G-Networks with Signals and Batch Removal

We consider queueing networks containing customers and signals that were recently introduced in Gelenbe [4]. Both customers and signals can be exogenous or can be obtained by a Markovian transition of a customer after service. A signal entering a queue forces a customer to move on to another queue according to a Markovian routing rule or to leave the network in batch mode. This synchronized or triggered motion is useful in representing the effect of tokens in Petri-nets, for systems in which customers and work can be instantaneously moved from one queue to the other on the arrival of a signal as well as for other network behaviors that are encountered in parallel computer system modelling. We show that this network has product form stationary solution and establish the non-linear customer flow equations that govern it. Network stability is discussed in this new context.