An MX/GI/1/N finite capacity queue with close-down time, vacation time
and exhaustive service discipline is considered under the partial batch
acceptance strategy as well as under the whole batch acceptance strategy.
Applying the supplementary variable technique the queue length distribution at an arbitrary instant and at a departure epoch is obtained under
both strategies, where no assumption on the batch size distribution is
made. The loss probabilities and the Laplace-Stieltjes transforms of the
waiting time distribution of the first customer and of an arbitrary customer of a batch are also given. Numerical examples give some insight into
the behavior of the system.