Investigation in non-stationary mode of $G$-network with signal and group removal customers by successive approximation method

A study was conducted in the $G$-network transition mode with positive customers and signals, when they move the customers to another system or destroy a group of positive customers in it, reducing their number by a random amount, which is specified by some probability distribution. A signal arriving at a system in which there are no positive applications does not have any influence on the queuing network and immediately disappears from it. Streams of positive applications and signals coming to each of the network systems are independent. For nonstationary probabilities of network states, a system of Kolmogorov difference-differential equations is derived. A method for finding them is proposed. It is based on the use of a modified method of successive approximations, combined with the method of series. The properties of successive approximations are considered.