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Mathematical Problems in Engineering
Volume 2015, Article ID 165219, 6 pages
http://dx.doi.org/10.1155/2015/165219
Research Article

The Analysis, Optimization, and Simulation of a Two-Stage Tandem Queueing Model with Hyperexponential Service Time at Second Stage

1Department of Statistics, Faculty of Science and Arts, Ondokuz Mayıs University, 55200 Samsun, Turkey
2Department of Statistics, Faculty of Science and Arts, Amasya University, 5000 Amasya, Turkey

Received 15 May 2015; Accepted 28 October 2015

Academic Editor: Purushothaman Damodaran

Copyright © 2015 Vedat Sağlam 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

The aim of this paper is to analyze a tandem queueing model with two stages. The arrivals to the first stage are Poisson stream and the service time at this stage is exponential. There is no waiting room at first stage. The service time is hyperexponential and no waiting is allowed at second stage. The transition probabilities and loss probabilities of this model are obtained. In addition, the loss probability at second stage is optimized. Performance measures and the variance of the numbers of customers of this tandem queueing model are found. It is seen that the numbers of customers in first stage and second stage are dependent. Finally we have simulated this queueing model. For different values of parameters, exact values, simulated values, and optimal values of obtained performance measures of this model are numerically shown in tables and graphs.