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Statistical analysis of the estimates of some stationary performances of the unreliable M/M/1/N queue with Bernoulli feedback

Author

Listed:
  • Nita Hadjer

    (Laboratory of Applied Mathematics, Mathematics Department, University of Biskra, 07000, Biskra, Algeria)

  • Afroun Faïrouz

    (Laboratory of Pure and Applied Mathematics, University of Tizi-Ouzou, 15000, Tizi-Ouzou, Algeria)

  • Cherfaoui Mouloud

    (Mathematics Department, University of Biskra, 07000, Biskra, ; and Research Unit LaMOS (Modeling and Optimization of Systems), University of Bejaia, 06000 Bejaia, Algeria)

  • Aïssani Djamil

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

Abstract

In this work, we considered the parametric estimation of the characteristics of the M/M/1/N{M/M/1/N} waiting model with Bernoulli feedback. Through a Monte-Carlo simulation study, we have illustrated the effect of the estimation of the starting parameters of the considered waiting system on the statistical properties of its performance measures estimates, when these latter are obtained using the plug-in method. In addition, several types of convergence (bias, variance, MSE, in law) of these performance measure estimators have also been showed by simulation.

Suggested Citation

  • Nita Hadjer & Afroun Faïrouz & Cherfaoui Mouloud & Aïssani Djamil, 2023. "Statistical analysis of the estimates of some stationary performances of the unreliable M/M/1/N queue with Bernoulli feedback," Monte Carlo Methods and Applications, De Gruyter, vol. 29(4), pages 351-366, December.
    • Handle: RePEc:bpj:mcmeap:v:29:y:2023:i:4:p:351-366:n:2
    DOI: 10.1515/mcma-2023-2004
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