:1992:i:12:p:1792-1802
    DOI: 10.1287/mnsc.38.12.1792
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    Citations

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    Cited by:

    1. Benjaafar, Saifallah, 1996. "Modeling and analysis of machine sharing in manufacturing systems," European Journal of Operational Research, Elsevier, vol. 91(1), pages 56-73, May.
    2. Frank Karsten & Marco Slikker & Geert-Jan van Houtum, 2015. "Resource Pooling and Cost Allocation Among Independent Service Providers," Operations Research, INFORMS, vol. 63(2), pages 476-488, April.
    3. Nur Sunar & Yichen Tu & Serhan Ziya, 2021. "Pooled vs. Dedicated Queues when Customers Are Delay-Sensitive," Management Science, INFORMS, vol. 67(6), pages 3785-3802, June.
    4. Avishai Mandelbaum & Martin I. Reiman, 1998. "On Pooling in Queueing Networks," Management Science, INFORMS, vol. 44(7), pages 971-981, July.
    5. Brooks, James D. & Kar, Koushik & Mendonça, David J., 2016. "Allocation of flows in closed bipartite queueing networks," European Journal of Operational Research, Elsevier, vol. 255(2), pages 333-344.
    6. Xiuli Chao & Carlton Scott, 2000. "Several Results on the Design of Queueing Systems," Operations Research, INFORMS, vol. 48(6), pages 965-970, December.
    7. Benjaafar, Saifallah, 1995. "Performance bounds for the effectiveness of pooling in multi-processing systems," European Journal of Operational Research, Elsevier, vol. 87(2), pages 375-388, December.
    8. Suri Gurumurthi & Saif Benjaafar, 2004. "Modeling and analysis of flexible queueing systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(5), pages 755-782, August.
    9. 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.
    10. Andradóttir, Sigrún & Ayhan, Hayriye & Down, Douglas G., 2017. "Resource pooling in the presence of failures: Efficiency versus risk," European Journal of Operational Research, Elsevier, vol. 256(1), pages 230-241.
    11. Nilay Tanık Argon & Sigrún Andradóttir, 2017. "Pooling in tandem queueing networks with non-collaborative servers," Queueing Systems: Theory and Applications, Springer, vol. 87(3), pages 345-377, December.
    12. Arie Harel, 2011. "Convexity Results for the Erlang Delay and Loss Formulae When the Server Utilization Is Held Constant," Operations Research, INFORMS, vol. 59(6), pages 1420-1426, December.
    13. 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.
    14. 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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