Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 348262, 20 pages
Research Article

Performance Evaluation and Dimensioning of 𝐺 𝐼 𝑋 / 𝑀 / 𝑐 / 𝑁 Systems through Kernel Estimation

1Departamento de Estatística, Universidade Federal de Minas Gerais, 31270-901 Belo Horizonte, MG, Brazil
2Department of OMIT and the Research Center GREGHEC, HEC School of Management, 78351 Paris, France

Received 26 May 2011; Accepted 31 July 2011

Academic Editor: Ming Li

Copyright © 2011 G. M. Gontijo et al. 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.


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 𝐺 𝐼 𝑋 / 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.