On Modelling of Fair Throughput Allocation in Overlay Multicast Networks

  • Michal Kucharzak
  • Krzysztof Walkowiak
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6869)


Overlay-based multicast has been proposed as an efficient solution to ensure multicast communication in the Internet. This paper focuses on modelling of various aspects of fairness in overlay multicast networks aimed at throughput maximization. Two distinct linear programs are proposed. The first formulation employs conceptual flows and provides optimal data rate allocation, whereas the second, relaxed version is derived from fractional Steiner trees. In addition, performance of two optimization tools (CPLEX and GUROBI) is compared in relation of time and result quality meanings. The paper reports that the fractional trees-based formulation provides better time efficiency while its solutions’ quality might reach maximum obtainable data rates.


Overlay multicast simulated annealing tree packing 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Akbari, B., Rabiee, H.R., Ghanbari, M.: An optimal discrete rate allocation for overlay video multicasting. Computer Communications 31(3), 551–562 (2008)CrossRefGoogle Scholar
  2. 2.
    Benslimane, A. (ed.): Multimedia Multicast on the Internet. ISTE (2007)Google Scholar
  3. 3.
    Bharambe, A.R., Herley, C., Padmanabhan, V.N.: Analyzing and improving a bittorrent networks performance mechanisms. In: Proc. 25th IEEE Int. Conf. Computer Communications, INFOCOM 2006, pp. 1–12 (2006)Google Scholar
  4. 4.
    Chu, Y.-h., Rao, S.G., Zhang, H.: A case for end system multicast. In: Proceedings of ACM Sigmetrics, pp. 1–12 (2000)Google Scholar
  5. 5.
    Deering, S.E., Cheriton, D.R.: Multicast routing in datagram internetworks and extended lans. ACM Transactions on Computer Systems 8, 85–110 (1990)CrossRefGoogle Scholar
  6. 6.
    Gurobi Optimization: Gurobi optimizer 3.0 (2010),
  7. 7.
    IBM ILOG CPLEX 12.1: User’s Manual for CPLEX (2009)Google Scholar
  8. 8.
    Jain, K., Mahdian, M., Salavatipour, M.R.: Packing steiner trees. In: SODA 2003: Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 266–274. Society for Industrial and Applied Mathematics, Philadelphia (2003)Google Scholar
  9. 9.
    Kucharzak, M., Walkowiak, K.: Optimization of flows in level-constrained multiple trees for p2p multicast system. In: The Second International Conference on Advances in P2P Systems, AP2PS 2010, Florence, Italy (October 2010)Google Scholar
  10. 10.
    Lao, L., Hong Cui, J., Gerla, M.: Multicast service overlay design. In: Proc. of Second International Symposium on Wireless Communication Systems, ISWCS 2005, Philadelphia, Pennsylvania, USA (2005)Google Scholar
  11. 11.
    Leuf, B.: Peer to Peer: Collaboration and Sharing over the Internet. Addison-Wesley Longman Publishing Co., Inc., Boston (2002)Google Scholar
  12. 12.
    Pióro, M., Medhi, D.: Routing, Flow, and Capacity Design in Communication and Computer Networks. Morgan Kaufmann Publishers, San Francisco (2004)zbMATHGoogle Scholar
  13. 13.
    Rawls, J.: The Theory of Justice. Harvard University Press, Cambridge (1971)Google Scholar
  14. 14.
    Sen, A.: On Economic Inequality. Clarendon Press, Oxford (1973)CrossRefGoogle Scholar
  15. 15.
    Sentinelli, A., Marfia, G., Gerla, M., Kleinrock, L., Tewari, S.: Will iptv ride the peer-to-peer stream? peer-to-peer multimedia streaming. IEEE Communications Magazine 45(6), 86–92 (2007)CrossRefGoogle Scholar
  16. 16.
    Shi, S., Turner, J.S.: Multicast routing and bandwidth dimensioning in overlay networks. IEEE Journal on Selected Areas in Communications 20, 1444–1455 (2002)CrossRefGoogle Scholar
  17. 17.
    Walkowiak, K.: Network Design Problem for P2P Multicasting. In: International Network Optimization Conference, INOC 2009 (April 2009)Google Scholar
  18. 18.
    Walkowiak, K.M.: Offline Approach to Modeling and Optimization of Flows in Peer-to-Peer Systems. In: New Technologies, Mobility and Security, NTMS 2008, pp. 1–5. IEEE Press, Tangier (2008)CrossRefGoogle Scholar
  19. 19.
    Wu, C., Li, B.: Optimal peer selection for minimum-delay peer-to-peer streaming with rateless codes. In: P2PMMS 2005: Proceedings of the ACM Workshop on Advances in Peer-to-Peer Multimedia Streaming, pp. 69–78. ACM, New York (2005)CrossRefGoogle Scholar
  20. 20.
    Wu, C., Li, B.: Optimal rate allocation in overlay content distribution. Networking, 678–690 (2007)Google Scholar
  21. 21.
    Wu, C., Li, B.: On meeting p2p streaming bandwidth demand with limited supplies. In: Proc. of the Fifteenth Annual SPIE/ACM International Conference on Multimedia Computing and Networking (2008)Google Scholar
  22. 22.
    Wu, G., Chiueh, T.: Peer to peer file download and streaming. rpe report, tr-185 (2005)Google Scholar
  23. 23.
    Young, H.P.: Equity in Theory and Practice. Princeton University Press, Princeton (1994)Google Scholar
  24. 24.
    Zhu, Y., Li, B.: Overlay networks with linear capacity constraints. IEEE Trans. Parallel Distrib. Syst. 19(2), 159–173 (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Michal Kucharzak
    • 1
  • Krzysztof Walkowiak
    • 1
  1. 1.Department of Systems and Computer NetworksWroclaw University of TechnologyPoland

Personalised recommendations