G-Networks with Signals and Batch Removal
- 1 January 1993
- journal article
- research article
- Published by Cambridge University Press (CUP) in Probability in the Engineering and Informational Sciences
- Vol. 7 (3) , 335-342
- https://doi.org/10.1017/s0269964800002953
Abstract
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.Keywords
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