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The use of variance reduction, relative error and bias in testing the performance of M/G/1 retrial queues estimators in Monte Carlo simulation

Author

Listed:
  • Tamiti Kenza

    (Laboratoire de Mathématiques Appliquées, FSE, Université de Bejaia, 06000Bejaia, Algeria)

  • Ourbih-Tari Megdouda

    (Centre Universitaire Morsli Abdellah de Tipaza, 42000Tipaza; and Laboratoire de Mathématiques Appliquées, FSE, Université de Bejaia, 06000 Bejaia, Algeria)

  • Aloui Abdelouhab

    (LiMed, FSE, Université de Bejaia, 06000Bejaia, Algeria)

  • Idjis Khelidja

    (Laboratoire de Mathématiques Appliquées, FSE, Université de Bejaia, 06000Bejaia, Algeria)

Abstract

This paper deals with Monte Carlo simulation and focuses on the use of the concepts of variance reduction, relative error and bias in testing the performance of stationary M/G/1 retrial queues estimators using either Random Sampling (RS) or Refined Descriptive Sampling (RDS) to generate input samples. For this purpose, a software under Linux system using the C compiler was designed and realized providing the performance measures of such system and the statistical concepts of bias, relative error and accuracy using both sampling methods. As a conclusion, it has been shown that the performance of stationary M/G/1 retrial queues estimators is better using RDS than RS and sometimes by a substantial variance reduction factor.

Suggested Citation

  • Tamiti Kenza & Ourbih-Tari Megdouda & Aloui Abdelouhab & Idjis Khelidja, 2018. "The use of variance reduction, relative error and bias in testing the performance of M/G/1 retrial queues estimators in Monte Carlo simulation," Monte Carlo Methods and Applications, De Gruyter, vol. 24(3), pages 165-178, September.
    • Handle: RePEc:bpj:mcmeap:v:24:y:2018:i:3:p:165-178:n:2
    DOI: 10.1515/mcma-2018-0015
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    References listed on IDEAS

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    1. Leila Baiche & Megdouda Ourbih-Tari, 2017. "Large-sample variance of simulation using refined descriptive sampling: Case of independent variables," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(1), pages 510-519, January.
    2. Charles E. Clark, 1961. "Importance Sampling in Monte Carlo Analyses," Operations Research, INFORMS, vol. 9(5), pages 603-620, October.
    3. Nils Löhndorf & Stefan Minner, 2013. "Simulation optimization for the stochastic economic lot scheduling problem," IISE Transactions, Taylor & Francis Journals, vol. 45(7), pages 796-810.
    4. Megdouda Ourbih-Tari & Mahdia Azzal, 2017. "Survival function estimation with non parametric adaptive refined descriptive sampling algorithm: A case study," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(12), pages 5840-5850, June.
    5. J.R. Artalejo & M. Pozo, 2002. "Numerical Calculation of the Stationary Distribution of the Main Multiserver Retrial Queue," Annals of Operations Research, Springer, vol. 116(1), pages 41-56, October.
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