Distributed Computing

, Volume 28, Issue 6, pp 391–406 | Cite as

Stable and scalable universal swarms

  • Ji ZhuEmail author
  • Stratis Ioannidis
  • Nidhi Hegde
  • Laurent Massoulié


Hajek and Zhu (Stoch Syst 1(2):246–273, 2011) recently showed that the BitTorrent protocol can become unstable when peers depart immediately after downloading all pieces of a file. In light of this result, Zhou et al. (2011) propose bundling swarms together, allowing peers to exchange pieces across different swarms, and claim that such “universal swarms” can increase BitTorrent’s stability region. In this work, we formally characterize the stability region of universal swarms and show that they indeed exhibit excellent properties. In particular, bundling allows a single seeder with limited upload capacity to serve an arbitrary number of disjoint swarms if the arrival rate of peers in each swarm is lower than the seeder upload capacity. Our result also shows that the stability region is insensitive to peers’ upload capacity, piece selection policies and number of swarms.


Arrival Rate Stability Region Sojourn Time Autonomous Mode Universal Mode 
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.



This work was supported by the National Science Foundation under Grant NSF CCF 10-16959, and was partially funded by the European Commission under the FIRE SCAMPI (FP7- IST-258414) Project.


  1. 1.
    Foster, F.: On the stochastic matrices associated with certain queuing processes. Ann. Math. Stat. 24(3), 355–360 (1953)zbMATHCrossRefGoogle Scholar
  2. 2.
    Hajek, B.: An exploration of random processes for engineers (December 20, 2011).
  3. 3.
    Hajek, B., Zhu, J.: The missing piece syndrome in peer-to-peer communication. Stoch. Syst. 1(2), 246–273 (2011)zbMATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Han, J., Chung, T., Kim, S., Kwon, T.T., Kim, H.c., Choi, Y.: How prevalent is content bundling in bittorrent. In: ACM SIGMETRICS (2011)Google Scholar
  5. 5.
    Kingman, J.: Some inequalities for the queue gi/g/1. Biometrika 49(3–4), 315–324 (1962)zbMATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Massoulié, L., Vojnović, M.: Coupon replication systems. In: ACM SIGMETRICS (2005)Google Scholar
  7. 7.
    Mathieu, F., Reynier, J.: Missing piece issue and upload strategies in flashcrowds and p2p-assisted filesharing. In: AICT-ICIW’06, pp. 112–112. IEEE (2006)Google Scholar
  8. 8.
    Menasché, D.S., de A Rocha, A.A., de Souza e Silva, E.A., Towsley, D., Meri Leäo, R.M.: Implications of peer selection strategies by publishers on the performance of p2p swarming systems. ACM SIGMETRICS 39(3), 55–57 (2011)Google Scholar
  9. 9.
    Menasché, D.S., Massoulié, L., Towsley, D.: Reciprocity and barter in peer-to-peer systems. In: IEEE INFOCOM, pp. 1505–1513. IEEE (2010)Google Scholar
  10. 10.
    Menasche, D.S., Rocha, A.A., Li, B., Towsley, D., Venkataramani, A.: Content availability and bundling in swarming systems. In: ACM CoNEXT (2009)Google Scholar
  11. 11.
    Menasché, D.S., Rocha, A.A., de Souza e Silva, E.A., Leao, R.M., Towsley, D., Venkataramani, A.: Estimating self-sustainability in peer-to-peer swarming systems. Perform. Eval. 67(11), 1243–1258 (2010)CrossRefGoogle Scholar
  12. 12.
    Norros, I., Reittu, H., Eirola, T.: On the stability of two-chunk file-sharing systems. Queueing Syst. 67(3), 183–206 (2011) Google Scholar
  13. 13.
    Núnez-Queija, R., Prabhu, B.: Scaling laws for file dissemination in p2p networks with random contacts. In: IWQoS 2008, pp. 75–79. IEEE (2008)Google Scholar
  14. 14.
    Oğuz, B., Anantharam, V., Norros, I.: Stable, distributed p2p protocols based on random peer sampling. In: IEEE Allerton, pp. 915–919 (2012)Google Scholar
  15. 15.
    Wu, D., Liu, Y., Ross, K.W.: Queuing network models for multi-channel P2P live streaming systems. In: IEEE INFOCOM (2009)Google Scholar
  16. 16.
    Zhou, X., Ioannidis, S., Massoulié, L.: On the stability and optimality of universal swarms. In: ACM SIGMETRICS (2011)Google Scholar
  17. 17.
    Zhu, J., Hajek, B.: Stability of a peer-to-peer communication system. IEEE Trans. Inf. Theory (2012)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Ji Zhu
    • 1
    Email author
  • Stratis Ioannidis
    • 2
  • Nidhi Hegde
    • 3
  • Laurent Massoulié
    • 4
  1. 1.University of Illinois at Urbana-ChampaignUrbanaUSA
  2. 2.TechnicolorPalo AltoUSA
  3. 3.TechnicolorIssy les MoulineauxFrance
  4. 4.MSR-INRIAPalaiseauFrance

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