Characterising the Finite CapacityGI/M/1 Queue with Renewal Output

Abstract

This note proves that the only stationary GI / M /1/ N queueing systems (i.e., systems having fixed waiting room capacity N (0 ≦ N ≦ ∞)) with renewal output are the M / M /1/0 and stable (traffic intensity < 1) M / M /1/∞ systems.