Dynamic Model of Growing File-Sharing P2P Network

Abstract

This work considers the model of developing the P2P file exchange network organized by a torrent tracker. The model is constructed on the basis of ordinary differential equations. The phase variables describing the status of a torrent tracker and the network organized by it (at a first approximation this means the number of the tracker’s users, who actively participate in the information exchange, and the number of active torrents) are defined, and the factors influencing the change in the numbers of users and torrents analyzed. The analysis is used to develop a system of differential equations for describing, at a first approximation, the file exchange network organized by the torrent tracker — the hard dynamic model of the torrent tracker’s evolution. The equilibrium points of the hard model of the tracker’s evolution are analyzed, their possible quantity and type is described. All of the configurations of the general provision, possible in the hard model of the tracker’s evolution are described. The phase portrait of the hard model is represented. The analysis of the hard model is used to derive the system of differential equations that describes the evolution of a file exchange network, considering the dependence of the intensity of the influx of new users on the total size of the torrent tracker’s potential audience, and also the dependence of the torrent dying out rate on the number of users per torrent — the soft dynamic model of the torrent tracker’s evolution. The special points in the soft model are analyzed and their possible number and type described. All of the configurations of the general provision possible in the soft model of evolution are described. The phase portraits of each configuration are represented. The correlation of the parameters necessary for the tracker’s stability is calculated. The influence of various administrative measures on the tracker’s overall stability margin is analyzed. The need for supporting torrents by administrations of highly specialized torrent trackers with a small potential audience is shown.

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Correspondence to A. I. Kononova or L. G. Gagarina.

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The authors declare that they have no conflicts of interest.

ADDITIONAL INFORMATION

Alexandra I. Kononova, orcid.org/0000-0002-4178-3828, PhD.

Larisa G. Gagarina, orcid.org/0000-0003-2371-9045, Doctor of Engineering Sciences.

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Translated by S. Kuznetsov

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Kononova, A.I., Gagarina, L.G. Dynamic Model of Growing File-Sharing P2P Network. Aut. Control Comp. Sci. 54, 645–651 (2020). https://doi.org/10.3103/S014641162007010X

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Keywords:

  • file-sharing network
  • ordinary differential equations (ODEs)
  • dynamical systems
  • stability