IDEAS home Printed from https://ideas.repec.org/a/spr/ijsaem/v15y2024i6d10.1007_s13198-024-02250-w.html
   My bibliography  Save this article

Bayesian estimation of finite buffer size in single server Markovian queuing system

Author

Listed:
  • Arpita Basak

    (Gauhati University)

  • Amit Choudhury

    (Gauhati University)

Abstract

For operating any new finite capacity (say K) queuing system in which customers arrive according to a Poisson process and are served by a single server under exponential service time (in Kendall’s notation M/M/1/K system), the assumption of fixing K and estimating the parameter traffic intensity $$\rho$$ ρ , is quite practical. But in situation of any pre-existing M/M/1/K queuing system, it is essential to determine an estimator of K to increase system efficiency for fixed value of $$\rho$$ ρ . This paper therefore considered the problem of estimating the parameter finite buffer (K). A Bayes estimator of K is proposed and compared it with classical estimator based on maximum likelihood principal, under the assumption that $$\rho$$ ρ is known. A simulation study is carried out to establish the efficacy and effectiveness of the proposed approaches. A real life situation is analyzed to illustrate the applicability of the developed algorithms.

Suggested Citation

  • Arpita Basak & Amit Choudhury, 2024. "Bayesian estimation of finite buffer size in single server Markovian queuing system," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 15(6), pages 2366-2373, June.
    • Handle: RePEc:spr:ijsaem:v:15:y:2024:i:6:d:10.1007_s13198-024-02250-w
    DOI: 10.1007/s13198-024-02250-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13198-024-02250-w
    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/s13198-024-02250-w?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. C. Armero & D. Conesa, 1998. "Inference and prediction in bulk arrival queues and queues with service in stages," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 14(1), pages 35-46, March.
    2. Emilio Suyama & Roberto C. Quinino & Frederico R. B. Cruz, 2018. "Simple and Yet Efficient Estimators for Markovian Multiserver Queues," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-7, December.
    3. M. A. C. Almeida & F. R. B. Cruz & F. L. P. Oliveira & G. Souza, 2020. "Bias correction for estimation of performance measures of a Markovian queue," Operational Research, Springer, vol. 20(2), pages 943-958, June.
    4. Shi, Chuan & Gershwin, Stanley B., 2009. "An efficient buffer design algorithm for production line profit maximization," International Journal of Production Economics, Elsevier, vol. 122(2), pages 725-740, December.
    5. Saroja Kumar Singh, 2022. "Change point problem for Markovian arrival queueing models: Bayes factor approach," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(6), pages 2847-2854, December.
    6. Frederico R. B. Cruz & Márcio A. C. Almeida & Marcos F. S. V. D’Angelo & Tom van Woensel, 2018. "Traffic Intensity Estimation in Finite Markovian Queueing Systems," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-15, June.
    Full references (including those not matched with items on IDEAS)

    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. Singh, Saroja Kumar & Acharya, Sarat Kumar & Cruz, F.R.B. & Cançado, André L.F., 2023. "Change point estimation in an M/M/2 queue with heterogeneous servers," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 182-194.
    2. Armero, Carmen & Conesa, David, 2004. "Statistical performance of a multiclass bulk production queueing system," European Journal of Operational Research, Elsevier, vol. 158(3), pages 649-661, November.
    3. M. A. C. Almeida & F. R. B. Cruz & F. L. P. Oliveira & G. Souza, 2020. "Bias correction for estimation of performance measures of a Markovian queue," Operational Research, Springer, vol. 20(2), pages 943-958, June.
    4. Guan Wang & Yang Woo Shin & Dug Hee Moon, 2016. "Comparison of three flow line layouts with unreliable machines and profit maximization," Flexible Services and Manufacturing Journal, Springer, vol. 28(4), pages 669-693, December.
    5. George Liberopoulos, 2020. "Comparison of optimal buffer allocation in flow lines under installation buffer, echelon buffer, and CONWIP policies," Flexible Services and Manufacturing Journal, Springer, vol. 32(2), pages 297-365, June.
    6. Nahas, Nabil & Nourelfath, Mustapha & Gendreau, Michel, 2014. "Selecting machines and buffers in unreliable assembly/disassembly manufacturing networks," International Journal of Production Economics, Elsevier, vol. 154(C), pages 113-126.
    7. Cruz, F.R.B. & Van Woensel, T. & Smith, J. MacGregor, 2010. "Buffer and throughput trade-offs in M/G/1/K queueing networks: A bi-criteria approach," International Journal of Production Economics, Elsevier, vol. 125(2), pages 224-234, June.
    8. Patrik Grznár & Milan Gregor & Štefan Mozol & Martin Krajčovič & Ľuboslav Dulina & Martin Gašo & Michal Major, 2019. "A System to Determine the Optimal Work-in-Progress Inventory Stored in Interoperation Manufacturing Buffers," Sustainability, MDPI, vol. 11(14), pages 1-36, July.
    9. Przemysław Korytkowski & Tomasz Wiśniewski, 2011. "Performance analysis of commercial offset printing under dynamic priority rules," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 21(1), pages 53-64.
    10. repec:cte:wsrepe:ws014126 is not listed on IDEAS
    11. repec:cte:wsrepe:ws013019 is not listed on IDEAS
    12. Puchkova, Alena & McFarlane, Duncan & Srinivasan, Rengarajan & Thorne, Alan, 2020. "Resilient planning strategies to support disruption-tolerant production operations," International Journal of Production Economics, Elsevier, vol. 226(C).
    13. Shi, Chuan & Gershwin, Stanley B., 2016. "Part sojourn time distribution in a two-machine line," European Journal of Operational Research, Elsevier, vol. 248(1), pages 146-158.

    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:ijsaem:v:15:y:2024:i:6:d:10.1007_s13198-024-02250-w. 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.