Control Charts for the Expected System Size of Markovian Queues under F-policy

ABSTRACT

In F-policy queues, the system stops allowing the entry of customers when it is full and allows customers to enter until the system size is reduced to the threshold F. A well-designed control policy has a relative influence on the waiting time of customers as well as the service quality of the system. For queues controlling the arrival of customers, the expected number of customers in the system is an important characteristic. To maintain the stability, managers need to quickly notice changes in the expected system size and take appropriate action once such changes occur. In this study, we develop six control charts for monitoring the expected system size in the F-policy M/M/1/K queueing system with exponential start-up times. Two methods of system parameters estimation associated with three approaches for control limit calculations are provided. Based on the numerical simulations conducted, the average run length is employed to measure and compare the performances of the control charts obtained. Finally, we present an application example for illustrative purposes.

KEYWORDS:

• Average run length
• control chart
• f-policy
• queue
• system size

Acknowledgments

The authors would like to thank two anonymous referees for their valuable comments and suggestions, which improve the manuscript. This work was partially supported by the Ministry of Science and Technology, Taiwan, under grants MOST 108-2221-E-141-001-MY2 and MOST 109-2221-E-009-069-MY3.

Additional information

Funding

This work was supported by the Ministry of Science and Technology, Taiwan [MOST 109-2221-E-009-069-MY3]; Ministry of Science and Technology, Taiwan [MOST 108-2221-E-141-001-MY2].

Notes on contributors

Chia-Huang Wu

Chia-Huang Wu received a Ph.D. degree in Industrial Engineering and Management from National Chiao-Tung University, Hsinchu, Taiwan. He is currently an assistant professor at National Chiao-Tung University. His research interests include process capability analysis, applied statistics, queueing systems, and optimization theory. He has published more than 50 papers on various SCI journals such as Quality and Reliability Engineering International, European Journal of Industrial Engineering, Applied Mathematical Modelling, Computers and Operations Research, Computers and Industrial Engineering, etc.

Dong-Yuh Yang

Dong-Yuh Yang is a Professor at Institute of Information and Decision Sciences, National Taipei University of Business, Taiwan. He received his Ph.D. degree in Industrial Engineering and Management from National Chiao Tung University, Taiwan. His research interests include reliability, queueing theory, applied statistics, and stochastic models.