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

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.