Dynamics of Content Propagation and Reciprocity in p2p File Sharing

Fernando Paganini

Universidad ORT Uruguay

Abstract

Recent trends in networking move away from detailed models of the underlying infrastructure, to an increasingly abstracted view of the network “cloud”, over which overlays such as peer-to-peer are defined. Yet even with an idealized infrastructure, non-trivial performance questions arise: in particular, p2p networks have dynamic populations and a feedback structure since capacity scales with population.  In this talk we present a partial differential equation model for such dynamics that keeps track of both population and download progress. Postulating that upload bandwidth is equally distributed among downloading peers (a processor-sharing discipline), we can characterize the resulting equilibrium, and use control theory techniques to analyze its stability, variability and transient performance. These give very tight predictions of practical Bit-Torrent systems, in the case of peers with homogeneous access parameters.

We also present ongoing work on deriving the large scale bandwidth sharing behavior from microscopic mechanisms of reciprocity embedded in p2p protocols, such the tit-for-tat strategy of BitTorrent. In particular, a proportional version of reciprocity can be modeled through a finite matrix and the so-called Sinkhorn iteration, a strategy for row and column renormalization. In the case of homogeneous access bandwidths for all peers, this implies convergence to the processor-sharing bandwidth distribution. We also discuss extensions to the heterogeneous case.

Biography

Fernando Paganini received his Electrical Engineering and Mathematics degrees from Universidad de la República, Uruguay, in 1990, and his M.S. (1992) and PhD (1996) degrees in Electrical Engineering from Caltech, Pasadena, CA. From 1996 to 1997 he was a postdoctoral associate at MIT. From 1997 to 2005 he was on the Faculty at the UCLA Electrical Engineering Department. Since 2005 he is Professor of Engineering at Universidad ORT, Uruguay.

Prof. Paganini is the recipient of the 1995 O. Hugo Schuck best paper award, the Caltech 1996 Wilts and Clauser Prizes for his PhD Thesis, the 1999 NSF CAREER Award, the 1999 Packard Fellowship, the 2004 George S. Axelby Award, and  the 2010 Elsevier Scopus Prize. He has held editorial positions in the IEEE/ACM Transactions on Networking and the IEEE Transactions on Automatic Control. He is a member of the Uruguayan National Academy of Sciences. His research interests are control and networks.