Realizable Performance Vectors of a Finite-Source Queue

We study a scheduling problem on a finite-source queueing model which is identical to a two-stage closed Markovian cyclic queue consisting of a single-server (“processor”) and an infinite-server (“terminals”); each job has a distinct mean service time at the processor. We obtain a necessary and sufficient condition for a performance vector consisting of utilization factors (or average response times) of the processor for the jobs to be achievable by some scheduling strategy. The result is analogous to that obtained by Coffman and Mitrani on infinite-source single-server queues.