On sojourn times in the finite capacity M/M/1M/M/1 queue with processor sharing

We consider a processor shared M/M/1M/M/1 queue that can accommodate at most a finite number KK of customers. We give an exact expression for the sojourn time distribution in this finite capacity model, in terms of a Laplace transform. We then give the tail behavior, for the limit K→∞K→∞.