Geodesic
Dynamic model of growing file-sharing P2P network
Modelirovanie i analiz informacionnyh sistem, Tome 26 (2019) no. 3, pp. 351-359 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this work, the model of development of the P2P file exchange network organized by a torrent tracker is considered. The model is constructed on the basis of ordinary differential equations. The phase variables describing a status of a torrent tracker and the network organized by it (in first approximation is the number of the users of the tracker who are actively participate in information exchange, and the number of active torrents) are defined, the factors influencing the change of users number and the number of torrents are analyzed. On the basis of the analysis the system of differential equations, in first approximation describing evolution of the file exchange network organized by the torrent tracker — a hard dynamic model of evolution of the torrent tracker is written. Equilibrium points of hard model of evolution of the tracker are investigated, their possible quantity and type is described. All configurations of the general provision, possible in a hard model of evolution of the torrent tracker are described. The phase portrait of the hard model is represented. On the basis of the analysis of the hard model the system of differential equations describing evolution of a file exchange network with accounting of dependence of new users inflow intensity on a total quantity of potential audience of the torrent tracker, and also dependences of speed of torrents extinction on the number of users falling on one torrent — a soft dynamic model of evolution of a torrent tracker is written. Equilibrium points of a soft model of tracker evolution are investigated, their possible quantity and type is described. All configurations of the general provision, possible in a soft model of evolution of the torrent tracker are described. Phase portraits of each configuration are represented. The ratio of parameters necessary for the stability of the tracker a stable status is received. The influence of different administrative measures on a stock of the tracker stability in whole is analyzed. The need of support of torrents by administration at highly specialized torrent trackers with small potential audience is shown.
Keywords: file-sharing network, dynamical systems, stability.
Mots-clés : ODEs 
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A. I. Kononova; L. G. Gagarina. Dynamic model of growing file-sharing P2P network. Modelirovanie i analiz informacionnyh sistem, Tome 26 (2019) no. 3, pp. 351-359. http://geodesic.mathdoc.fr/item/MAIS_2019_26_3_a2/

[1] Cohen B., The BitTorrent Protocol Specification, , 2008 https://www.bittorrent.org/beps/bep_0003.html

[2] Andronov A. A. et al., Kachestvennaya teoriya dinamicheskih sistem vtorogo poryadka, Nauka, M., 1966, 568 pp. (in Russian)

[3] Bautin N. N., Leontovich E. A., Metody i priyomy kachestvennogo issledovaniya dinamicheskih sistem na ploskosti, Nauka, M., 1990 (in Russian)

[4] Kononova A. I., “Dynamic Model of single Torrent with File-Sharing P2P Network”, Modeling and Analysis of Information Systems, 25:4 (2018), 421–434 (in Russian) | MR

[5] Arnold V. I., ““Hard” and “soft” mathematical models”, Butl. Soc. Catalana Mat., 13:1 (1998), 7–26 (in English) | MR

[6] Ilyashenko Yu. I., “Attractors of dynamical systems and philosophy of generic position”, Images de Mathematique, 18:5 (2006), 58–63 (in French)

[7] Makarov I. M., Menskij B. M., Linejnye avtomaticheskie sistemy: Elementy teorii, metody rascheta i spravochnyj material, Mashinostroenie, 1982 (in Russian)

[8] Ye K. Z., Portnov E. M., Gagarina L. G., Lin K. Z., “Method for increasing reliability for transmission state of power equipment energy”, IEEE GlobalSIP (2015), 433–437