Bi-objective optimization of a retrial model with synchronous working vacation interruption

ABSTRACT

The present research considers a multiserver retrial model with synchronous working vacation, vacation interruption and impatience customers under a constant retrial policy. In such a system, as soon as no customer is in orbit at the completion of the service, all servers will go on vacation synchronously and also provide service for customers at a relatively low-rate service rate. The vacation will be interrupted as the low-rate service is completed and the system satisfies the administrative policy. When all servers are occupied, arriving customers may enter orbit or depart the system without service. Steady-state probability distribution has been derived in matrix-form. Some performance measures are assessed numerically. A bi-objective optimization analysis is performed using MATLAB software to minimize the expected system operating cost and the expected waiting time of customers in orbit. An application of the proposed analytical method is illustrated in the manufacturing system. This makes it possible to achieve an appropriate balance between system operating cost and service quality.

KEYWORDS:

• Optimization analysis
• retrial model
• synchronous working vacation
• vacation interruption
• impatient customers

Disclosure statement

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

Additional information

Funding

This research was supported by the National Science and Technology Council of Taiwan under Grant NSTC 111-2221-E-025-002-MY3.

Notes on contributors

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.

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.

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.