Analysis of networks with positive and negative messages at transient behavior

The object of research is queueing network with one-line systems, positive and negative messages which can be used to model the behavior of viruses in the information and telecommunication systems and networks. It is obtained a system of difference-differential equations for the non-stationary states probabilities of the network. To find the state probabilities of the network applied a methodology based on the use of the apparatus of multidimensional generating functions. It is obtained an expression for generating function. Also is conducted an investigation of such a network with incomes (HM-networks). It is considered the case: when the incomes from the state transition networks are deterministic functions depending on network states and time. It is obtained a system of difference-differential equations for the expected incomes of systems in the network. It is proposed the ways of solving it.