Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 324604, 26 pages
http://dx.doi.org/10.1155/2012/324604
Research Article

A Tandem B M A P / 𝐺 / 1 → • / 𝑀 / 𝑁 / 0 Queue with Group Occupation of Servers at the Second Station

Chesoong Kim,1 Alexander Dudin,2 Valentina Klimenok,2 and Olga Taramin2

1Department of Industrial Engineering, Sangji University, Wonju, Kangwon 220-702, Republic of Korea
2Department of Applied Mathematics and Computer Science, Belarusian State University, 4 Nezavisimosti Avenue, 220030 Minsk, Belarus

Received 21 July 2011; Accepted 13 September 2011

Academic Editor: M. D. S. Aliyu

Copyright © 2012 Chesoong Kim 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

We consider a two-stage tandem queue with single-server first station and multiserver second station. Customers arrive to Station 1 according to a batch Markovian arrival process (BMAP). A batch may consist of heterogeneous customers. The type of a customer is determined upon completion of a service at Station 1. The customer's type is classified based on the number of servers required to process the request of the customer at Station 2. If the required number of servers is not available, the customer may leave the system forever or block Station 1 by waiting for the required number of servers. We determine the stationary distribution of the system states at embedded epochs and derive the Laplace-Stieltjes transform of the sojourn time distribution. Some key performance measures are calculated, and illustrative numerical results are presented.