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Maximum Likelihood Estimates and Confidence Intervals of an M/M/R Queue with Heterogeneous Servers

Author

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  • Tsung-Yin Wang
  • Jau-Chuan Ke
  • Kuo-Hsiung Wang
  • Siu-Chuen Ho

Abstract

This paper studies maximum likelihood estimates as well as confidence intervals of an M/M/R queue with heterogeneous servers under steady-state conditions. We derive the maximum likelihood estimates of the mean arrival rate and the three unequal mean service rates for an M/M/3 queue with heterogeneous servers, and then extend the results to an M/M/R queue with heterogeneous servers. We also develop the confidence interval formula for the parameter ρ, the probability of empty system P 0 , and the expected number of customers in the system E[N], of an M/M/R queue with heterogeneous servers Copyright Springer-Verlag 2006

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:63:y:2006:i:2:p:371-384
    DOI: 10.1007/s00186-005-0047-z
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    Citations

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    Cited by:

    1. Yijie Peng & Michael C. Fu & Bernd Heidergott & Henry Lam, 2020. "Maximum Likelihood Estimation by Monte Carlo Simulation: Toward Data-Driven Stochastic Modeling," Operations Research, INFORMS, vol. 68(6), pages 1896-1912, November.
    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. Chen Li & Junjun Zheng & Hiroyuki Okamura & Tadashi Dohi, 2023. "Performance Evaluation of a Cloud Datacenter Using CPU Utilization Data," Mathematics, MDPI, vol. 11(3), pages 1-16, January.
    4. Aleksandrina Goeva & Henry Lam & Huajie Qian & Bo Zhang, 2019. "Optimization-Based Calibration of Simulation Input Models," Operations Research, INFORMS, vol. 67(5), pages 1362-1382, September.
    5. Dmitry Efrosinin & Anastasia Winkler & Pinzger Martin, 2015. "Confidence Intervals for Performance Measures of M/M/1 Queue with Constant Retrial Policy," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(06), pages 1-12, December.

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