Abstract
We consider a Poisson arrival queueing system with finite capacity and a general vacation policy as described in Loris-Teghem [Queueing Systems 3 (1988), 41-52]. From our previous results regarding the stationary queue length distributions immediately after a departure and at an arbitrary epoch, we derive a relation between both distributions which extends a result given in Frey and Takahashi [Operations Research Letters 21 (1997), 95-100] for the particular case of an exhaustive service multiple vacation policy.