A stochastic model for BitTorrent-like systems

Abstract

BitTorrent (BT) [1] is a P2P protocol designed for fast and efficient distribution of large files. Many factors contribute to the BT system dynamics, such as the arrival and departure of peers, and the terminations of connections when peers find better neighbors. Qiu and Srikant [6] consider the arrival and departure process as the main source of dynamics. Liao et al. [3] study the connection dynamics, in particular, they consider the effect of optimistic unchoking and tit-for-tat, and estimate the average download rates for heterogeneous peers. However, as far as we know, no work has considered these two types of dynamics together. This paper takes into account these dynamics, and presents a stochastic model to study the fractions of peers with different connection numbers, from which we can compute the average number of connections per peer. In practice, to limit P2P applications, some ISPs charge users by the numbers of TCP connections, so it is important to estimate the average number of connections per peer. Using this model, BT users can estimate the average number of connections per peer, and then choose the numbers of TCP connections to minimize their costs. Since we assume homogeneous peers, the average download rate is equal to the upload rate, so it is trivial to estimate the average download rate or the average file download time in this model.