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On the stability of a polling system with an adaptive service mechanism

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  • Natalia Chernova
  • Sergey Foss
  • Bara Kim

Abstract

We consider a single-server cyclic polling system with three queues where the server follows an adaptive rule: if it finds one of queues empty in a given cycle, it decides not to visit that queue in the next cycle. In the case of limited service policies, we prove stability and instability results under some conditions which are sufficient but not necessary, in general. Then we discuss open problems with identifying the exact stability region for models with limited service disciplines: we conjecture that a necessary and sufficient condition for the stability may depend on the whole distributions of the primitive sequences, and illustrate that by examples. We conclude the paper with a section on the stability analysis of a polling system with either gated or exhaustive service disciplines. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Natalia Chernova & Sergey Foss & Bara Kim, 2012. "On the stability of a polling system with an adaptive service mechanism," Annals of Operations Research, Springer, vol. 198(1), pages 125-144, September.
    • Handle: RePEc:spr:annopr:v:198:y:2012:i:1:p:125-144:10.1007/s10479-011-0963-7
    DOI: 10.1007/s10479-011-0963-7
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    References listed on IDEAS

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    1. Hong Chen & Avi Mandelbaum, 1991. "Discrete Flow Networks: Bottleneck Analysis and Fluid Approximations," Mathematics of Operations Research, INFORMS, vol. 16(2), pages 408-446, May.
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    Cited by:

    1. Sergey Foss, 2018. "Comments on: Polling: past, present and perspective," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 374-378, October.
    2. Vladimir Vishnevsky & Olga Semenova, 2021. "Polling Systems and Their Application to Telecommunication Networks," Mathematics, MDPI, vol. 9(2), pages 1-30, January.

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