A stochastic epidemiological model and a deterministic limit for BitTorrent-like peer-to-peer file-sharing networks

TL;DR

This paper introduces a stochastic model for BitTorrent-like networks, deriving deterministic limits and analyzing stability, incentives, and file-sharing efficiency, with implications for optimizing peer-to-peer systems.

Contribution

It presents a novel stochastic model for P2P networks, establishes its deterministic fluid limit as a coagulation process, and analyzes incentives and stability in file-sharing.

Findings

Deterministic limits are coagulation-type models similar to epidemiological SIR models.

Incentives can lead to shorter file acquisition times compared to client-server systems.

Stability and convergence properties of the model are established.

Abstract

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.