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Dynamic Model of Growing File-Sharing P2P Network
Automatic Control and Computer Sciences Pub Date : 2021-02-08 , DOI: 10.3103/s014641162007010x
A. I. Kononova , L. G. Gagarina

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.



中文翻译:

增长的文件共享P2P网络的动态模型

摘要

这项工作考虑了由洪流跟踪器组织的开发P2P文件交换网络的模型。该模型是基于常微分方程构建的。定义了阶段变量,这些阶段变量描述了洪流跟踪器及其组织的网络的状态(第一近似表示,这是跟踪器的积极参与信息交换的用户数,以及活动的洪流数),并且影响用户数量和激流数量变化的因素。该分析用于开发一个微分方程组,用于近似地描述由洪流跟踪器组织的文件交换网络-洪流跟踪器演变的硬动态模型。分析了跟踪器演化的硬模型的平衡点,描述了它们的可能数量和类型。描述了在跟踪器演变的硬模型中可能使用的一般规定的所有配置。表示了硬模型的相图。硬模型的分析用于导出描述文件交换网络演化的微分方程组,其中考虑了新用户涌入的强度与洪流跟踪器的潜在受众总大小之间的相关性。洪流消灭率对每个洪流用户数量的依赖性-洪流跟踪器演变的软动态模型。分析了软模型中的特殊点,并描述了它们的可能数量和类型。描述了在演化的软模型中可能的一般配置的所有配置。表示每种配置的相图。计算跟踪器稳定性所必需的参数的相关性。分析了各种管理措施对跟踪器总体稳定性的影响。显示了由潜在受众很少的高度专业的洪流跟踪器的管理部门支持洪流的需求。

更新日期:2021-02-08
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