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Scheduling Networks of Queues: Heavy Traffic Analysis of a Multistation Closed Network

Author

Listed:
  • Philippe B. Chevalier

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

  • Lawrence M. Wein

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

Abstract

We consider the problem of finding an optimal dynamic priority sequencing policy to maximize the mean throughput rate in a multistation, multiclass closed queueing network with general service time distributions and a general routing structure. Under balanced heavy loading conditions, this scheduling problem can be approximated by a control problem involving Brownian motion. Although a unique, closed-form solution to the Brownian control problem is not derived, an analysis of the problem leads to an effective static sequencing policy, and to an approximate means of comparing the relative performance of arbitrary static policies. Several examples are provided that illustrate the effectiveness of our procedure.

Suggested Citation

  • Philippe B. Chevalier & Lawrence M. Wein, 1993. "Scheduling Networks of Queues: Heavy Traffic Analysis of a Multistation Closed Network," Operations Research, INFORMS, vol. 41(4), pages 743-758, August.
    • Handle: RePEc:inm:oropre:v:41:y:1993:i:4:p:743-758
    DOI: 10.1287/opre.41.4.743
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    Citations

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    Cited by:

    1. Gregory Dobson & Tolga Tezcan & Vera Tilson, 2013. "Optimal Workflow Decisions for Investigators in Systems with Interruptions," Management Science, INFORMS, vol. 59(5), pages 1125-1141, May.
    2. Martin I. Reiman & Lawrence M. Wein, 1998. "Dynamic Scheduling of a Two-Class Queue with Setups," Operations Research, INFORMS, vol. 46(4), pages 532-547, August.
    3. Barış Ata, 2006. "Dynamic Control of a Multiclass Queue with Thin Arrival Streams," Operations Research, INFORMS, vol. 54(5), pages 876-892, October.
    4. Narahari, Y. & Khan, L. M., 1998. "Asymptotic loss of priority scheduling policies in closed re-entrant lines: A computational study," European Journal of Operational Research, Elsevier, vol. 110(3), pages 585-596, November.
    5. Melanie Rubino & Barış Ata, 2009. "Dynamic Control of a Make-to-Order, Parallel-Server System with Cancellations," Operations Research, INFORMS, vol. 57(1), pages 94-108, February.
    6. Li, Hui & Liu, Liming, 2006. "Production control in a two-stage system," European Journal of Operational Research, Elsevier, vol. 174(2), pages 887-904, October.
    7. Wendell G. Gilland, 2001. "Effective Sequencing Rules for Closed Manufacturing Networks," Operations Research, INFORMS, vol. 49(5), pages 759-770, October.

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