This paper considers a finite-buffer discrete-time GeoX/GY/1/K + B queue with multiple vacations that has a wide range of applications including high-speed digital telecommunication systems and various related areas. The main purpose of this paper is to present a performance analysis of this system. For this purpose, we first derive a set of linear equations to compute the steady-state departure-epoch probabilities based on the embedded Markov chain technique. Next, we present numerically stable relationships for the steady-state probabilities of the queue lengths of three different epochs: departure, random, and arrival. Finally, based on these relationships, we present various useful performance measures of interest such as the moments of the number of packets in the queue at three different epochs, the mean delay in the queue of a packet, the loss probability and the probability that server is busy with computational experiences.
