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Bayesian sample size determination in a single-server deterministic queueing system

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  • Singh, Saroja Kumar
  • Acharya, Sarat Kumar
  • Cruz, Frederico R.B.
  • Quinino, Roberto C.

Abstract

Although queueing models in the mathematical field of queueing theory are mainly studied in the steady-state regime and practical applications are interested mostly in queues in transient situations subject to burst arrivals and congestion, their use is still justified as a first step towards a more complex and thorough analysis. In these practical applications, parameters such as the traffic intensity, which is the ratio between the arrival rate and service rate, are unknown and need to be estimated statistically. In this study, a Markovian arrival and deterministic single-server queueing system, known in Kendall notation as an M∕D∕1 queueing model, is considered. This is one of the simplest queueing models with deterministic service time and may be seen as an approximation of a variety of applications in the performance evaluation of production management, telecommunications networks, and other areas. The main goal of this manuscript is to propose a methodology to determine the sample size for an M∕D∕1 queueing system under the Bayesian setup by observing the number of customer arrivals during the service time of a customer. To verify the efficiency and efficacy of the proposed approach, an extensive set of numerical results is presented and discussed.

Suggested Citation

  • Singh, Saroja Kumar & Acharya, Sarat Kumar & Cruz, Frederico R.B. & Quinino, Roberto C., 2021. "Bayesian sample size determination in a single-server deterministic queueing system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 17-29.
    • Handle: RePEc:eee:matcom:v:187:y:2021:i:c:p:17-29
    DOI: 10.1016/j.matcom.2021.02.010
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    References listed on IDEAS

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    1. Saroja Kumar Singh & Sarat Kumar Acharya, 2019. "Equivalence between Bayes and the maximum likelihood estimator in M/M/1 queue," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(19), pages 4780-4793, October.
    2. Amit Choudhury & Arun Borthakur, 2008. "Bayesian inference and prediction in the single server Markovian queue," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 67(3), pages 371-383, April.
    3. E. Rahme & L. Joseph & T. W. Gyorkos, 2000. "Bayesian sample size determination for estimating binomial parameters from data subject to misclassification," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 49(1), pages 119-128.
    4. Sarat Kumar Acharya & Saroja Kumar Singh, 2019. "Asymptotic properties of maximum likelihood estimators from single server queues: A martingale approach," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(14), pages 3549-3557, July.
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    Cited by:

    1. Singh, Saroja Kumar & Cruz, Gabriel M.B. & Cruz, Frederico R.B., 2024. "Change point estimation of service rate in M/M/1/m queues: A Bayesian approach," Applied Mathematics and Computation, Elsevier, vol. 465(C).
    2. 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.
    3. 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.
    4. Gorbunova, A.V. & Lebedev, A.V., 2022. "Nontransitivity of tuples of random variables with polynomial density and its effects in Bayesian models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 181-192.

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