Application of a z-transforms method for investigation of Markov G-networks

The purpose of this research paper is to find the expected incomes in open Markov queueing networks with incomes, positive and negative messages at any time by the multidimensional transformations. Investigations were carried out in cases when incomes from the network transitions between the states are deterministic functions not dependent on network states and time. It is assumed that all network systems are one-line. It was proved the theorem on the expression for the multidimensional z-transform. An algorithm was proposed for calculation of expected incomes. It is calculated an example on the PC.