Diffusion Models for Peer-to-Peer (P2P) Media Distribution: On the Impact of Decentralized, Constrained Supply

In peer-to-peer (P2P) media distribution, users obtain content from other users who already have it. This form of decentralized product distribution demonstrates several unique features. Only a small fraction of users in the network are queried when a potential adopter seeks a file, and many of these users might even free-ride, i.e., not distribute the content to others. As a result, generated demand might not always be fulfilled immediately. We present mixing models for product diffusion in P2P networks that capture decentralized product distribution by current adopters, incomplete demand fulfillment and other unique aspects of P2P product diffusion. The models serve to demonstrate the important role that P2P search process and distribution referrals---payments made to users that distribute files---play in efficient P2P media distribution. We demonstrate the ability of our diffusion models to derive normative insights for P2P media distributors by studying the effectiveness of distribution referrals in speeding product diffusion and determining optimal referral policies for fully decentralized and hierarchical P2P networks.

[1]  M. Opper,et al.  Advanced mean field methods: theory and practice , 2001 .

[2]  Sunil Kumar,et al.  Diffusion of Innovations Under Supply Constraints , 2003, Oper. Res..

[3]  Aravind Srinivasan,et al.  Modelling disease outbreaks in realistic urban social networks , 2004, Nature.

[4]  S. D. Chatterji.  Proceedings of the International Congress of Mathematicians , 1995 .

[5]  Karl Reiner Lang,et al.  A Pricing Mechanism for Digital Content Distribution Over Peer-to-Peer Networks , 2005, Proceedings of the 38th Annual Hawaii International Conference on System Sciences.

[6]  F. Bass.  The Relationship between Diffusion Rates, Experience Curves, and Demand Elasticities for Consumer Durable Technological Innovations , 1980 .

[7]  Karl Reiner Lang,et al.  A Pricing Mechanism for Digital Content Distribution Over Computer Networks , 2005, J. Manag. Inf. Syst..

[8]  Rick Durrett,et al.  Stochastic Spatial Models , 1999, SIAM Rev..

[9]  F. Brauer,et al.  Mathematical Models in Population Biology and Epidemiology , 2001 .

[10]  M. Newman,et al.  Mean-field solution of the small-world network model. , 1999, Physical review letters.

[11]  Guillaume Urvoy-Keller,et al.  Hierarchical Peer-To-Peer Systems , 2003, Parallel Process. Lett..

[12]  Ramayya Krishnan,et al.  An Empirical Analysis of Network Externalities in Peer-to-Peer Music Sharing Networks , 2003, ICIS.

[13]  H. Andersson,et al.  Stochastic Epidemic Models and Their Statistical Analysis , 2000 .

[14]  Peter Druschel,et al.  Peer-to-peer systems : First International Workshop, IPTPS 2002, Cambridge, MA, USA, March 7-8, 2002 : revised papers , 2002 .

[15]  M. Merabti,et al.  CasPaCE: A Framework for Cascading Payments in Peer-to-Peer Digital Content Exchange , 2003 .

[16]  Eytan Adar,et al.  Free Riding on Gnutella , 2000, First Monday.

[17]  Madjid Merabti,et al.  P2P commercial digital content exchange , 2005, Electron. Commer. Res. Appl..

[18]  Christian Becker,et al.  An epidemic model for information diffusion in MANETs , 2002, MSWiM '02.

[19]  Hector Garcia-Molina,et al.  Incentives for Combatting Freeriding on P2P Networks , 2003, Euro-Par.

[20]  Jasmine Novak,et al.  Geographic routing in social networks , 2005, Proc. Natl. Acad. Sci. USA.

[21]  Frank M. Bass,et al.  A New Product Growth for Model Consumer Durables , 2004, Manag. Sci..

[22]  D. Horsky,et al.  Advertising and the Diffusion of New Products , 1983 .

[23]  Christian Terwiesch,et al.  Managing Demand and Sales Dynamics in New Product Diffusion Under Supply Constraint , 2002, Manag. Sci..

[24]  Ian T. Foster,et al.  Small-world file-sharing communities , 2003, IEEE INFOCOM 2004.

[25]  Jeffrey O. Kephart,et al.  Directed-graph epidemiological models of computer viruses , 1991, Proceedings. 1991 IEEE Computer Society Symposium on Research in Security and Privacy.

[26]  L. Fourt,et al.  Early Prediction of Market Success for New Grocery Products , 1960 .

[27]  V. Mahajan,et al.  Innovation Diffusion in the Presence of Supply Restrictions , 1991 .

[28]  Frank M. Bass,et al.  Impact of a Late Entrant on the Diffusion of a New Product/Service , 2000 .

[29]  O. Diekmann,et al.  Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation , 2000 .

[30]  Mark Lillibridge,et al.  Incentives for Sharing in Peer-to-Peer Networks , 2001, WELCOM.

[31]  Håkan Andersson,et al.  Limit theorems for a random graph epidemic model , 1998 .

[32]  Venkata N. Padmanabhan,et al.  The Case for Cooperative Networking , 2002, IPTPS.

[33]  Vijay Mahajan,et al.  Chapter 8 New-product diffusion models , 1993, Marketing.

[34]  Donald F. Towsley,et al.  The effect of network topology on the spread of epidemics , 2005, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies..

[35]  Mikel Izal,et al.  Dissecting BitTorrent: Five Months in a Torrent's Lifetime , 2004, PAM.

[36]  O. Diekmann.  Mathematical Epidemiology of Infectious Diseases , 1996 .