Discrete-time queueing models have been studied for many years because of their direct applicability in the performance evaluation of digital communication system and networks, where buffers are used to temporarily store information packets which cannot be transmitted instantaneously. In this paper, we investigate the behavior of a discrete-time multiserver buffer system with infinite buffer size. Packets arrive in the system according to a two-state correlated arrival process. The service times of the packets are assumed to be independent and identically distributed according to a geometric distribution. We present an analytical technique, based on the use of generating functions, for the analysis of the system. Explicit expressions are obtained for the mean values, the variances and the tail distributions of the system contents and the packet delay. The influence of the various model parameters on the behavior of the system is shown by means of some numerical examples.