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

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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

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Authors and Affiliations

  1. Department of Industrial Engineering and Management, National Chiao Tung University, Hsinchu, 300, Taiwan

    Tsung-Yin Wang

  2. Department of statistics, National Taichung Institute of Technology, Taichung, 404, Taiwan

    Jau-Chuan Ke

  3. Department of Applied Mathematics, National Chung-Hsing University, Taichung, 402, Taiwan

    Kuo-Hsiung Wang & Siu-Chuen Ho

Authors
  1. Tsung-Yin Wang
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  2. Jau-Chuan Ke
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  3. Kuo-Hsiung Wang
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  4. Siu-Chuen Ho
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Correspondence to Kuo-Hsiung Wang.

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Wang, TY., Ke, JC., Wang, KH. et al. Maximum Likelihood Estimates and Confidence Intervals of an M/M/R Queue with Heterogeneous Servers. Math Meth Oper Res 63, 371–384 (2006). https://doi.org/10.1007/s00186-005-0047-z

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  • DOI: https://doi.org/10.1007/s00186-005-0047-z

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