Displaying similar documents to “Dobrushin's approach to queueing network theory.”

Product form solution for g-networks with dependent service

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 c n 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...

Study of Queuing Systems with a Generalized Departure Process

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....

Fluid limits for the queue length of jobs in multiserver open queueing networks

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...