Translated by O. Pismenov
The article considers a file distribution model in a peer-to-peer file-sharing network based on ordinary differential equations. Phase variables describing the file-sharing state are determined (in the first approximation, this is the number of users, i.e., seeders and leechers of the shared file). The factors affecting file sharing and the change in the number of peers are analyzed. The system of differential equations describing the evolution of a torrent, or a file-sharing session (FSS), i.e., the dynamic FSS evolution model, is constructed based on the analysis. The life cycle of a FSS in the file-sharing network consisting of four stages, i.e., file sharing initiation, rapid increase in the number of leechers, stabilization, and fading (for files that lose relevance over time), is considered. Each stage is characterized by its own ratio of model parameters. The parameters change over time. The process of measuring the state of real FSSs is described. An example of a trajectory corresponding to the evolution of a real FSS on a large torrent tracker is given. Next, the FSS stabilization stage characterized by parameters that are constant in the first approximation is considered. Equilibrium points of the dynamic model of the FSS evolution are investigated. Their possible number and type are described. All generic position configurations that are possible in the FSS evolution model of a peer-to-peer file-sharing network are described. Phase portraits of each configuration are presented. The impact of various administrative measures on FSS stability margin is analyzed. The ambiguity of the effect of the rating system on FSS stability is shown. The positive effects of a system of time bonuses, feedback, and absorption of FSSs are also shown.