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Stability of Multiclass Queueing Networks Under Priority Service Disciplines

Author

Listed:
  • Hong Chen

    (Faculty of Commerce and Business Administration, University of British Columbia, Canada)

  • Hanqin Zhang

    (Institute of Applied Mathematics, Academia Sinica, Beijing, China)

Abstract

In this paper, we establish a sufficient condition for the stability of a multiclass fluid network and queueing network under priority service disciplines. The sufficient condition is based on the existence of a linear Lyapunov function, and it is stated in terms of the feasibility of a set of linear inequalities that are defined by network parameters. In all the networks we have tested, this sufficient condition actually gives a necessary and sufficient condition for their stability.

Suggested Citation

  • Hong Chen & Hanqin Zhang, 2000. "Stability of Multiclass Queueing Networks Under Priority Service Disciplines," Operations Research, INFORMS, vol. 48(1), pages 26-37, February.
    • Handle: RePEc:inm:oropre:v:48:y:2000:i:1:p:26-37
    DOI: 10.1287/opre.48.1.26.12456
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    References listed on IDEAS

    as
    1. J. G. Dai & G. Weiss, 1996. "Stability and Instability of Fluid Models for Reentrant Lines," Mathematics of Operations Research, INFORMS, vol. 21(1), pages 115-134, February.
    2. Hong Chen & Hanqin Zhang, 1997. "Stability of Multiclass Queueing Networks Under FIFO Service Discipline," Mathematics of Operations Research, INFORMS, vol. 22(3), pages 691-725, August.
    3. Bertsimas, Dimitris & Gamarnik, David. & Tsitsiklis, John N., 1995. "Stability conditions for multiclass fluid queueing networks," Working papers 3790-95., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    4. James R. Jackson, 1963. "Jobshop-Like Queueing Systems," Management Science, INFORMS, vol. 10(1), pages 131-142, October.
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    Citations

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    Cited by:

    1. J. G. Dai & O. B. Jennings, 2004. "Stabilizing Queueing Networks with Setups," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 891-922, November.
    2. Bruneel, Herwig & Maertens, Tom & Walraevens, Joris, 2014. "Class clustering destroys delay differentiation in priority queues," European Journal of Operational Research, Elsevier, vol. 235(1), pages 149-158.
    3. Heng-Qing Ye & David D. Yao, 2008. "Heavy-Traffic Optimality of a Stochastic Network Under Utility-Maximizing Resource Allocation," Operations Research, INFORMS, vol. 56(2), pages 453-470, April.
    4. Rosario Delgado, 2010. "State space collapse and stability of queueing networks," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(3), pages 477-499, December.
    5. Itai Gurvich, 2014. "Validity of Heavy-Traffic Steady-State Approximations in Multiclass Queueing Networks: The Case of Queue-Ratio Disciplines," Mathematics of Operations Research, INFORMS, vol. 39(1), pages 121-162, February.
    6. Edvinas Greičius & Saulius Minkevičius, 2017. "Diffusion limits for the queue length of jobs in multi-server open queueing networks," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 27(4), pages 71-84.
    7. Zhao, Yaping & Xu, Xiaoyun & Li, Haidong & Liu, Yanni, 2016. "Prioritized customer order scheduling to maximize throughput," European Journal of Operational Research, Elsevier, vol. 255(2), pages 345-356.
    8. J. G. Dai & Caiwei Li, 2003. "Stabilizing Batch-Processing Networks," Operations Research, INFORMS, vol. 51(1), pages 123-136, February.

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