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G-Networks with Signals and Batch Removal

Published online by Cambridge University Press:  27 July 2009

Erol Gelenbe
Erol Gelenbe
Affiliation:
Duke University, Department of Electrical EngineeringDurham, North Carolina 27706
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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.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 7 , Issue 3 , July 1993 , pp. 335 - 342
Copyright
Copyright © Cambridge University Press 1993

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References

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