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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
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    References listed on IDEAS

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    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.
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