The main objective of this paper is study and analytical modeling of a cluster system. A closed G-network with positive and negative requests is used as a mathematical model of the cluster system. Negative requests are associated with negative impact of malicious code and errors on model nodes. In addition, in the G-network there is a sequence of rewards or earnings that is generated in the process of transmitting requests between cluster nodes. The model is studied in the asymptotic case of a large number of requests being processed. The purpose of this paper is to calculate the expected total reward of the cluster system model in the asymptotic case. An ordinary differential equation for the expected reward that the cluster model will earn in a time t if it starts in a given initial state is derived. The presented technique allows to analyse the cluster system efficiency with mathematically specified accuracy.