A Discrete-Time Geo/G/1 Retrial Queue with Two Different Types of Vacations. (28th April 2015)

• Record Type: Journal Article
• Authors: Zhang, Feng; Zhu, Zhifeng
• Other Names: Dudin Alexander N. Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2015(2015)
• Publication Date: 2015-04-28
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2015/835158
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : We analyze a discrete-timeG e o / G / 1 retrial queue with two different types of vacations and general retrial times. Two different types of vacation policies are investigated in this model, one of which is nonexhaustive urgent vacation during serving and the other is normal exhaustive vacation. For this model, we give the steady-state analysis for the considered queueing system. Firstly, we obtain the generating functions of the number of customers in our model. Then, we obtain the closed-form expressions of some performance measures and also give a stochastic decomposition result for the system size. Moreover, the relationship between this discrete-time model and the corresponding continuous-time model is also investigated. Finally, some numerical results are provided to illustrate the effect of nonexhaustive urgent vacation on some performance characteristics of the system.