Optimal threshold policies in a two-class preemptive priority queue with admission and termination control

We consider a two-class $$M^{\lambda_1, \lambda_2}|M^{\mu}|1$$1 preemptive priority queue in which there are two essential, on-line decisions that have to be taken. The first is the decision to either accept or reject new type-1 or type-2 jobs. The second is the decision to abort jobs, i.e., to remove any type-1 or type-2 jobs from the system. We show that there exist optimal threshold policies for these two types of, decisions.