Priority queues with threshold switching and setup time

In present paper, we propose and analyze a single-server two-queue priority system with setup time and threshold switching. At first, for the case of Poisson arrivals, exponential service times and setup times, preemptive and non-preemptive service are discussed respectively. And then the case of general service times and setup times for non-preemptive service is further studied. When the system is steady the joint probability generating functions of the lengths of two queues are obtained. We can use these generating functions to calculate performance measures of the system, for example, the mean queue lengths, and then by means of Little formula, the mean delay can be computed.