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A Bayesian inference to estimate change point for traffic intensity in M/M/1 queueing model

Author

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  • Saroja Kumar Singh

    (Sambalpur University)

  • Sarat Kumar Acharya

    (Sambalpur University)

Abstract

The paper is concerned with the problem of change point for the inter arrival time distribution for the M/M/1 queueing system by considering the number of customers present in the system. Bayesian estimators of traffic intensities, before the change $$(\rho _1)$$ ( ρ 1 ) and after the change $$(\rho _2)$$ ( ρ 2 ) , and the change point m are derived using the informative as well as non-informative priors under different loss functions. Finally a numerical example along with a practical example is given to illustrate the results.

Suggested Citation

  • Saroja Kumar Singh & Sarat Kumar Acharya, 2022. "A Bayesian inference to estimate change point for traffic intensity in M/M/1 queueing model," OPSEARCH, Springer;Operational Research Society of India, vol. 59(1), pages 166-206, March.
    • Handle: RePEc:spr:opsear:v:59:y:2022:i:1:d:10.1007_s12597-021-00535-3
    DOI: 10.1007/s12597-021-00535-3
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    References listed on IDEAS

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    1. Lee, Chung-Bow, 1998. "Bayesian analysis of a change-point in exponential families with applications," Computational Statistics & Data Analysis, Elsevier, vol. 27(2), pages 195-208, April.
    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. Sarat Kumar Acharya & César Emilio Villarreal-Rodríguez, 2013. "Change point estimation of service rate in an M/M/1/m queue," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 5(1), pages 110-120.
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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. 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.

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