Throughput bounding and simple approximation methods for exponential fork/join queueing networks with blocking

Exponential fork/join queueing networks (FJQNs) with finite buffers have been used as a major tool for evaluating the performances of manufacturing systems. In this study, we first suggest the throughput upper and lower bounds. Our upper-bounding method is elaborated on with general network configuration (acyclic configuration), while our lower bounds can be obtained only for networks with more specialized configuration. Next, developed is a simple approximation method for throughputs, which are based on decomposition/aggregation principles and structurally equivalent relations between different configurations.