Abstract
Investigation of the G-network with multiple classes of positive and negative customers has been carried out in the article. The purpose of the investigation is to analyze such a network at a transient regime, finding expected revenues in the network systems depending on time. A negative customer arriving to the system and destroys a positive customer of its class. Streams of positive and negative customers arriving to each of the network systems are independent. Services of positive customers of all types occur in accordance with a random selection of them for service. For the expected revenues, a system of Kolmogorov's difference-differential equations has been derived. A method for their finding is proposed. It is based on the use of a modified method of successive approximations, combined with the method of series. A model example illustrating the finding of time-dependent expected revenues of network systems has been calculated, which shows that the expected revenues of network systems can be either increasing or decreasing time functions. The obtained results can be applied in forecasting losses in information and telecommunication systems and networks from the penetration of computer viruses into it and conducting computer attacks.
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