We consider a single-server queuing system with two job classes under service policies of threshold type. The server switches from type 1 to type 2 when either the former queue is empty or the latter reaches size T; it switches from type 2 to type 1 when the former queue size drops below T and the latter is not empty. The joint queue-length distribution is determined for preemptive and nonpreemptive implementations using both analytic techniques and the power series algorithm.
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