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Performance Evaluation and Dimensioning of GIX/M/c/N Systems Through Kernel Estimation

Author

Listed:
  • Laoucine Kerbache

    (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique)

  • G. M. Gontijo
  • G. S. Atuncar
  • F.R.B. Cruz

Abstract

We extend the analysis of queueing systems for real-life situations, where the arrival pattern of customers is unknown. In real systems, we must understand how the choice of a method of estimation influences the configuration of the system. Using kernel smoothing, we evaluate algorithms to estimate performance measures of a GIx/M/c/N system, including the invariant probability distribution of the number of customers in the system, the blocking probability, the average queue size, and the average client queue time. We successfully apply the method to the arrivals to a call center to plan and improve the performance of these important queueing systems.

Suggested Citation

  • Laoucine Kerbache & G. M. Gontijo & G. S. Atuncar & F.R.B. Cruz, 2011. "Performance Evaluation and Dimensioning of GIX/M/c/N Systems Through Kernel Estimation," Post-Print hal-00796342, HAL.
    • Handle: RePEc:hal:journl:hal-00796342
    DOI: 10.1155/2011/348262
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    Citations

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    Cited by:

    1. Tom van Woensel & Frederico R B Cruz, 2014. "Optimal Routing in General Finite Multi-Server Queueing Networks," PLOS ONE, Public Library of Science, vol. 9(7), pages 1-15, July.
    2. Mohan L. Chaudhry & James J. Kim, 2016. "Analytically elegant and computationally efficient results in terms of roots for the $$GI^{X}/M/c$$ G I X / M / c queueing system," Queueing Systems: Theory and Applications, Springer, vol. 82(1), pages 237-257, February.
    3. F. R. B. Cruz & M. A. C. Santos & F. L. P. Oliveira & R. C. Quinino, 2021. "Estimation in a general bulk-arrival Markovian multi-server finite queue," Operational Research, Springer, vol. 21(1), pages 73-89, March.
    4. Lin, Lei & Wang, Qian & Sadek, Adel W., 2014. "Border crossing delay prediction using transient multi-server queueing models," Transportation Research Part A: Policy and Practice, Elsevier, vol. 64(C), pages 65-91.
    5. M. A. C. Almeida & F. R. B. Cruz & F. L. P. Oliveira & G. Souza, 2020. "Bias correction for estimation of performance measures of a Markovian queue," Operational Research, Springer, vol. 20(2), pages 943-958, June.

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