Abstract
The article is devoted to the development of mathematical functional and statistical models of objects of control and management, analysis of differential systems of equations, which are determined using the following methods: method of differential equations, quasilinear equations, Monte Carlo method. When developing a mathematical functional-statistical model, it is taken into account that the network as an object of control can consist of systems of various classes and types. These systems can be autonomous and non-autonomous, closed and open, stationary and non-stationary, continuous and discrete. Therefore, to build a mathematical functional statistical model, it is necessary to use a fairly general mathematical apparatus, which with appropriate changes can be extended to individual cases. In addition, when building a mathematical functional and statistical model of the object, it is also necessary to have an idea of the main criteria by which the optimization of the characteristics of the control and management process.These criteria primarily include: the time required to complete the process as a whole and its components; probability of trouble-free operation; the probability of performing the task by various network elements included in the object, and the object as a whole; probability of error; delay in the transmission of control information; readiness factor; packet loss percentage; accuracy of work of various components of an infocommunication network (size of deviation of parameters from norm); cost, energy consumption and other important indicators. The analysis and construction of the system of equations is carried out, which allows to determine the functional state of the object, the complex of the control system and to evaluate its efficiency. This will directly determine the probability of gradual failures of the object's systems both in normal mode and in the event of a crisis situation, maximum loads. For control and management can be any equipment, as well as the entire network as a whole. Criteria for optimal operation of the control system are its performance and reliability, which are determined by specific evaluation indicators (response time, error rate, system cost, etc.). These parameters, which directly or indirectly affect the criteria of optimality, can be varied in order to improve the efficiency of the control system.
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