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Mathematical Problems in Engineering
Volume 2013, Article ID 182497, 8 pages
http://dx.doi.org/10.1155/2013/182497
Research Article

The Geo/Geo/1+1 Queueing System with Negative Customers

1College of Science, Yanshan University, Qinhuangdao 066004, China
2School of Economics & Management, Yanshan University, Qinhuangdao 066004, China

Received 11 September 2013; Accepted 28 October 2013

Academic Editor: Yuji Liu

Copyright © 2013 Zhanyou Ma 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 study a Geo/Geo/1+1 queueing system with geometrical arrivals of both positive and negative customers in which killing strategies considered are removal of customers at the head (RCH) and removal of customers at the end (RCE). Using quasi-birth-death (QBD) process and matrix-geometric solution method, we obtain the stationary distribution of the queue length, the average waiting time of a new arrival customer, and the probabilities of servers in busy or idle period, respectively. Finally, we analyze the effect of some related parameters on the system performance measures.