Equivalence relation between Fork-Join systems and N-stage queueing networks.

Queueing networks with Fork-Join primitives are commonly used to model several systems with parallel activities. Unfortunately, these models are rather hard to solve analytically, as the limited results that appear in literature testify. The main concern of this paper is to show the equivalence between Fork-Join models, with n parallel servers and n- stage queueing networks with suitable state-dependent service rates. The equivalence relation is demonstrated by observing the isomorphism between the state transition diagrams of the Markovian processes relating to the two systems (both in the open and the short-circuited cases). This equivalence allows us to analytically solve the Fork-Join system with two and three parallel servers by analysis of the n-stage queueing network. The accuracy of this approach is