We study congestion periods in a finite fluid buffer when the net inputrate depends upon a recurrent Markov process; congestion occurs whenthe buffer content is equal to the buffer capacity. Similarly to [10], weconsider the duration of congestion periods as well as the associated volumeof lost information. While these quantities are characterized by their Laplacetransform in that paper, we presently derive their distributions in a typicalstationary busy period of the buffer. Our goal is to compute the exactexpression of the loss probability in the system, which is usually approximatedby the probability that the occupancy of the infinite buffer isgreater than the buffer capacity under consideration. Moreover, by using general results of thetheory of Markovian arrival processes, we show that the duration of congestionand the volume of lost information have phase-type distributions.