A Stochastic Epidemiological Model and a Deterministic Limit for BitTorrent-Like Peer-to-Peer File-Sharing Networks

  • George Kesidis
  • Takis Konstantopoulos
  • Perla Sousi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5425)


We propose a stochastic model for a file-sharing peer-to-peer network which resembles the popular BitTorrent system: large files are split into chunks and a peer can download or swap from another peer only one chunk at a time. We exhibit the fluid and diffusion limits of a scaled Markov model of this system and look at possible uses of them to draw practical conclusions.


Upload Bandwidth Swap Rate Deterministic Limit Branch Process Model Network Code System 
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  1. 1.
  2. 2.
    Cohen, B.: Incentives Build Robustness in BitTorrent. In: Workshop on Economics of Peer-to-Peer Systems, Berkeley, CA, USA (May 2003)Google Scholar
  3. 3.
    Daley, D.J., Gani, J.: Epidemic Modeling, an Introduction. Cambridge University Press, Cambridge (1999)CrossRefzbMATHGoogle Scholar
  4. 4.
    DC Info (Distributed Systems Newsletter) vol. XXII(8), June 30 (2008),
  5. 5.
    Ethier, S.N., Kurtz, T.G.: Markov Processes: Characterization and Convergence. Wiley, New York (1986)CrossRefzbMATHGoogle Scholar
  6. 6.
    Darling, R.W.R., Norris, J.R.: Differential equation approximations for Markov chains. Probability Surveys 5, 37–79 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Foss, S., Konstantopoulos, T.: An overview of some stochastic stability methods. Journal of the Operations Research Society of Japan 47, 275–303 (2004)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Ge, Z., Figueiredo, D.R., Jaiswal, S., Kurose, J., Towsley, D.: Modeling peer-to-peer file sharing systems. In: Proc. IEEE INFOCOM, San Francisco (April 2004)Google Scholar
  9. 9.
    Guo, L., Chen, S., Xiao, Z., Tan, E., Ding, X., Zhang, X.: Measurements, modeling and analysis of BitTorrent-like systems. In: Proc. Internet Measurement Conference (IMC) (October 2005)Google Scholar
  10. 10.
    Kesidis, G., Jin, Y., Mortazavi, B., Konstantopoulos, T.: An epidemiological model for file-sharing with BitTorrent-like incentives. In: Proc. IEEE GLOBECOM (November 2006)Google Scholar
  11. 11.
    Kesidis, G., Konstantopoulos, T., Sousi, P.: A stochastic epidemiological model and a deterministic limit for BitTorrent-like peer-to-peer file-sharing networks (November 2008),
  12. 12.
    Kesidis, G., Vojnovic, M., Hamadeh, I., Jin, Y., Jiwasurat, S.: A Model of the Spread of Randomly Scanning Internet Worms that Saturate Access Links. In: ACM TOMACS (May 2008)Google Scholar
  13. 13.
    Kurtz, T.: Approximation of Population Processes. SIAM, Philadelphia (1981)CrossRefzbMATHGoogle Scholar
  14. 14.
    Legout, A., Liogkas, N., Kohler, E., Zhang, L.: Clustering and sharing incentives in BitTorrent systems. ACM SIGMETRICS Performance Evaluation Review 35(1) (June 2007)Google Scholar
  15. 15.
    Massoulié, L., Vojnovic, M.: Coupon replication systems. In: Proc. ACM SIGMETRICS, Banff, Alberta, Canada (2005)Google Scholar
  16. 16.
    Maymounkov, P., Mazieres, D.: Kademlia: a peer-to-peer information system based on the XOR metric. In: Proc. IPTPS, Cambridge, MA, USA (March 2002)Google Scholar
  17. 17.
    Mortazavi, B., Kesidis, G.: A peer-to-peer content-distribution game with a reputation-based incentive mechanism. In: Proc. IEEE Workshop on Information Theory and its Applications (ITA), UC San Diego (February 2006)Google Scholar
  18. 18.
    Qiu, D., Srikant, R.: Modeling and performance analysis of BitTorrent-like peer-to-peer networks. In: Proc. ACM SIGCOMM, Portland, Oregon (2004)Google Scholar
  19. 19.
    Turner, B.: Generalizing BitTorrent: how to build data exchange markets (and profit from them!) (January 2005),
  20. 20.
    Walsh, K., Sirer, E.G.: Fighting peer-to-peer SPAM and decoys with object reputation. In: Proc. Workshop on Economics of Peer-to-Peer Systems (p2pecon), Philadelphia, PA (August 2005)Google Scholar
  21. 21.
    Yang, X., de Veciana, G.: Service capacity of peer to peer networks. In: Proc. IEEE INFOCOM, San Francisco (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • George Kesidis
    • 1
  • Takis Konstantopoulos
    • 2
  • Perla Sousi
    • 3
  1. 1.CSE and EE DepartmentsPennsylvania State UniversityUniversity ParkUSA
  2. 2.School of Mathematical & Computer Sciences and the Maxwell Institute for Mathematical SciencesHeriot-Watt UniversityEdinburghUK
  3. 3.Statistical Laboratory, Centre for Mathematical SciencesUniversity of CambridgeCambridgeUK

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