Modelling the Population Dynamics and the File Availability in a BitTorrent-Like P2P System with Decreasing Peer Arrival Rate

  • Riikka Susitaival
  • Samuli Aalto
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4124)


Many measurement studies of P2P file sharing systems suggest that the request rate for a file changes over time and the system is thus non-stationary. For this reason we study the population dynamics and the availability of a file in a BitTorrent-like file sharing system, when the arrival rate for file requests decreases exponentially. We study the system first by a deterministic fluid model and then by a more detailed Markov chain analysis that allows estimating the life time of a single chunk exactly. Simple approximation for the life time is also derived. In addition, we simulate the life time of a file consisting multiple chunks in order to verify the analytical results to be applicable also to a more complex system.


Arrival Rate Life Time Markov Chain Model Service Capacity Sharing System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Karagiannis, T., Broido, A., Brownlee, N., Claffy, K.C., Faloutsos, M.: Is P2P dying or just hiding? In: Globecom (2004)Google Scholar
  2. 2.
  3. 3.
    Cohen, B.: Incentives Build Robustness in BitTorrent, 2003. In: Proc. of First Workshop on Economics of Peer-to-Peer Systems (June 2003),
  4. 4.
    Qiu, D., Srikant, R.: Modeling and Performance Analysis of BitTorrent-Like Peer-to-Peer Networks. In: Proc. of SIGCOMM (2004)Google Scholar
  5. 5.
    Izal, M., Urvoy-Keller, G., Biersack, E.W., Felber, P., Al Hamra, A., Garcés-Erice, L.: Dissecting BitTorrent: Five Months in a Torrent’s Lifetime. In: Barakat, C., Pratt, I. (eds.) PAM 2004. LNCS, vol. 3015, pp. 1–11. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  6. 6.
    Pouwelse, J., Garbacki, P., Epema, D.H.J., Sips, H.J.: The bittorrent P2P file-sharing system: Measurements and analysis. In: Castro, M., van Renesse, R. (eds.) IPTPS 2005. LNCS, vol. 3640, pp. 205–216. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  7. 7.
    Massoulié, L., Vojnović, M.: Coupon replication Systems. In: Proc. of SIGMETRICS (2005)Google Scholar
  8. 8.
    Yang, X., de Veciana, G.: Service Capacity of Peer to Peer Networks. In: Proc. of INFOCOM 2004 (2004)Google Scholar
  9. 9.
    Ramachandran, K.K., Sikdar, B.: An Analytic Framework for Modeling Peer to Peer Networks. In: Proc. of INFOCOM 2005 (2005)Google Scholar
  10. 10.
    Tian, Y., Wu, D., Wing Ng, K.: Modeling, Analysis and Improvement for BitTorrent-Like File Sharing Networks. In: Proc. of INFOCOM 2006 (2006)Google Scholar
  11. 11.
    Guo, L., Chen, S., Xiao, Z., Tan, E., Ding, X., Zhang, X.: Measurement, Analysis, and Modeling of bitTorrent-like Systems. In: Proc. of Internet Measurement Conference of USENIX Association (2005)Google Scholar
  12. 12.
    Susitaival, R., Aalto, S., Virtamo, J.T.: Analyzing the dynamics and resource usage of P2P file sharing by a spatio-temporal model. In: Alexandrov, V.N., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds.) ICCS 2006. LNCS, vol. 3994, pp. 420–427. Springer, Heidelberg (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Riikka Susitaival
    • 1
  • Samuli Aalto
    • 1
  1. 1.Helsinki University of TechnologyFinland

Personalised recommendations