Abstract—

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.

中文翻译：

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对等网络中信息交换过程的动态模型

摘要-

本文考虑了基于常微分方程的点对点文件共享网络中的文件分发模型。确定描述文件共享状态的阶段变量（在第一个近似值中，这是用户数量，即共享文件的种子和获取者数量）。分析了影响文件共享和对等体数量变化的因素。在分析的基础上，构建了描述洪流演化或文件共享会话（FSS）的微分方程系统，即动态FSS演化模型。考虑了文件共享网络中FSS的生命周期，该生命周期包括四个阶段，即文件共享启动，抓取者数量快速增加，稳定和褪色（对于随时间而失去相关性的文件）。每个阶段都有自己的比例模型参数。参数随时间变化。描述了测量实际FSS状态的过程。给出了一个与大型洪流跟踪器上的真实FSS演变相对应的轨迹示例。接下来，考虑以在第一近似中恒定的参数为特征的FSS稳定阶段。研究了FSS演化动力学模型的平衡点。描述了它们的可能数量和类型。描述了对等文件共享网络的FSS演化模型中所有可能的通用位置配置。给出了每种配置的相图。分析了各种行政措施对FSS稳定裕度的影响。显示了评级系统对FSS稳定性的影响的模棱两可。还显示了时间奖励，反馈和FSS吸收系统的积极效果。