Characterization of the departure process in a closed fork-join synchronization network

In this article we consider a closed fork-join synchronization Markovian network, where a queueing model consisting of two finite input buffers, B1 and B2, fed by arrivals from two finite populations of sizes K1 and K2 is investigated. The first population feeds the first buffer and the second population feeds the second buffer. As soon as there is one part in each buffer, two parts one from each buffer are joined and exit immediately. We provide model analysis and characterization of the departure process; in particular we provide the marginal distribution of inter-departure times.