BitTorrent-like对等文件共享网络的随机流行病模型和确定性极限
A stochastic epidemiological model and a deterministic limit for BitTorrent-like peer-to-peer file-sharing networks
摘要：
在本文中，我们提出了一个随机模型的文件共享对等网络，类似于流行的BitTorrent系统：大文件被分割成块，一个对等体可以下载或交换从另一个对等体只有一块的时间。我们证明了这个系统的标度马尔可夫模型的流体极限是凝结形式，其特例是众所周知的流行病（SIR）模型。此外，李雅普诺夫稳定性和稳定时间的结果进行了探讨。我们得出的条件下，BitTorrent的激励措施，考虑在较短的平均文件获取时间的同行相比，客户端-服务器（单块）系统。最后给出了一个扩散近似，并讨论了一些问题。
英文摘要：
In this paper, we propose a stochastic model for a file-sharing peer-to-peer network which resembles the popular BitTorrent system: large files are split into chunks and a peer can download or swap from another peer only one chunk at a time. We prove that the fluid limits of a scaled Markov model of this system are of the coagulation form, special cases of which are well-known epidemiological (SIR) models. In addition, Lyapunov stability and settling-time results are explored. We derive conditions under which the BitTorrent incentives under consideration result in shorter mean file-acquisition times for peers compared to client-server (single chunk) systems. Finally, a diffusion approximation is given and some open questions are discussed.
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