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

Jau-Chuan Ke, Kai-Bin Huang and Ching-Chang Kuo

International Journal of Industrial and Systems Engineering, 2017, vol. 27, issue 4, 500-525

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.

Keywords: delayed repair; mean time to the first failure; MTTFF; randomised vacation; reliability; supplementary variable technique. (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:ids:ijisen:v:27:y:2017:i:4:p:500-525

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