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Computational analysis of the queue with working breakdowns and delaying repair under a Bernoulli-schedule-controlled policy

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  • Tao Jiang
  • Baogui Xin

Abstract

This paper considers a single server queueing system with working breakdowns and delaying repair under a Bernoulli-schedule-controlled policy. At a breakdown instant, the system either goes to repair period immediately with probability p, or continues to provide auxiliary service for the current customers with probability q = 1 − p. While the system resides in the auxiliary service period, it may go to repair period if there is no customer at the epoch of service completion or the occurrence of breakdown. By using the matrix analytic method and the spectral expansion method, we respectively obtain the steady state distribution to make the straightforward computation of performance measures and the Laplace-Stieltjes transform of the stationary sojourn time of an arbitrary customer. In addition, some numerical examples are presented to show the impact of parameters on the performance measures.

Suggested Citation

  • Tao Jiang & Baogui Xin, 2019. "Computational analysis of the queue with working breakdowns and delaying repair under a Bernoulli-schedule-controlled policy," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(4), pages 926-941, February.
    • Handle: RePEc:taf:lstaxx:v:48:y:2019:i:4:p:926-941
    DOI: 10.1080/03610926.2017.1422756
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    Cited by:

    1. Miaomiao Yu & Yinghui Tang, 2022. "Analysis of a renewal batch arrival queue with a fault-tolerant server using shift operator method," Operational Research, Springer, vol. 22(3), pages 2831-2858, July.
    2. Yang, Dong-Yuh & Wu, Chia-Huang, 2021. "Evaluation of the availability and reliability of a standby repairable system incorporating imperfect switchovers and working breakdowns," Reliability Engineering and System Safety, Elsevier, vol. 207(C).

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