AUTHORS: Eugene Lebedev, Hanna Livinska
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ABSTRACT: In this paper stationary properties of queueing network with exponentially distributed service times are investigated provided that an input flow is controlled by a Markov chain. We consider two cases. In the case, where we have one node only, a generating function of a stationary distribution is obtained. The form of the generating function is a matrix version of the Takacs formula. In the second case, a network with service nodes is considered. For a multivariate service process the condition of a stationary regime existence and a correlation matrix are found.
KEYWORDS: Multi-channel queueing networks, controlled input, stationary regime
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