Admission and termination control of a two class loss system

We consider dynamic admission and termination control policies in a Markovian loss system with two classes, each with a fixed reward, a termination cost, an arrival and service rate. The system may admit or reject an arriving job or admit it by terminating a job in the system to maximize its total expected discounted reward. We prove that (1) when there is an idle server, it is never optimal to terminate a job, (2) there exists an optimal threshold policy for both admission and termination decisions. Furthermore, we identify the conditions which ensure that a class is "preferred" or "strongly preferred. "