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.
Publisher
Cambridge University Press (CUP)
Subject
Industrial and Manufacturing Engineering,Management Science and Operations Research,Statistics, Probability and Uncertainty,Statistics and Probability
Reference8 articles.
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3. 2. Gelenbe E. (to appear). Non-linear resolvents for very large linear systems. In Proceedings of the Institute for Mathematics and Its Applications Workshop on Numerical Methods in Markov Chains, 01 1991, University of Minnesota, Minneapolis.
4. Stability of Product Form G-Networks
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