Optimization of retrial queue with unreliable servers subject to imperfect coverage and reboot delay

ABSTRACT

A retrial queue with constant retrial policy, unreliable servers and the failed servers may not be detected is investigated in this paper. Upon arrival, a customer either is attended to one of the available servers or enters a retrial orbit and retries in a random time as all servers are not available. The unreliable server can be breakdown when he is working. The breakdown server may not be detected due to some fault matters. Under such a situation, the repair facility will issue a reboot operation to locate the non-detected breakdown server. Once the breakdown server is detected and located, he will be sent for repair. After utilizing the general theory of matrix-geometric approach to determine the stationary distribution, some performance measures are proposed. A single-objective model aiming at minimizing the average cost is constructed. We apply particle swarm optimization algorithm and genetic algorithm to find the optimum combination of parameters. We also formulate a bi-objective model aiming at minimizing the expect cost and the mean waiting time of customers in orbit. Two multi-objective algorithms are developed to solve it.

KEYWORDS:

• Bi-objective optimization
• delay reboot
• imperfect coverage
• Pareto front
• retrial queue

Acknowledgments

The authors thank Editor and the anonymous referees for the valuable comments and suggestions, which significantly improved the quality of the paper. This research was partly supported by the Ministry of Science and Technology of Taiwan, under Grant No. MOST 108-2221-E-025-003-MY3.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Tzu-Hsin Liu

Tzu-Hsin Liu received her Masters and PhD degrees in applied mathematics from National Chung-Hsing University, Taiwan, in 2005 and 2011, respectively. Her current research interests include queueing theory, maintenance policy and statistics.

Fu-Min Chang

Fu-Min Chang is a Professor in the Department of Finance, Chao Yang University of Technology, Taiwan. He received his Master and PhD degrees from National Chung-Hsing University, Taiwan, ROC, in 1992 and 2005, respectively. His current research interests include the area of queueing network, network performance evaluation, and system and network management.

Jau-Chuan Ke

Jau-Chuan Ke is a Professor of Applied Statistics at the National Taichung University of Science and Technology, Taiwan. He received his Ph.D. degree in Applied Mathematics from National Chung-Hsing University, Taiwan. He is an editorial board member of Applied Mathematical Modelling, Quality Technology & Quantitative Management and Queueing Models and Service Management. His research interests include queueing theory, reliability, statistics, and decision theory.

Shey-Huei Sheu

Shey-Huei Sheu is a Chair Professor in the Department of Business Administration, Asia University, and a consultant to the Department of Medical Research, China Medical University Hospital, China Medical University. He was an Honorary Chair Professor of the Department of Industrial Management at the National Taiwan University of Science and Technology. He received his M.S. degree (1979) in applied mathematics from the National Tsing Hua University and his Ph.D. degree (1987) in statistics from the University of Kentucky. He has published over one hundred and fifty papers in several prestigious journals in the fields of statistics, reliability, operations research, and systems engineering.