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Analysis of a non-Markovian queueing model: Bayesian statistics and MCMC methods

Author

Listed:
  • Braham Hayette

    (Laboratory of Applied Mathematics, Faculty of Exact Sciences, University of Bejaia, 06000Bejaia, Algeria)

  • Berdjoudj Louiza

    (Research Unit LaMOS (Modeling and Optimization of Systems), Faculty of Exact Sciences, University of Bejaia, 06000Bejaia, Algeria)

  • Boualem Mohamed

    (Research Unit LaMOS (Modeling and Optimization of Systems), Faculty of Technology, University of Bejaia, 06000Bejaia, Algeria)

  • Rahmania Nadji

    (Paul Painleve-UMR Laboratory CNRS 8524, University of Lille, Lille, France)

Abstract

The stationary distribution is the key of any queueing system; its determination is sufficient to infer the corresponding characteristics. This paper deals with the Er/M/1{\mathrm{Er}/M/1} queue. Bayesian inference is developed to estimate the system parameters, specially the root of the relative equation which allows the determination of the stationary distribution. A numerical study is performed with MCMC methods to support the results, and a comparison with another existing method in the literature (moments method) is provided.

Suggested Citation

  • Braham Hayette & Berdjoudj Louiza & Boualem Mohamed & Rahmania Nadji, 2019. "Analysis of a non-Markovian queueing model: Bayesian statistics and MCMC methods," Monte Carlo Methods and Applications, De Gruyter, vol. 25(2), pages 147-154, June.
    • Handle: RePEc:bpj:mcmeap:v:25:y:2019:i:2:p:147-154:n:3
    DOI: 10.1515/mcma-2019-2035
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    References listed on IDEAS

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    1. Qian Zhang & Xingzhong Xu & Shiyun Mi, 2016. "A generalized p-value approach to inference on the performance measures of an M/Ek/1 queueing system," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(8), pages 2256-2267, April.
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    1. Shovan Chowdhury, 2019. "On the Estimation of Performance Measures in a Single M/Ek/1 Queue," Working papers 301, Indian Institute of Management Kozhikode.

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