Constructing the mathematical model of a recommender system for decentralized peer-to-peer computer networks

Recommender systems make it easier to search with a large amount of content, supplementing or replacing the classic search output with recommendations. In P2P networks, their use can have additional benefits. Because of indexing and search problems, previously added files may not be available to P2P network users. If the user cannot find the file he is looking for, one can provide him with a list of recommendations based on his preferences and search query. The object of research is the process of creating recommendations for users of decentralized P2P networks to facilitate data search. The urgent task of increasing the accuracy of mathematical modeling of recommender systems by taking into account the requirements for reliability and data security during changes in the structure of a decentralized P2P network is solved. An analytical model of the recommender system of a decentralized P2P network has been developed, the main feature of which is taking into account the requirements of reliability and security of recommendation messages. This was done by introducing the following indicators into the general model of the decentralized recommender system – the probability of reliable packet transmission and the probability of safe packet transmission. The developed analytical model makes it possible to conduct a comparative analysis of different methods of operation of recommender systems and to set acceptable parameters under which the degree of relevance does not fall below a certain threshold. The developed mathematical model of the system based on the GERT scheme differs from the known ones by taking into account the reliability and security requirements during changes in the structure of the decentralized P2P network. This has made it possible to improve the accuracy of simulation results up to 5 %. The proposed mathematical model could be used for prototyping recommender systems in various fields of activity