Reflecting diffusions and queueing networks.
Williams, R.J. (1998)
Documenta Mathematica
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Williams, R.J. (1998)
Documenta Mathematica
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J. P. Keller (1978)
Publications du Département de mathématiques (Lyon)
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Cristian Coletti, Glauco Valle (2014)
Annales de l'I.H.P. Probabilités et statistiques
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We introduce a system of one-dimensional coalescing nonsimple random walks with long range jumps allowing paths that can cross each other and are dependent even before coalescence. We show that under diffusive scaling this system converges in distribution to the Brownian Web.
Alfred Aanu Akinsete (2001)
Kragujevac Journal of Mathematics
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Daduna, Hans (1991)
Journal of Applied Mathematics and Stochastic Analysis
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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...
B. Popovic (1980)
Publications de l'Institut Mathématique [Elektronische Ressource]
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Pavel Bocharov, Ciro D'Apice, Evgeny Gavrilov, Alexandre Pechinkin (2004)
RAIRO - Operations Research - Recherche Opérationnelle
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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: (0) an exponential node with servers, infinite buffer and FIFO discipline; (1) an infinite-server node; (2) a single-server node with infinite buffer and LIFO PR discipline; (3) a...
Karpelevich, F.I., Pechersky, E.A., Suhov, Yu.M. (1996)
Journal of Applied Mathematics and Stochastic Analysis
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Lawler, Gregory F. (1998)
Mathematical Physics Electronic Journal [electronic only]
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K. L. Arya, E. Stachowski (1972)
Applicationes Mathematicae
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Nizar Demni, Dominique Lépingle (2012)
Rendiconti del Seminario Matematico della Università di Padova
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Sznitman, Alain-Sol (1998)
Documenta Mathematica
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Dirnböck, Hans, Stachel, Hellmuth (1997)
Journal for Geometry and Graphics
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Soucaliuc, Florin, Werner, Wendelin (2002)
Electronic Communications in Probability [electronic only]
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