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Mathematical Problems in Engineering
Volume 2014, Article ID 178108, 13 pages
Research Article

Analysis of Multiserver Queueing System with Opportunistic Occupation and Reservation of Servers

1School of Economics and Management, Inner Mongolia University of Science and Technology, Baotou 014010, China
2Inner Mongolia Industry Informatization and Innovation Research Center, Inner Mongolia University of Science and Technology, Baotou 014010, China
3Institute of Information and Communication, Chonbuk National University, Jeonju 561-765, Republic of Korea
4Department of Applied Mathematics and Computer Science, Belarusian State University, 4 Nezavisimosti Avenue, 220030 Minsk, Belarus

Received 3 February 2014; Revised 8 April 2014; Accepted 8 April 2014; Published 7 May 2014

Academic Editor: Jyh-Hong Chou

Copyright © 2014 Bin Sun 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 consider a multiserver queueing system with two input flows. Type-1 customers have preemptive priority and are lost during arrival only if all servers are occupied by type-1 customers. If all servers are occupied, but some provide service to type-2 customers, service of type-2 customer is terminated and type-1 customer occupies the server. If the number of busy servers is less than the threshold during type-2 customer arrival epoch, this customer is accepted. Otherwise, it is lost or becomes a retrial customer. It will retry to obtain service. Type-2 customer whose service is terminated is lost or moves to the pool of retrial customers. The service time is exponentially distributed with the rate dependent on the customer’s type. Such queueing system is suitable for modeling cognitive radio. Type-1 customers are interpreted as requests generated by primary users. Type-2 customers are generated by secondary or cognitive users. The problem of optimal choice of the threshold is the subject of this paper. Behavior of the system is described by the multidimensional Markov chain. Its generator, ergodicity condition, and stationary distribution are given. The system performance measures are obtained. The numerical results show the effectiveness of considered admission control.