Multiserver queueing networks and the tandem queue model.
Le Gall, Pierre (1998)
Journal of Applied Mathematics and Stochastic Analysis
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Le Gall, Pierre (1998)
Journal of Applied Mathematics and Stochastic Analysis
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Mirtchev, Seferin, Statev, Stanimir (2008)
Serdica Journal of Computing
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This work was supported by the Bulgarian National Science Fund under grant BY-TH-105/2005. This paper deals with a full accessibility loss system and a single server delay system with a Poisson arrival process and state dependent exponentially distributed service time. We use the generalized service flow with nonlinear state dependence mean service time. The idea is based on the analytical continuation of the Binomial distribution and the classic M/M/n/0 and M/M/1/k system....
Le Gall, Pierre (1997)
Journal of Applied Mathematics and Stochastic Analysis
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H. G. Perros (1981)
RAIRO - Operations Research - Recherche Opérationnelle
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Bérczes, Tamás (2008)
Annales Mathematicae et Informaticae
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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...
Muh, David C.R. (1993)
Journal of Applied Mathematics and Stochastic Analysis
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Kasahara, Shoji, Takagi, Hideaki, Takahashi, Yutaka, Hasegawa, Toshiharu (1996)
Journal of Applied Mathematics and Stochastic Analysis
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Erol Gelenbe (2004)
RAIRO - Operations Research - Recherche Opérationnelle
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Cooper, Robert B., Niu, Shun-Chen, Srinivasan, Mandyam M. (1998)
Journal of Applied Mathematics and Stochastic Analysis
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Gang Chen, Zhong Yang (2014)
International Journal of Applied Mathematics and Computer Science
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Gang Chen, Zhong Yang (2014)
International Journal of Applied Mathematics and Computer Science
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Le Gall, Pierre (2001)
Journal of Applied Mathematics and Stochastic Analysis
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Andrzej Chydziński, Łukasz Chróst (2011)
International Journal of Applied Mathematics and Computer Science
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Queueing systems in which an arriving job is blocked and lost with a probability that depends on the queue size are studied. The study is motivated by the popularity of Active Queue Management (AQM) algorithms proposed for packet queueing in Internet routers. AQM algorithms often exploit the idea of queue-size based packet dropping. The main results include analytical solutions for queue size distribution, loss ratio and throughput. The analytical results are illustrated via numerical...