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A new look at a smart polling model

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  • Brian Fralix

    (Clemson University)

Abstract

We analyze a Markovian smart polling model, which is a special case of the smart polling models studied in the work of Boon et al. (Queueing Syst 66:239–274, 2010), as well as a generalization of the gated M / M / 1 queue considered in Resing and Rietman (Stat Neerlandica 58:97–110, 2004). We first derive tractable expressions for the stationary distribution (when it exists) as well as the Laplace transforms of the transition functions of this polling model—while further assuming the system is empty at time zero—and we also present simple necessary and sufficient conditions for ergodicity of the smart polling model. Finally, we conclude the paper by briefly explaining how these techniques can be used to study other interesting variants of this smart polling model.

Suggested Citation

  • Brian Fralix, 2018. "A new look at a smart polling model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(3), pages 339-367, December.
    • Handle: RePEc:spr:mathme:v:88:y:2018:i:3:d:10.1007_s00186-018-0638-0
    DOI: 10.1007/s00186-018-0638-0
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    References listed on IDEAS

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    1. Fralix, Brian, 2015. "When are two Markov chains similar?," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 199-203.
    2. Jacques Resing & Ronald Rietman, 2004. "The M/M/1 queue with gated random order of service," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(1), pages 97-110, February.
    3. Joseph Abate & Ward Whitt, 1995. "Numerical Inversion of Laplace Transforms of Probability Distributions," INFORMS Journal on Computing, INFORMS, vol. 7(1), pages 36-43, February.
    4. Jori Selen & Brian Fralix, 2017. "Time-dependent analysis of an M / M / c preemptive priority system with two priority classes," Queueing Systems: Theory and Applications, Springer, vol. 87(3), pages 379-415, December.
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    Cited by:

    1. Brian Fralix, 2022. "Stationary distributions and the random-product representation," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 193-195, April.

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