BitTorrent Analysis

Modeling and Performance Analysis of BitTorrent Like PeertoPeer Networks
Dongyu Qiu and R. Srikant, UIUC

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• Fluid model:
• • Downloader: dx/dt = arrive rate - abandon rate - min {total download rate, total upload rate}
  • Seed: dy/dt = min {total download rate, total upload rate}- seed leave rate
  • By Little's law: T = 1/(abandon rate + 1/(max {1/download rate, (1/upload rate - 1/seed leave rate)/share efficiency }
  • By eigenvalues of maxtrix: system is stable
  • By stochastic Ornstein-Uhlenbeck process, analyze the variance of x and y
• Peer selection:
• • Assumption: selfish agent, non-cooperative game.
  • Game theory: Nash equilibrium point exist if upload rate = download rate for each peer
• Sharing Effectiveness
• • Assumption: N pieces distributed uniformly.
  • 1 - P{ no piece is required by others } = 1 - C(k)/N, k: one peer's connection number. In BT, up to 40. C(k) = 1 + 1/2exp(k) + .... + 1/Nexp(k)
  • BT has good sharing efficiency.

[My Opinion]

• The result is not so exciting. Anyway, it is just analysis. P2P is more an engineering problem. In Internet area, there is still lack of powerful analysis mathematic methods. TCP protocol design is an example, now P2P faces same problem.
• Why use the non-cooperative game to analysis the peer selection. The core of BT is cooperation. It is wrong. Maybe it is because no other theory tool to anlayze this problem. So it is unsurprising that no meaningful result is obtained.
• Fluid model is simple and easy to understand. Other methods includes model as a closed queueing system (D. Towsley), Markov chain (G. de Veciana).

[Future Reading]

• M. Ripeanu, I. Foster, and A. Iamnitchi. Mapping the gnutella network: Properties of large-scale peer-to-peer systems and implications for system design.
  IEEE Internet Computing Journal, 6(1), 2002.
• T. S. Eugene Ng, Y.-H. Chu, S. G. Rao, K. Sripanidkulchai, and Hui Zhang.
  Measurement-Based Optimization Techniques for Bandwidth-Demanding Peer-To-Peer Systems. In Proceedings of IEEE INFOCOM, 2003.

Technorati : BitTorrent, P2P