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State space collapse and stability of queueing networks

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  • Rosario Delgado

Abstract

We study the stability of subcritical multi-class queueing networks with feedback allowed and a work-conserving head-of-the-line service discipline. Assuming that the fluid limit model associated to the queueing network satisfies a state space collapse condition, we show that the queueing network is stable provided that any solution of an associated linear Skorokhod problem is attracted to the origin in finite time. We also give sufficient conditions ensuring this attraction in terms of the reflection matrix of the Skorokhod problem, by using an adequate Lyapunov function. State space collapse establishes that the fluid limit of the queue process can be expressed in terms of the fluid limit of the workload process by means of a lifting matrix. Copyright Springer-Verlag 2010

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:72:y:2010:i:3:p:477-499
    DOI: 10.1007/s00186-010-0329-y
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    References listed on IDEAS

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    1. James R. Jackson, 1957. "Networks of Waiting Lines," Operations Research, INFORMS, vol. 5(4), pages 518-521, August.
    2. Jiashan Tang & Yiqiang Zhao, 2008. "Stationary tail asymptotics of a tandem queue with feedback," Annals of Operations Research, Springer, vol. 160(1), pages 173-189, April.
    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.
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