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

Authors: Jau-Chuan Ke; Kai-Bin Huang; Ching-Chang Kuo

Addresses: Department of Applied Statistics, National Taichung University of Science and Technology, Taichung 404, Taiwan ' Department of Measurement and Calibration Technology, Electronics Testing Center (ETC), Taoyuan 333, Taiwan ' Department of Applied Statistics, National Taichung University of Science and Technology, Taichung 404, Taiwan

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.

DOI: 10.1504/IJISE.2017.087831

International Journal of Industrial and Systems Engineering, 2017 Vol.27 No.4, pp.500 - 525

Received: 10 Jul 2015
Accepted: 11 Oct 2015
Published online: 06 Nov 2017 *

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