Abstract
The GI/E_k/1 queue with finite waiting room is investigated by using a combination of the supplementary variable and phase techniques. We start by studying the steady-state joint distribution of the number of phases present and the elapsed time since the last arrival. From this distribution, we obtain the distributions of the number of customers both at an arbitrary moment and just after an arrival. Furthermore, we show some interesting properties on the mean number of customers from numerical examples.
