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Empirical Bayes estimation for queueing systems and networks

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Abstract

Empirical Bayes estimators are derived for standardM/M/1 queues,M/M/1 queues with state-dependent arrival and service rates, finite capacityM/M/1 queues with state-dependent rates and for open Jackson networks. The asymptotic properties of the empirical Bayes estimators are derived both with respect to the conditional distribution of the observations given the parameters, and with respect to the joint distribution of the observations and the parameters.

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References

  1. I.V. Basawa and N.U. Prabhu, Estimation in single server queues, Naval Res. Log. Quart. 28(1981) 475–487.

    Google Scholar 

  2. I.V. Basawa and N.U. Prabhu, Large sample inference from single server queues, Queueing Systems 3(1988)298–304.

    Google Scholar 

  3. U.N. Bhat and S.S. Rao, Statistical analysis of queueing systems, Queueing Systems 1(1987) 217–247.

    Google Scholar 

  4. E.L. Lehmann,Theory of Point Estimation (Wiley, New York, 1983).

    Google Scholar 

  5. J.S. Maritz and T. Lwin,Empirical Bayes Methods, 2nd ed. (Chapman and Hall, London, 1989).

    Google Scholar 

  6. M.R. McGrath, D. Gross and N.D. Singpurwalla, A subjective Bayesian approach to the theory of queues I-Modeling, Queueing Systems 1(1987)317–333.

    Google Scholar 

  7. M.R. McGrath and N.D. Singpurwalla, A subjective approach to the theory of queues II — Inference and information inM/M/1 queues, Queueing Systems 1(1987)335–353.

    Google Scholar 

  8. C.N. Morris, Parametric empirical Bayes inference: Theory and applications, J. Amer. Statist. Assoc. 78(1983)47–65.

    Google Scholar 

  9. H. Robbins, The empirical Bayes approach to statistical decision problems, Ann. Math. Statist. 35(1964)1–20.

    Google Scholar 

  10. H. Robbins, Some thoughts on empirical Bayes estimation, Ann. Statist. 11(1983)713–723.

    Google Scholar 

  11. R.J. Serfling,Approximation Theorems of Mathematical Statistics (Wiley, New York, 1980).

    Google Scholar 

  12. D. Thiruvaiyaru, I.V. Basawa and U.N. Bhat, Estimation for a class of simple queueing networks, Queueing Systems 9(1991)301–312.

    Google Scholar 

  13. R.W. Wolff, Problems of statistical inference for birth-and-death queueing models, Oper. Res. 13(1965)343–357.

    Google Scholar 

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Authors and Affiliations

  1. Department of Statistics, University of Georgia, 30602, Athens, GA, USA

    Dharma Thiruvaiyaru & Ishwar V. Basawa

Authors
  1. Dharma Thiruvaiyaru
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  2. Ishwar V. Basawa
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Thiruvaiyaru, D., Basawa, I.V. Empirical Bayes estimation for queueing systems and networks. Queueing Syst 11, 179–202 (1992). https://doi.org/10.1007/BF01163999

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  • DOI: https://doi.org/10.1007/BF01163999

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