Performance analysis of a queueing system with flexible, reserved and specialized servers

We consider a finite-capacity services system in which there are multiple servers, called flexible servers, serving two types of customers: ordinary customers and priority customers. In this system, we want to maintain a. no-wait priority for priority customers. If the system is full, any arriving customer will be lost. When system is not full but all the servers are busy, an arriving priority customer will be considered lost, however, an arriving ordinary customer will joint the queue. The loss rates are defined as a measure of the Quality of Service(QoS). In order to have a. smaller loss rate for the priority customers and fulfill the pre-detemined QoS, we may reserve a. certain number of flexible servers, called reserved servers, for the priority customer, or, we may consider adding some specialized servers that only serve priority customers. The purpose of this paper is to study the models with both flexible and specialized servers and to determine the number of reserved servers to maximize the utilization of the flexible servers