Stochastic properties of fork/join multi-stage production systems with general blocking

For tandem queues and fork/join queueing networks with communication blocking, the stochastic comparison, reversibility and other equivalence properties have been studied. In this paper, we consider a fork/join multi-stage production system with general blocking which includes the above models as special cases. Under the weak conditions of the initial numbers of items, we formulate this system into a generalized semi-Markov process (GSMP). Then we show the convex property of the GSMP, the stochastic comparison with respect to stochastic and convex ordering, the reversibility and the structural equivalence.