On network flow equations and splitting formulas for sojourn times in queueing networks.
Daduna, Hans (1991)
Journal of Applied Mathematics and Stochastic Analysis
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Daduna, Hans (1991)
Journal of Applied Mathematics and Stochastic Analysis
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Tie Qiu, Lin Feng, Feng Xia, Guowei Wu, Yu Zhou (2011)
Computer Science and Information Systems
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Karpelevich, F.I., Pechersky, E.A., Suhov, Yu.M. (1996)
Journal of Applied Mathematics and Stochastic Analysis
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Alfred Aanu Akinsete (2001)
Kragujevac Journal of Mathematics
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K. L. Arya, E. Stachowski (1972)
Applicationes Mathematicae
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J. P. Keller (1978)
Publications du Département de mathématiques (Lyon)
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Pavel Bocharov, Ciro D'Apice, Evgeny Gavrilov, Alexandre Pechinkin (2010)
RAIRO - Operations Research
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We consider a G-network with Poisson flow of positive customers. Each positive customer entering the network is characterized by a set of stochastic parameters: customer route, the length of customer route, customer volume and his service length at each route stage as well. The following node types are considered: Negative customers arriving at each node also form a Poisson flow. A negative customer entering a node with customers in service, with probability chooses one of served...
Erol Gelenbe (2004)
RAIRO - Operations Research - Recherche Opérationnelle
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Walenty Oniszczuk (2009)
International Journal of Applied Mathematics and Computer Science
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This paper describes an analytical study of open two-node (tandem) network models with blocking and truncation. The study is based on semi-Markov process theory, and network models assume that multiple servers serve each queue. Tasks arrive at the tandem in a Poisson fashion at the rate λ, and the service times at the first and the second node are nonexponentially distributed with means sA and sB , respectively. Both nodes have buffers with finite capacities. In this type of network,...
Joanna Domańska, Adam Domański, Dariusz Augustyn, Jerzy Klamka (2014)
International Journal of Applied Mathematics and Computer Science
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Saulius Minkevičius (2014)
RAIRO - Operations Research - Recherche Opérationnelle
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The object of this research in the queueing theory is a theorem about the Strong-Law-of-Large-Numbers (SLLN) under the conditions of heavy traffic in a multiserver open queueing network. SLLN is known as a fluid limit or fluid approximation. In this work, we prove that the long-term average rate of growth of the queue length process of a multiserver open queueing network under heavy traffic strongly converges to a particular vector of rates. SLLN is proved for the values of an important...
Bérczes, Tamás (2008)
Annales Mathematicae et Informaticae
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Živko Bojović, Emil Šećerov, Vlado Delić (2010)
Computer Science and Information Systems
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