The signals bring commands to the service nodes and may trigger customers to move instantly within the network. We consider a network of queues with multiple classes of customers, signals, and arbitrary service time distributions. Network stability is discussed in this new context. We show that this new class of network has product-form stationary solution, and establish the non-linear customer flow equations which govern it. This synchronized 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.

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. 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. The generalized queueing networks (G-networks) which we introduce in this paper contain customers and signals. We prove that the steady-state distribution for such a network of queues has a product form solution. As usual, after completion of its service, a customer moves to another queue and may become a When a signal enters a queue, it changes the phase of the customer Here, we propose a new generalization of this model with But most papers assume to obtain a productįorm such that the service times follow exponential distributions. Sci., 7, 335–342), generalized networks of queues have received considerable attention. (1993) G-Networks with signals and batch removal. (1993) G-networks with instantaneous customer movement.

(1991) Product-form queueing networks with negative and positive customers. Since the seminal papers by Gelenbe in theĮarly 1990s (Gelenbe, E. We consider a queueing network of symmetric G-queues with customers and signals.

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