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For tandem queues and forkljoin queueing networks with communication blocking, the stochas- tic comparison, reversibility and other equivalence properties have been studied. In this paper, we consider a forkljoin 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.

STOCHASTIC PROPERTIES OF FORK/JOIN MULTI-STAGE PRODUCTION SYSTEMS WITH GENERAL BLOCKING