G-networks by triggered customer movement

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Abstract
The generalized queueing networks (G-networks) which we introduce in this paper contain customers and signals. Both customers and signals can be exogenous, or can be obtained by a Markovian movement of a customer from one queue to another after service transforming itself into a signal or remaining a customer. A signal entering a queue forces a customer to move instantaneously to another queue according to a Markovian routing rule, or to leave the network, while customers request service. This synchronised or triggered motion is useful in representing the effect of tokens in Petri nets, in modelling systems in which customers and work can be instantaneously moved from one queue to the other upon certain events, and also for certain behaviours encountered in parallel computer system modelling. We show that this new class of network has product-form stationary solution, and establish the non-linear customer flow equations which govern it. Network stability is discussed in this new context.

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