To improve the efficiency of networks, fully automate the processes of network management, administration and technological, reduce the time to market for modern services, ensure the introduction of new technologies throughout the network, and not gradually introduce them at individual sites, operators are starting the practical use of software-defined networks with virtualization network functions. The optimality of the decisions made, largely depends on the capabilities of the control plane in the SDN architecture. To obtain optimal solutions, a mathematical formulation of control problems is required, using real indicators of the functioning of telecommunication networks as input data. The paper proposes mathematical models of the process of functioning of the SDN network in the main modes of operation: in the mode of planned changes in the structure of the network, in the mode of normal functioning, when all performance indicators are within the specified values, in the overload mode. The results obtained make it possible to determine the list of required network elements, to distribute functions between the elements of the control system, to develop requirements for the monitoring system to collect the necessary initial data and to determine the interaction algorithm of the elements to obtain optimal solutions in the process of network management.