An upper bound for carriers in a three-workstation closed serial production system operating under production blocking

We develop and prove a rule for an upper bound on the optimal number of carriers (with respect to throughput) in a three-workstation closed serial production system with finite buffers, operating under production blocking (blocking-after-service). This system is, in fact, a three server (single server) closed tandem queueing system with finite buffers. Our assumptions regarding service time distributions are nonrestrictive and include the case of iid random variables.