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Mathematical Problems in Engineering
Volume 2018, Article ID 3018758, 15 pages
https://doi.org/10.1155/2018/3018758
Research Article

Traffic Intensity Estimation in Finite Markovian Queueing Systems

1Departamento de Estatística, Universidade Federal de Minas Gerais, 31270-901 Belo Horizonte, MG, Brazil
2Pró-Reitoria de Planejamento e Desenvolvimento, Universidade Federal do Pará, 66075-110 Belém, PA, Brazil
3Departamento de Ciência da Computação, Universidade Estadual de Montes Claros, 39401-089 Montes Claros, MG, Brazil
4Department of Industrial Engineering & Innovation Sciences, Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands

Correspondence should be addressed to Frederico R. B. Cruz; rb.gmfu.tse@zurcf

Received 5 January 2018; Revised 10 April 2018; Accepted 16 May 2018; Published 26 June 2018

Academic Editor: Jason Gu

Copyright © 2018 Frederico R. B. Cruz 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.

Abstract

In many everyday situations in which a queue is formed, queueing models may play a key role. By using such models, which are idealizations of reality, accurate performance measures can be determined, such as traffic intensity (), which is defined as the ratio between the arrival rate and the service rate. An intermediate step in the process includes the statistical estimation of the parameters of the proper model. In this study, we are interested in investigating the finite-sample behavior of some well-known methods for the estimation of for single-server finite Markovian queues or, in Kendall notation, queues, namely, the maximum likelihood estimator, Bayesian methods, and bootstrap corrections. We performed extensive simulations to verify the quality of the estimators for samples up to 200. The computational results show that accurate estimates in terms of the lowest mean squared errors can be obtained for a broad range of values in the parametric space by using the Jeffreys’ prior. A numerical example is analyzed in detail, the limitations of the results are discussed, and notable topics to be further developed in this research area are presented.