The article is devoted to the study of the problem of optimizing the hierarchical structure of a multicommodity communication network with discrete flows when changing its important parameters, such as the capacity of network arcs in transport blocks and the size of the transport block for transportation of the discrete small-lot cargo or of the data transmission in a digital communication network. The network has three levels of hierarchy - a backbone, a zonal and an internal and four types of nodes - backbone nodes of the first, second and third types, forming the backbone and zonal levels of the network, and nodes of the fourth type, which subordinate to each backbone node and forming the internal levels of the network. Types of nodes differ from each other in terms of functionality. The main task of the study is to establish how the structure of the backbone network changes (the number and location of backbone nodes of the first, second, and third types), the flow processing and distribution scheme, and the technical and economic indicators of the network's functioning for different values of its parameters. The principles of organization of sorting and distribution of flows in a three-level network and its mathematical model are given. A mathematical model of the optimization problem of the backbone network structure and flow sorting and distribution scheme is formulated. Computer modeling of the problem on a network containing 10 nodes at the specified change in the both parameters is carried out.