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.

摘要

在F 策略队列中，系统在满员时停止允许客户进入，并允许客户进入，直到系统大小减小到阈值F。一个设计良好的控制策略对客户的等待时间以及系统的服务质量有相对的影响。对于控制客户到达的队列，系统中的预期客户数量是一个重要特征。为了保持稳定性，管理人员需要快速注意到预期系统规模的变化，并在发生此类变化时采取适当的措施。在这项研究中，我们开发了六个控制图来监控F 中的预期系统规模-具有指数启动时间的策略 M/M/1/K 排队系统。提供了与控制极限计算的三种方法相关联的两种系统参数估计方法。基于所进行的数值模拟，使用平均运行长度来测量和比较获得的控制图的性能。最后，为了说明目的，我们提供了一个应用示例。