Dynamic Model of Single Torrent with File-Sharing P2P Network

Abstract

In this work, a model of distribution of the file in P2P file-sharing network constructed on the basis of ordinary differential equations is considered. The phase variables which describe a condition of distribution of the file (as a first approximation is the number of users – seeder and leecher on distribution) are defined, the factors which influence the file distribution and the change of the number of users participating in exchange are analysed. On the basis of the analysis the system of the differential equations describing distribution evolution – dynamic model of evolution of distribution is written down. The life cycle of distribution in file-sharing network consisting of four stages – distribution creation, a fast gain leechers, stabilization and (for distributions of the files losing over time relevance) fading is considered. To each stage there corresponds the ratio of model parameters, and parameters change over time. The process of measuring the condition of real distributions is described. An example of the trajectory corresponding to the evolution of real distribution at a large torrent tracker is shown. Further, the distribution stabilization stage which is characterized by constants as a first approximation parameters is considered. Equilibrium points of the dynamic model of distribution evolution are investigated, their possible quantity and type are described. All configurations of the general position, possible in the model of distribution evolution in a file-sharing P2P network are described. Phase portraits of each configuration are represented. The influence of various administrative measures on a stock of distribution stability is analysed. Ambiguity of the influence of a rating accounting system on the stability of distributions is shown. The positive influence of a system of timebonus, feedback and absorption of distributions is also shown.