A Discrete-Time Unreliable Geo/G/1 Retrial Queue with Balking Customers, Second Optional Service, and General Retrial Times. (29th December 2013)

• Record Type: Journal Article
• Authors: Zhang, Feng; Zhu, Zhifeng
• Other Names: Lin Yi-Kuei Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2013(2013)
• Publication Date: 2013-12-29
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2013/832318
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : This paper deals with the steady-state behavior of a discrete-time unreliable Geo/G/1 retrial queueing system with balking customers and second optional service. The server may break down randomly while serving the customers. If the server breaks down, the server is sent to be repaired immediately. We analyze the Markov chain underlying the considered system and its ergodicity condition. Then, we obtain some performance measures based on the generating functions. Moreover, a stochastic decomposition result of the system size is investigated. Finally, some numerical examples are provided to illustrate the effect of some parameters on main performance measures of the system.