On Stationary Regime for Queueing Networks with Controlled Input

摘要

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 r > 1 service nodes is considered. For a multivariate service process the condition of a stationary regime existence and a correlation matrix are found.