Probabilistic Decomposition Method on the ServerIndices of an Mξ/G/1 Vacation Queue. (23rd January 2014)

• Record Type: Journal Article
• Authors: Liu, Renbin
• Other Names: Ezzat Magdy A. Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2014(2014)
• Publication Date: 2014-01-23
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2014/241636
• Languages: English
• ISSNs: 1110-757X

Abstract

Abstract : This paper develops a probabilistic decomposition method for anM ξ /G/1 repairable queueing system with multiple vacations, in which the customers who arrive during server vacations enter the system with probability p . Such a novel method is used to analyze the main performance indices of the server, such as the unavailability and the mean failure number during( 0, t ] . It is derived that the structures of server indices are two convolution equations. Further, comparisons with existing methods indicate that our method is effective and applicable for studying server performances in single-serverM ξ /G/1 vacation queues and their complex variants. Finally, a stochastic order and production system with a multipurpose production facility is numerically presented for illustrative purpose.