**MATHEMATICAL AND SIMULATION MODELING OF A CLOSED DISTRIBUTED REGISTRY WITH A CONTROL NODE **

UDC 004.942

DOI:10.26102/2310-6018/2020.29.2.001

V.A. Evsin, S.N. Shirobokova, S.P. Vorobyov, V.A. Evsina

*This article presents mathematical and simulation modeling of a distributed registry with a control node on the example of the raft consensus algorithm. The process of interaction between individual nodes of the distributed registry network is described, special attention is paid to the algorithm for conducting transactions within this network. The key aspect of this article is the development of a mathematical model of a distributed registry network as a Queuing system using queue theory. We consider the conceptual models of both the distributed registry as a whole and the model of the information process for accessing a cluster of notary nodes. Mathematical modeling of the distributed registry network, as well as the information process of obtaining access to the control node of the network. The state space is represented in a distributed registry with a control node. The description of an infinitesimal matrix for estimating the probability of transitions between States in a distributed registry is formed, the transition probabilities and the intensity of these processes are described. The characteristic of the laws of distribution of indicators in the system under consideration is described. Another important aspect of this article is the simulation of the process in order to identify the best combination of parameters to achieve maximum efficiency. A stack of variable indicators of the simulation model is formed. Tests were carried out on the basis of which the most effective set of characteristics was selected empirically. The results of mathematical and simulation modeling of a distributed registry with a control node are presented.
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**Keywords:**distributed registry, DLT system, consensus algorithm, mathematical modeling, infinitesimal matrix, Queuing theory, queue theory, simulation modeling.

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