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Computing the Performance Measures in Queueing Models via the Method of Order Statistics

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  • Yousry H. Abdelkader
  • Maram Al-Wohaibi

Abstract

This paper focuses on new measures of performance in single‐server Markovian queueing system. These measures depend on the moments of order statistics. The expected value and the variance of the maximum (minimum) number of customers in the system as well as the expected value and the variance of the minimum (maximum) waiting time are presented. Application to an M/M/1 model is given to illustrate the idea and the applicability of the proposed measures.

Suggested Citation

  • Yousry H. Abdelkader & Maram Al-Wohaibi, 2011. "Computing the Performance Measures in Queueing Models via the Method of Order Statistics," Journal of Applied Mathematics, John Wiley & Sons, vol. 2011(1).
    • Handle: RePEc:wly:jnljam:v:2011:y:2011:i:1:n:790253
    DOI: 10.1155/2011/790253
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    References listed on IDEAS

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    1. H. M. Barakat & Y. H. Abdelkader, 2004. "Computing the moments of order statistics from nonidentical random variables," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 13(1), pages 15-26, April.
    2. Jesus R. Artalejo & Antonis Economou & M. J. Lopez-Herrero, 2007. "Algorithmic Analysis of the Maximum Queue Length in a Busy Period for the M/M/c Retrial Queue," INFORMS Journal on Computing, INFORMS, vol. 19(1), pages 121-126, February.
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