Properties of fork/join queueing networks with blocking under various operating mechanisms

In a recent paper, Dallery-Liu-Towsley (1994) considered a special class of queueing networks with fork/join mechanisms and finite-capacity buffers called basic fork/join queueing networks with blocking (B-FJQN/B). For this class of networks, they established duality, reversibility, symmetry, and concavity properties. However, in order to be able to accurately model the various operating mechanisms (blocking, loading, and unloading mechanisms) encountered in manufacturing systems, it is necessary to consider a larger class of networks that will be referred to as FJQN/B. The purpose of this paper is to introduce this class of queueing networks and investigate its properties. The approach is to first show that any FJQN/B can be equivalently represented as a B-FJQN/B and then use results derived in the Dallery-Liu-Towsley paper for the underlying B-FJQN/B to establish the properties of the model under consideration. This approach is also used to compare the behavior of two models having different operating mechanisms. The usefulness of these results for performance evaluation and optimization of manufacturing systems is illustrated through a few examples.