Reliability-based measures for a batch-arrival queue with an unreliable server and delayed repair under randomised vacations
by Jau-Chuan Ke; Kai-Bin Huang; Ching-Chang Kuo
International Journal of Industrial and Systems Engineering (IJISE), Vol. 27, No. 4, 2017

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.

Online publication date: Mon, 06-Nov-2017

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