Finding non-stationary state probabilities of G-network with signals and customers batch removal

What is it about?

The article is devoted to the research of an open Markov queueing network with positive customers and signals, and positive customers batch removal. A way of finding in a non-stationary regime time-dependent state probabilities has been proposed. The Kolmogorov system of difference-differential equations (DDE) for state probabilities of such network was derived. The technique of it’s building, based on the use of the modified method of successive approximations combined with a series method, has been proposed. It is proved that the successive approximations converge over time to the stationary state probabilities, and the sequence of approximations converges to the unique solution of the Kolmogorov equations. Any successive approximation can be represented as a convergent power series with infinite radius of convergence, the coefficients of which satisfy the recurrence rela-tions; that is useful for estimations. Model example illustrating the finding of time-dependent state probabilities of the network has been provided.

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Why is it important?

In the paper an investigation of the Markovian G-network with signals was conducted in the case when a negative customer or signal can destroy a random batch of positive customers. For this network, non-stationary state probabilities were found by the method of successive approximations, com-bined with the method of series.

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