Journal of Applied Mathematics
Volume 2011 (2011), Article ID 790253, 12 pages
http://dx.doi.org/10.1155/2011/790253
Research Article

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

Yousry H. Abdelkader1,2 and Maram Al-Wohaibi2

1Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt
2Department of Mathematics, Girls College, Dammam University, P.O. Box 838, Dammam 31113, Saudi Arabia

Received 7 July 2011; Accepted 23 September 2011

Academic Editor: Yansheng Liu

Copyright © 2011 Yousry H. Abdelkader and Maram Al-Wohaibi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.