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Gated polling with stationary ergodic walking times, Markovian routing and random feedback

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  • Dieter Fiems
  • Eitan Altman

Abstract

We investigate a gated polling system with semi-linear feedback and Markovian routing. We thereby relax the classical independence assumption on the walking times; the walking times constitute a sequence of stationary ergodic random variables. It is shown that the dynamics of this polling system can be described by semi-linear stochastic recursive equations in a Markovian environment. We obtain expressions for the first and second order moments of the workload and queue content at polling instants and for the mean queue content and workload at random instants. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Dieter Fiems & Eitan Altman, 2012. "Gated polling with stationary ergodic walking times, Markovian routing and random feedback," Annals of Operations Research, Springer, vol. 198(1), pages 145-164, September.
    • Handle: RePEc:spr:annopr:v:198:y:2012:i:1:p:145-164:10.1007/s10479-012-1093-6
    DOI: 10.1007/s10479-012-1093-6
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    References listed on IDEAS

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    1. Mandyam M. Srinivasan, 1991. "Nondeterministic Polling Systems," Management Science, INFORMS, vol. 37(6), pages 667-681, June.
    2. Leonard Kleinrock & Hanoch Levy, 1988. "The Analysis of Random Polling Systems," Operations Research, INFORMS, vol. 36(5), pages 716-732, October.
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    Cited by:

    1. Dieter Fiems & Koen De Turck, 2023. "Analysis of Discrete-Time Queues with Branching Arrivals," Mathematics, MDPI, vol. 11(4), pages 1-13, February.
    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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