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Scheduling Networks of Queues: Heavy Traffic Analysis of a Multistation Network with Controllable Inputs

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  • Lawrence M. Wein

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

Abstract

Motivated by a factory scheduling problem, we consider the problem of input control (subject to a specified input mix) and priority sequencing in a multistation, multiclass queueing network with general service time distributions and a general routing structure. The objective is to minimize the long-run expected average number of customers in the system subject to a constraint on the long-run expected average output rate. Under balanced heavy loading conditions, this scheduling problem can be approximated by a control problem involving Brownian motion. Linear programming is used to reduce the workload formulation of this control problem to a constrained singular control problem for a multidimensional Brownian motion. The finite difference approximation method is then used to find a linear programming solution to the latter problem. The solution is interpreted in terms of the original queueing system to obtain an effective scheduling policy. The priority sequencing policy is based on dynamic reduced costs from a linear program, and the workload regulating input policy releases a customer into the system whenever the workload process enters a particular region. An example is provided that illustrates the procedure and demonstrates its effectiveness.

Suggested Citation

  • Lawrence M. Wein, 1992. "Scheduling Networks of Queues: Heavy Traffic Analysis of a Multistation Network with Controllable Inputs," Operations Research, INFORMS, vol. 40(3-supplem), pages 312-334, June.
    • Handle: RePEc:inm:oropre:v:40:y:1992:i:3-supplement-2:p:s312-s334
    DOI: 10.1287/opre.40.3.S312
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    Citations

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    Cited by:

    1. Yoni Nazarathy & Gideon Weiss, 2009. "Near optimal control of queueing networks over a finite time horizon," Annals of Operations Research, Springer, vol. 170(1), pages 233-249, September.
    2. Land, Martin & Gaalman, Gerard, 1996. "Workload control concepts in job shops A critical assessment," International Journal of Production Economics, Elsevier, vol. 46(1), pages 535-548, December.
    3. Kathryn E. Caggiano & John A. Muckstadt & James A. Rappold, 2006. "Integrated Real-Time Capacity and Inventory Allocation for Reparable Service Parts in a Two-Echelon Supply System," Manufacturing & Service Operations Management, INFORMS, vol. 8(3), pages 292-319, August.
    4. Land, Martin J. & Gaalman, Gerard J.C., 1995. "Workload control concepts in job shops: a critical assessment," Research Report 95A42, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    5. Lambrecht, Marc R. & Vandaele, Nico J., 1996. "A general approximation for the single product lot sizing model with queueing delays," European Journal of Operational Research, Elsevier, vol. 95(1), pages 73-88, November.
    6. J. G. Dai & Wuqin Lin, 2005. "Maximum Pressure Policies in Stochastic Processing Networks," Operations Research, INFORMS, vol. 53(2), pages 197-218, April.
    7. Barış Ata, 2006. "Dynamic Control of a Multiclass Queue with Thin Arrival Streams," Operations Research, INFORMS, vol. 54(5), pages 876-892, October.
    8. 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.
    9. repec:dgr:rugsom:95a42 is not listed on IDEAS
    10. Ick-Hyun Nam, 2001. "Dynamic Scheduling for a Flexible Processing Network," Operations Research, INFORMS, vol. 49(2), pages 305-315, April.

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