The article presents a novel approach to solving complex problems of queuing theory in general and to the analysis of closed queuing networks, in particular. The main idea is to combine a simulation on a limited set of input parameters with data mining methods. As an example of applying this approach, the paper evaluates the main performance parameters of a closed exponential queuing network, for which, as is known, methods of analytical and numerical analysis have been developed with some restrictions on its structure. The specified network was chosen in order to qualitatively test the proposed approach, as well as to demonstrate its effectiveness on a very large amount of input data, which is an essential distinguishing feature of this work. The maximum approximation error of the estimates of the mean sojourn times of customers obtained in the study, as well as their average number in the network nodes, does not exceed 5%. The new approach is universal in nature, and its field of application is not limited to studies of only exponential networks, therefore, it can be used to study more complex queuing networks.