Equivalence relations in queueing models of Fork/Join networks with blocking

Fork/join (F/J) networks can be used to model parallel processing computer systems.and manufacturing systems. In this paper, we present some fundamental equivalence properties that hold for F/J networks with blocking. Two networks that are equivalent may appear different, but their behavior is closely related. Their throughputs are the same and there is a simple relationship between their average buffer levels. We study a model of F/J networks where processing times are exponentially distributed. We prove a theorem that provides a test for equivalence and illustrate it with several examples.