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Brownian Approximations of Multiclass Open-Queueing Networks

Author

Listed:
  • Hong Chen

    (Faculty of Commerce and Business Administration, University of British Columbia, Vancouver, British Columbia, Canada, V6T 1Z2)

  • Xinyang Shen

    (Faculty of Commerce and Business Administration, University of British Columbia, Vancouver, British Columbia, Canada, V6T 1Z2)

  • David D. Yao

    (Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

Abstract

We study a multiclass open-queueing network with a set of single-server stations that operate under a combination of FIFO (first-in-first out) and priority service disciplines, and are subject to random breakdowns. Assuming that the primitive processes---in particular, external arrivals, service requirements, service capacities (up and down times), and the routing mechanism---follow two-moment approximations (based on functional central limit theorems), we develop a semi-martingale reflected Brownian motion (SRBM) approximation for the performance processes such as workload, queue lengths, and sojourn times. We illustrate through numerical examples in comparison against simulation that the SRBM approximation, while not always supported by a limit theorem, exhibits good accuracy in most cases. Through analyzing special networks, we also discuss the existence of the SRBM approximation in relation to the stability and the heavy traffic limits of the networks.

Suggested Citation

  • Hong Chen & Xinyang Shen & David D. Yao, 2002. "Brownian Approximations of Multiclass Open-Queueing Networks," Operations Research, INFORMS, vol. 50(6), pages 1032-1049, December.
    • Handle: RePEc:inm:oropre:v:50:y:2002:i:6:p:1032-1049
    DOI: 10.1287/opre.50.6.1032.349
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    References listed on IDEAS

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    1. J. Michael Harrison & Michael T. Pich, 1996. "Two-Moment Analysis of Open Queueing Networks with General Workstation Capabilities," Operations Research, INFORMS, vol. 44(6), pages 936-950, December.
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    5. J. Michael Harrison & Lawrence M. Wein, 1990. "Scheduling Networks of Queues: Heavy Traffic Analysis of a Two-Station Closed Network," Operations Research, INFORMS, vol. 38(6), pages 1052-1064, December.
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    7. William P. Peterson, 1991. "A Heavy Traffic Limit Theorem for Networks of Queues with Multiple Customer Types," Mathematics of Operations Research, INFORMS, vol. 16(1), pages 90-118, February.
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    Cited by:

    1. Przemysław Korytkowski & Tomasz Wiśniewski, 2011. "Performance analysis of commercial offset printing under dynamic priority rules," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 21(1), pages 53-64.

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