Departure process in a mixed fork–join synchronization network

In this article we consider a mixed fork–join synchronization Markovian queueing network consisting of two input buffers, B1B1 and B2B2, fed by arrivals from two populations. The first is a finite population of size KK and second population is infinite. The first population feeds the first buffer and the second population feeds the second finite 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, performance measures, and characterization of the departure process; in particular we provide the marginal distribution of inter-departure times.