IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v88y2018i3d10.1007_s00186-018-0638-0.html
   My bibliography  Save this article

A new look at a smart polling model

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00186-018-0638-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00186-018-0638-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    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. Fralix, Brian, 2015. "When are two Markov chains similar?," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 199-203.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Xiaoyuan Liu & Brian Fralix, 2019. "On Lattice Path Counting and the Random Product Representation, with Applications to the Er/M/1 Queue and the M/Er/1 Queue," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1119-1149, December.
    2. 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.
    3. Dassios, Angelos & Qu, Yan & Zhao, Hongbiao, 2018. "Exact simulation for a class of tempered stable," LSE Research Online Documents on Economics 86981, London School of Economics and Political Science, LSE Library.
    4. Richard L. Warr & Cason J. Wight, 2020. "Error Bounds for Cumulative Distribution Functions of Convolutions via the Discrete Fourier Transform," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 881-904, September.
    5. Yera, Yoel G. & Lillo, Rosa E. & Ramírez-Cobo, Pepa, 2019. "Fitting procedure for the two-state Batch Markov modulated Poisson process," European Journal of Operational Research, Elsevier, vol. 279(1), pages 79-92.
    6. He, Gang & Wu, Wenqing & Zhang, Yuanyuan, 2018. "Analysis of a multi-component system with failure dependency, N-policy and vacations," Operations Research Perspectives, Elsevier, vol. 5(C), pages 191-198.
    7. Shu, Yin & Feng, Qianmei & Liu, Hao, 2019. "Using degradation-with-jump measures to estimate life characteristics of lithium-ion battery," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    8. David H Collins & Richard L Warr & Aparna V Huzurbazar, 2013. "An introduction to statistical flowgraph models for engineering systems," Journal of Risk and Reliability, , vol. 227(5), pages 461-470, October.
    9. C. E. Phelan & D. Marazzina & G. Germano, 2020. "Pricing methods for α-quantile and perpetual early exercise options based on Spitzer identities," Quantitative Finance, Taylor & Francis Journals, vol. 20(6), pages 899-918, June.
    10. Harrison, Peter G., 2024. "On the numerical solution of functional equations with application to response time distributions," Applied Mathematics and Computation, Elsevier, vol. 472(C).
    11. Joseph Abate & Ward Whitt, 1999. "Computing Laplace Transforms for Numerical Inversion Via Continued Fractions," INFORMS Journal on Computing, INFORMS, vol. 11(4), pages 394-405, November.
    12. Dassios, Angelos & Zhang, You You, 2016. "The joint distribution of Parisian and hitting times of the Brownian motion with application to Parisian option pricing," LSE Research Online Documents on Economics 64959, London School of Economics and Political Science, LSE Library.
    13. Dirk Becherer & Todor Bilarev & Peter Frentrup, 2018. "Optimal liquidation under stochastic liquidity," Finance and Stochastics, Springer, vol. 22(1), pages 39-68, January.
    14. John F. Shortle & Martin J. Fischer & Percy H. Brill, 2007. "Waiting-Time Distribution of M/D N /1 Queues Through Numerical Laplace Inversion," INFORMS Journal on Computing, INFORMS, vol. 19(1), pages 112-120, February.
    15. Jeffrey P. Kharoufeh & Natarajan Gautam, 2004. "A fluid queueing model for link travel time moments," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(2), pages 242-257, March.
    16. Rama Cont & Sasha Stoikov & Rishi Talreja, 2010. "A Stochastic Model for Order Book Dynamics," Operations Research, INFORMS, vol. 58(3), pages 549-563, June.
    17. Svetlana Boyarchenko & Sergei Levendorskiu{i}, 2024. "Efficient inverse $Z$-transform and Wiener-Hopf factorization," Papers 2404.19290, arXiv.org, revised May 2024.
    18. Corsaro, Stefania & Kyriakou, Ioannis & Marazzina, Daniele & Marino, Zelda, 2019. "A general framework for pricing Asian options under stochastic volatility on parallel architectures," European Journal of Operational Research, Elsevier, vol. 272(3), pages 1082-1095.
    19. Abdel Belkaid & Frederic Utzet, 2017. "Efficient Computation of First Passage Times in Kou’s Jump-diffusion Model," Methodology and Computing in Applied Probability, Springer, vol. 19(3), pages 957-971, September.
    20. Steven Kou & Cindy Yu & Haowen Zhong, 2017. "Jumps in Equity Index Returns Before and During the Recent Financial Crisis: A Bayesian Analysis," Management Science, INFORMS, vol. 63(4), pages 988-1010, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:mathme:v:88:y:2018:i:3:d:10.1007_s00186-018-0638-0. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.