In this paper, we focus attention on discrete-time buffer models with general independent arrivals and multiple output links, a class of queueing models which is well-suited to address performance issues in slotted systems, such as ATM. Calculating the Cell Loss Ratio (CLR), a key performance measure whenever finite-capacity buffers are involved, requires solving a set of linear equations, the size of which depends on the buffer capacity J(. Therefore, the CLR is often approximated by some appropriate tail probability of the buffer contents in the corresponding infinite-capacity queueing model; however, how these two quantities are related, is generally not very well known. In this paper, using a generating-functions approach,. we establish an exact relation between the distribution of the number of cells lost pelf slot in a finite-capacity queue, and the distribution of the buffer contents in the corresponding iniinite-capacity queue. This eventually leads to an extremely accurate dosed-form approximation for the CLR in the finite-buffer system, that is easily evaluated.