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Closed G-networks with Resets: product form solution
Edinburgh, Scotland, UK September 17-September 19
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/QEST.2007.39Fourth International Conference on th ...
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Jean-Michel Foumeau, Universite de Versailles Saint-Quentin, France; Projet MESCAL INRIA, France
We consider a closed queueing network of generalized queues with customers and signals. Each queue has an infinite capacity and one server. The service time is exponential. After its service completion a customer moves to another queue and may become a signal. When the signal enters a non empty queue it vanishes while it resets the queue when it enters an empty queue. We prove that the steady state distribution for such a closed network of queues has a product form solution. To the best of our knowledge it is the first closed network of generalized queues with product form solution. We also consider a more complex system where the reset acts upon a set of queues rather than a single one. We also prove that the steady-state distribution exists and has a product form.
Citation:
Jean-Michel Foumeau, "Closed G-networks with Resets: product form solution," qest, pp.287-296, Fourth International Conference on the Quantitative Evaluation of Systems (QEST 2007), 2007
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