Dynamics of heterogeneous peer-to-peer networks

The most tractable models of population dynamics in peer-to-peer file sharing systems apply to a single class of peers with homogeneous network access parameters. When upload bandwidths are heterogeneous, reciprocity mechanisms lead to non-uniform download rates and a more complex multi-class dynamics. We consider first a model where mutual download bandwidths are allocated in proportion to the upload speed, plus a uniformly distributed server component. For an ordinary differential equation model of the multi-class peer populations, we characterize the equilibrium and establish its global stability, invoking results from monotone systems. We also analyze a partial differential equation model that tracks download progress of the populations; we establish the local asymptotic stability of the equilibrium. Finally, we extend the ODE model to include a mix of proportional and uniform bandwidth allocation, which better describes the mechanisms of BitTorrent systems; again we characterize equilibrium configurations and give a partial result on local stability.

[1]  Gustavo de Veciana,et al.  Performance of peer-to-peer networks: Service capacity and role of resource sharing policies , 2006, Perform. Evaluation.

[2]  Bruce E. Hajek,et al.  Stability of a Peer-to-Peer Communication System , 2012, IEEE Transactions on Information Theory.

[3]  Rayadurgam Srikant,et al.  Modeling and performance analysis of BitTorrent-like peer-to-peer networks , 2004, SIGCOMM 2004.

[4]  Florence Clévenot-Perronnin,et al.  Fluid Models for Content Distribution Systems. (Modèles fluides pour l'analyse des systèmes de distribution de contenu) , 2005 .

[5]  Fernando Paganini,et al.  PDE models for population and residual work applied to peer-to-peer networks , 2012, 2012 46th Annual Conference on Information Sciences and Systems (CISS).

[6]  David K. Y. Yau,et al.  Incentive and service differentiation in P2P networks: a game theoretic approach , 2006, TNET.

[7]  J. Gillis,et al.  Matrix Iterative Analysis , 1961 .

[8]  M. Hirsch,et al.  4. Monotone Dynamical Systems , 2005 .

[9]  Michael J. Freedman,et al.  Bilateral and Multilateral Exchanges for Peer-Assisted Content Distribution , 2010, IEEE/ACM Transactions on Networking.

[10]  M. Hirsch,et al.  Chapter 4 Monotone Dynamical Systems , 2006 .

[11]  Anders Rantzer,et al.  Distributed control of positive systems , 2011, IEEE Conference on Decision and Control and European Control Conference.

[12]  Gustavo de Veciana,et al.  Service capacity of peer to peer networks , 2004, IEEE INFOCOM 2004.

[13]  Bobby Bhattacharjee,et al.  Bittorrent is an auction: analyzing and improving bittorrent's incentives , 2008, SIGCOMM '08.

[14]  Richard S. Varga,et al.  Matrix Iterative Analysis , 2000, The Mathematical Gazette.

[15]  Fernando Paganini,et al.  Content dynamics in P2P networks from queueing and fluid perspectives , 2012, 2012 24th International Teletraffic Congress (ITC 24).

[16]  Eddie Kohler,et al.  Clustering and sharing incentives in BitTorrent systems , 2006, SIGMETRICS '07.

[17]  Tobias Hoßfeld,et al.  Efficient simulation of large-scale p2p networks: packet-level vs. flow-level simulations , 2007, UPGRADE '07.

[18]  Dongyu Qiu,et al.  Global stability of Peer-to-Peer file sharing systems , 2008, Comput. Commun..

[19]  Laurent Massoulié,et al.  Coupon replication systems , 2008, TNET.

[20]  Hans Zwart,et al.  An Introduction to Infinite-Dimensional Linear Systems Theory , 1995, Texts in Applied Mathematics.

[21]  Bin Fan,et al.  The design trade-offs of BitTorrent-like file sharing protocols , 2009, TNET.

[22]  George Kesidis,et al.  Modeling file-sharing with BitTorrent-like incentives , 2007, 2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP '07.

[23]  Fernando Paganini,et al.  Dynamics of content propagation in BitTorrent-like P2P file exchange systems , 2011, IEEE Conference on Decision and Control and European Control Conference.

[24]  Fang Wu,et al.  Proportional response dynamics leads to market equilibrium , 2007, STOC '07.

[25]  J. Lei.  Monotone Dynamical Systems , 2013 .

[26]  G. Veciana,et al.  Fairness, incentives and performance in peer-to-peer networks , 2003 .

[27]  B. Cohen,et al.  Incentives Build Robustness in Bit-Torrent , 2003 .

[28]  Francesca Lo Piccolo,et al.  The effect of heterogeneous link capacities in BitTorrent-like file sharing systems , 2004, 2004 International Workshop on Hot Topics in Peer-to-Peer Systems.

[29]  Richard Sinkhorn.  Diagonal equivalence to matrices with prescribed row and column sums. II , 1974 .