Reliability-based measures for a batch-arrival queue with an unreliable server and delayed repair under randomised vacations. (2017)

• Record Type: Journal Article
• Authors: Ke, Jau-Chuan; Huang, Kai-Bin; Kuo, Ching-Chang
• Is Part Of: International journal of industrial and systems engineering. Volume 27:Number 4(2017)
• Page Start: 500
• Page End: 525
• Publication Date: 2017
• Subjects: delayed repair -- mean time to the first failure -- MTTFF -- randomised vacation -- reliability -- supplementary variable technique; Systems engineering -- Periodicals; Industrial engineering -- Periodicals; 620.001171
• Languages: English
• ISSNs: 1748-5037

Abstract

This paper studies the transient and the steady-state behaviour of an M [x] /G/1 queueing system with a randomised vacation policy at most J vacations. Whenever the system is empty, the server immediately takes a vacation. If no customers are waiting for service at the end of a vacation, the server either remains idle with probability p or leaves for another vacation with probability 1 - p . This pattern continues until the number of vacations taken reaches J . Assume that the server may meet an unpredictable breakdown according to a Poisson process and the repair may be delayed, in which the repair time is a general random variable. Based on the supplementary variable technique, we developed the transient and the steady-state solutions for both queueing and reliability measures of the variant vacation system.