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Change point problem for Markovian arrival queueing models: Bayes factor approach

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  • Saroja Kumar Singh

    (Sambalpur University
    Central University of Odisha)

Abstract

This paper considers two Markovian arrival single server queueing models, namely M/M/1 and $$M/E_r/1$$ M / E r / 1 . Under the steady state condition, we observe the number of customer present at different time points for the M/M/1 queue while in case of an $$M/E_r/1$$ M / E r / 1 queue we consider the number of arrivals during the service time of a customer. A Bayesian approach is applied to study the change point problems. Testing of hypothesis for change versus no-change is carried out using predictive distributions. Further, Bayes factors are derived for change versus no-change for both the M/M/1 and $$M/E_r/1$$ M / E r / 1 queueing models under natural conjugate beta prior distribution. At last, numerical results are provided for the illustration.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:ijsaem:v:13:y:2022:i:6:d:10.1007_s13198-022-01750-x
    DOI: 10.1007/s13198-022-01750-x
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Bradley P. Carlin & Alan E. Gelfand & Adrian F. M. Smith, 1992. "Hierarchical Bayesian Analysis of Changepoint Problems," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(2), pages 389-405, June.
    4. 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.
    5. 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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