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Change point estimation in an M/M/2 queue with heterogeneous servers

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  • Singh, Saroja Kumar
  • Acharya, Sarat Kumar
  • Cruz, F.R.B.
  • Cançado, André L.F.

Abstract

The change point problem in the inter-arrival time of an M/M/2 queue with heterogeneous servers is studied here. In this model, it is assumed that the queue is in a steady state and that customers are served by the fastest available server and that there is no transfer of customers between servers. Maximum likelihood estimators are deducted for the arrival rates after and before the change point and for the service rates. Monte Carlo simulation results are presented that attest to the effectiveness and efficiency of the deduced estimators.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:212:y:2023:i:c:p:182-194
    DOI: 10.1016/j.matcom.2023.04.022
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    References listed on IDEAS

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    1. 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.
    2. Tsung-Yin Wang & Jau-Chuan Ke & Kuo-Hsiung Wang & Siu-Chuen Ho, 2006. "Maximum Likelihood Estimates and Confidence Intervals of an M/M/R Queue with Heterogeneous Servers," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(2), pages 371-384, May.
    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. Sarat Kumar Acharya & Sara Verónica Rodríguez-Sánchez & César Emilio Villarreal-Rodríguez, 2013. "Maximum likelihood estimates in an M/M/c queue with heterogeneous servers," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 5(4), pages 537-549.
    5. I. V. Basawa & N. U. Prabhu, 1981. "Estimation in single server queues," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 28(3), pages 475-487, September.
    6. 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.
    7. F. R. B. Cruz & M. A. C. Santos & F. L. P. Oliveira & R. C. Quinino, 2021. "Estimation in a general bulk-arrival Markovian multi-server finite queue," Operational Research, Springer, vol. 21(1), pages 73-89, March.
    8. 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.
    9. 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.
    10. 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.
    11. Saroja Kumar Singh & Sarat Kumar Acharya, 2021. "Bernstein-von Mises theorem and Bayes estimation from single server queues," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(2), pages 286-296, January.
    12. 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.
    13. 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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