G-NETWORKS WITH TRIGGERED CUSTOMER MOVEMENT

The generalized queueing networks (G-networks) which we introduce in t his paper contain customers and signals. Both customers and signals ca n be exogenous, or can be obtained by a Markovian movement of a custom er from one queue to another after service transforming itself into a signal or remaining a customer. A signal entering a queue forces a cus tomer to move instantaneously to another queue according to a Markovia n routing rule, or to leave the network, while customers request servi ce. This synchronised or triggered motion is useful in representing th e effect of tokens in Petri nets, in modelling systems in which custom ers and work can be instantaneously moved from one queue to the other upon certain events, and also for certain behaviours encountered in pa rallel computer system modelling. We show that this new class of netwo rk has product-form stationary solution, and establish the non-linear customer flow equations which govern it. Network stability is discusse d in this new context. AMS 1991 SUBJECT CLASSIFICATION: PRIMARY 60 K25