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

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.

KEYWORDS:

• Working breakdown
• Bernoulli-schedule-controlled
• Matrix analytic method
• Spectral expansion method
• Sojourn time.

MATHEMATICS SUBJECT CLASSIFICATION:

• 60K25
• 90B22

Acknowledgements

The authors would like to thank the editor and the referees for the helpful suggestions and comments to improve the quality of this paper.