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Diffusion limits for the queue length of jobs in multi-server open queueing networks

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  • Edvinas Greičius
  • Saulius Minkevičius

Abstract

A mathematical model of a multiserver open queueing network in heavy traffic is developed. This model is that of a multiserver computer system network in heavy traffic. A limit theorem for the length of the queue has been presented.

Suggested Citation

  • 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.
    • Handle: RePEc:wut:journl:v:4:y:2017:p:71-84:id:1303
    DOI: 10.5277/ord170404
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    References listed on IDEAS

    as
    1. Avishai Mandelbaum & Alexander L. Stolyar, 2004. "Scheduling Flexible Servers with Convex Delay Costs: Heavy-Traffic Optimality of the Generalized cμ-Rule," Operations Research, INFORMS, vol. 52(6), pages 836-855, December.
    2. Martin I. Reiman, 1984. "Open Queueing Networks in Heavy Traffic," Mathematics of Operations Research, INFORMS, vol. 9(3), pages 441-458, August.
    3. Hong Chen & Hanqin Zhang, 2000. "Stability of Multiclass Queueing Networks Under Priority Service Disciplines," Operations Research, INFORMS, vol. 48(1), pages 26-37, February.
    4. Sakalauskas, L. L. & Minkevicius, S., 2000. "On the law of the iterated logarithm in open queueing networks," European Journal of Operational Research, Elsevier, vol. 120(3), pages 632-640, February.
    5. Austin J. Lemoine, 1978. "State of the Art--Networks of Queues: A Survey of Weak Convergence Results," Management Science, INFORMS, vol. 24(11), pages 1175-1193, July.
    Full references (including those not matched with items on IDEAS)

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