Tzu-Hsin Liu1, Chih-Meng Wang2, Yih-Bey Lin1, Fu-Min Chang1*

1 Department of Finance, Chaoyang University of Technology, Taiwan
2 Ph.D. Program of Business Administration in Industrial Development, Chaoyang University of Technology, Taichung, Taiwan


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A robust power supply system with high availability and acceptable cost/benefit is essential for many service systems, such as communication networks and product manufacturing processes. This investigation is concerned with the evaluation of the cost-benefit of a standby retrial power supply system incorporating standby switching failure and general repair times, which is the first work on the comparative analysis of retrial availability systems incorporating switching failure and general repair times. Four different standby power supply retrial configurations are included and each configuration consists of a different number of primary and standby generators. The investigated system assumes that the time-to-failure and the time-to-repair of the primary and standby generators obey the exponential and general distributions, respectively. We also take that the switching over standbys may be failed into account. By using the supplementary variable technique, the explicit expressions of the steady-state availability for each configuration are derived. A comparative analysis of the availability and the cost-benefit ratio among four retrial systems is presented. We also rank the configurations based on the steady-state availability and cost-benefit ratio for two repair time distributions, Weibull and lognormal. The calculated numerical results can provide managers with decision reference for stable power supply system and cost reduction.

Keywords: Retrial queue, Availability, Switching failure, Cost-benefit, Supplementary variable.

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  1. Artalejo, J.R. 1990a. Accessible bibliography on retrial queues, Mathematical Computer Modelling, 30, 1–6.

  2. Artalejo, J.R. 1990b. A classified bibliography of research on retrial queues: progress in 1990-1999, Top, 7, 187–211.

  3. Artalejo, J.R., Gomez-Corral, A. 2008. Retrial queueing Systems: a computational approach, Springer-Verlag.

  4. Falin, G. 1990. A survey of retrial queues, Queueing Systems, 7, 127–67.

  5. Falin, G., Templeton J. 1997. Retrial queues, Chapman & Hall.

  6. Hsu, Y.L., Ke, J.C., Liu, T.H., Wu, C.H. 2014. Modeling of multiserver repair problem with switching failure and reboot delay and related profit analysis, Computers and Industrial Engineering, 69, 21–28.

  7. Hu, S.C., Chuah, Y.K. 2003. Power consumption of semiconductor fabs in Taiwan, Energy, 28, 895-907.

  8. Huang, H.I., Lin, C.H., Ke, J.C. 2006. Parametric nonlinear programming approach for a repairable system with switching failure and fuzzy parameters, Applied Mathematics and Computation, 183, 508–517.

  9. Ke, J.C., Yang, D.Y., Sheu, S.H., Kuo, C.C. 2013. Availability of a repairable retrial system with warm standby components, International Journal of Computer Mathematics, 90, 2279–97.

  10. Ke, J.C., Liu, T.H., Yang, D.Y. 2016. Machine repairing systems with standby switching failure, Computers and Industrial Engineering, 99, 223–228.

  11. Ke, J.C., Liu, T.H., Yang, D.Y. 2018. Modeling of machine interference problem with unreliable repairman and standbys imperfect switchover, Reliability Engineering & System Safety, 174, 12–18.

  12. Kuo, C.C., Sheu, S.H., Ke, J.C, Zhang, Z. 2014. Reliability-based measures for a retrial system with mixed standby components, Applied Mathematical Modelling, 38, 4640–51.

  13. Lee, Y. 2016. Availability analysis of redundancy model with generally distributed repair time, imperfect switchover, and interrupted repair, Electronic Letters, 52, 1851–1853.

  14. Liu, T.H., Ke, J.C., Hsu, Y.L., Hsu, Y.L. 2011. Bootstrapping computation of availability for a repairable system with standby subject to imperfect switching, Communications in Statistics - Simulation and Computation, 40, 469–483.

  15. Phung-Duc, T. 2019. Retrial queueing models, A survey on theory and applications, arXiv preprint arXiv:1906.09560.

  16. Wang, J. 2006. Reliability analysis M/G/1 queues with general retrial times and server breakdowns, Progress in Natural Science, 16, 464–73.

  17. Wang, J., Cao, J., Li, Q. 2001. Reliability analysis of the retrial queue with server breakdowns and repairs, Queueing Systems, 38, 363–80.

  18. Yang, T., Templeton, J.G.C. 1987. A survey on retrial queues, Queueing Systems, 2, 201–33.


Received: 2021-06-23
Revised: 2021-07-28
Accepted: 2021-10-01
Publication Date: 2021-12-01

Cite this article:

Liu, T.-H., Wang, C.-M., Lin, Y.-B., Chang, F.-M. 2021. Evaluation of the cost-benefit of standby retrial systems incorporating switching failure and general repair times. International Journal of Applied Science and Engineering, 18, 2021213.

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