Application of (Max, +)-algebra to the waiting times in deterministic 3-node tandem queues with blocking

In this paper, we consider characteristics of waiting times in single-server 3-node tandem queues with finite buffers, a Poisson arrival process and deterministic service times at all nodes. There are three buffers: one at the first node is infinite and the others are finite. We obtain the fact that sojourn time or departure process is independent of the capacities of the finite buffers and does not depend on the order of service times, which are the same results as in the literature. Moreover, the explicit expressions of stationary waiting times in all areas of the systems can be derived as functions of the finite buffer capacities. We also disclose a relationship of waiting times in subareas of the systems between two blocking policies: communication and manufacturing. Some numerical examples are also provided.