In this paper an analysis of the blocking probability in a finite-buffer queue fed by a batchMarkovian arrival process (BMAP) is carried out. In particular, the Laplace transform of the blocking probability is obtained, giving both, timedependent and stationary characteristics. Analytical results are illustrated via numerical calculations. Namely, sample transient and stationary blocking probabilities are shown and the impact of the auto-correlated structure of the arrival process on the blocking probability is presented.