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

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  • Jau-Chuan Ke
  • Kai-Bin Huang
  • Ching-Chang Kuo

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.

Suggested Citation

  • Jau-Chuan Ke & Kai-Bin Huang & Ching-Chang Kuo, 2017. "Reliability-based measures for a batch-arrival queue with an unreliable server and delayed repair under randomised vacations," International Journal of Industrial and Systems Engineering, Inderscience Enterprises Ltd, vol. 27(4), pages 500-525.
    • Handle: RePEc:ids:ijisen:v:27:y:2017:i:4:p:500-525
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    Cited by:

    1. Madhu Jain & Sandeep Kaur & Parminder Singh, 2021. "Supplementary variable technique (SVT) for non-Markovian single server queue with service interruption (QSI)," Operational Research, Springer, vol. 21(4), pages 2203-2246, December.

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