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Using mixture of Gamma distributions for Bayesian analysis in an M/G/1 queue with optional second service

Computational Statistics volume 28, pages683–700(2013)Cite this article

Abstract

The paper proposes Bayesian framework in an M/G/1 queuing system with optional second service. The semi-parametric model based on a finite mixture of Gamma distributions is considered to approximate both the general service and re-service times densities in this queuing system. A Bayesian procedure based on birth-death MCMC methodology is proposed to estimate system parameters, predictive densities and some performance measures related to this queuing system such as stationary system size and waiting time. The approach is illustrated with several numerical examples based on various simulation studies.

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Acknowledgments

The authors are grateful to the anonymous reviewers for their detailed and insightful comments.

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This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

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Affiliations

  1. Johann Bernoulli Institute, University of Groningen, Groningen, The Netherlands

    A. Mohammadi & E. C. Wit

  2. Department of statistics, Allameh Tabataba’i University, Tehran, Iran

    M. R. Salehi-Rad

Authors
  1. A. Mohammadi
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  2. M. R. Salehi-Rad
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  3. E. C. Wit
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Correspondence to A. Mohammadi.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Mohammadi, A., Salehi-Rad, M.R. & Wit, E.C. Using mixture of Gamma distributions for Bayesian analysis in an M/G/1 queue with optional second service. Comput Stat 28, 683–700 (2013). https://doi.org/10.1007/s00180-012-0323-3

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Keywords

  • Gamma mixtures
  • Bayesian inference
  • MCMC
  • Birth-death predictive distribution
  • M/G/1 queue
  • Optional service