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Comparing M/G/1 queue estimators in Monte Carlo simulation through the tested generator “getRDS” and the proposed “getLHS” using variance reduction

Author

Listed:
  • Boubalou Meriem

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

  • Ourbih-Tari Megdouda

    (Institut des Sciences, Centre Universitaire Morsli Abdellah de Tipaza, 42020, Tipaza; and Laboratoire de Mathématiques appliquées, FSE, Université de Bejaia, 06000, Bejaia, Algeria)

  • Aloui Abdelouhab

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

  • Zioui Arezki

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

Abstract

In this paper, we propose a Latin hypercube sampling (LHS) number generator in C language under Linux called getLHS in order to compare both methods LHS and refined descriptive sampling (RDS) method. It was highly tested by adequate statistical tests and compared statistically to the getRDS number generator. We noticed that getRDS has passed all tests better than the proposed getLHS generator. A simulation of M/G/1 queues is performed using getRDS to sample inputs from the RDS method and getLHS to sample inputs from the LHS method. The results obtained through simulation demonstrate that the RDS method produces more accurate point estimates of the true parameters than the LHS method. Moreover, the RDS method can significantly improve the performance of the studied queues compared to the well-known LHS method since its variance reduction factor is quite good in almost all cases. It is then proved that RDS is an improvement over LHS at least on queues.

Suggested Citation

  • Boubalou Meriem & Ourbih-Tari Megdouda & Aloui Abdelouhab & Zioui Arezki, 2019. "Comparing M/G/1 queue estimators in Monte Carlo simulation through the tested generator “getRDS” and the proposed “getLHS” using variance reduction," Monte Carlo Methods and Applications, De Gruyter, vol. 25(2), pages 177-186, June.
    • Handle: RePEc:bpj:mcmeap:v:25:y:2019:i:2:p:177-186:n:1
    DOI: 10.1515/mcma-2019-2033
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    References listed on IDEAS

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    1. Matthieu Petelet & Bertrand Iooss & Olivier Asserin & Alexandre Loredo, 2010. "Latin hypercube sampling with inequality constraints," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 94(4), pages 325-339, December.
    2. 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.
    3. Christoph Aistleitner & Markus Hofer & Robert Tichy, 2012. "A Central Limit Theorem For Latin Hypercube Sampling With Dependence And Application To Exotic Basket Option Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(07), pages 1-20.
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