Tandem queues provide good mathematical models of computer systems and networks, and their detailed examination is important for theory and applications. The study presented in this paper is based on performance analysis of a two-server computer network with blocking and deadlocking. New, practical results provided describe performance of a three-node Markovian queuing network with finite capacity buffers. The results highlight an area where measures of effectiveness, such as Quality of Service (QoS) are essential. In conclusion, a two-dimensional state graph is constructed, followed by a set of steady-state equations along with their probabilities for each of the states.