Triangle Inequality and Routing Policy Violations in the Internet

  • Cristian Lumezanu
  • Randy Baden
  • Neil Spring
  • Bobby Bhattacharjee
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5448)


Triangle inequality violations (TIVs) are the effect of packets between two nodes being routed on the longer direct path between them when a shorter detour path through an intermediary is available. TIVs are a natural, widespread and persistent consequence of Internet routing policies. By exposing opportunities to improve the delay between two nodes, TIVs can help myriad applications that seek to minimize end-to-end latency. However, sending traffic along the detour paths revealed by TIVs may influence Internet routing negatively. In this paper we study the interaction between triangle inequality violations and policy routing in the Internet. We use measured and predicted AS paths between Internet nodes to show that 25% of the detour paths exposed by TIVs are in fact available to BGP but are simply deemed “less efficient”. We also compare the AS paths of detours and direct paths and find that detours use AS edges that are rarely followed by default Internet paths, while avoiding others that BGP seems to prefer. Our study is important both for understanding the various interactions that occur at the routing layer as well as their effects on applications that seek to use TIVs to minimize latency.


Relay Node Direct Path Latency Reduction Detour Path Transit Cost 
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.


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  1. 1.
    Wang, G., Zhang, B., Ng, T.S.E.: Towards network triangle inequality violation aware distributed systems. In: IMC (2007)Google Scholar
  2. 2.
    Dabek, F., Cox, R., Kaashoek, F., Morris, R.: Vivaldi: a decentralized network coordinate system. In: SIGCOMM (2004)Google Scholar
  3. 3.
    Lumezanu, C., Levin, D., Spring, N.: PeerWise discovery and negotiation of faster paths. In: HotNets (2007)Google Scholar
  4. 4.
    Zheng, H., Lua, E.K., Pias, M., Griffin, T.G.: Internet routing policies and round-trip times. In: Passive and Active Measurement Workshop (2005)Google Scholar
  5. 5.
    Savage, S., Anderson, T., Aggarwal, A., Becker, D., Cardwell, N., Collins, A., Hoffman, E., Snell, J., Vahdat, A., Voelker, G., Zahorjan, J.: Detour: A case for informed Internet routing and transport. IEEE Micro. 19(1), 50–59 (1999)CrossRefGoogle Scholar
  6. 6.
    Bharambe, A., Douceur, J.R., Lorch, J.R., Moscibroda, T., Pang, J., Seshan, S., Zhuang, X.: Donnybrook: Enabling large-scale, high-speed, peer-to-peer games. In: ACM SIGCOMM (2008)Google Scholar
  7. 7.
    Kho, W., Baset, S.A., Schulzrinne, H.: Skype relay calls: Measurements and experiments. In: IEEE Global Internet Symposium (2008)Google Scholar
  8. 8.
    Lumezanu, C., Baden, R., Levin, D., Spring, N., Bhattacharjee, B.: Symbiotic relationships in Internet routing overlays. In: NSDI (2009)Google Scholar
  9. 9.
    Andersen, D.G., Balakrishnan, H., Kaashoek, M.F., Morris, R.: Resilient overlay networks. In: SOSP (2001)Google Scholar
  10. 10.
    Qiu, L., Yang, Y.R., Zhang, Y., Shenker, S.: On selfish routing in Internet-like environments. In: ACM SIGCOMM (2003)Google Scholar
  11. 11.
    Savage, S., Collins, A., Hoffman, E., Snell, J., Anderson, T.: The end-to-end effects of Internet path selection. In: SIGCOMM (1999)Google Scholar
  12. 12.
    Lee, S., Zhang, Z.L., Sahu, S., Saha, D.: On suitability of euclidean embedding of internet hosts. In: Sigmetrics (2006)Google Scholar
  13. 13.
    Lua, E.K., Griffin, T., Pias, M., Zheng, H., Crowcroft, J.: On the accuracy of the embeddings for Internet coordinate systems. In: IMC (2005)Google Scholar
  14. 14.
    Ng, T.S.E., Zhang, H.: Predicting Internet network distance with coordinates-based approaches. In: INFOCOM (2002)Google Scholar
  15. 15.
    Wong, B., Slivkins, A., Sirer, E.G.: Meridian: A lightweight network location service without virtual coordinates. In: SIGCOMM (2005)Google Scholar
  16. 16.
    Gummadi, K., Saroiu, S., Gribble, S.: King: Estimating latency between arbitrary Internet end hosts. In: IMW (2002)Google Scholar
  17. 17.
    Madhyastha, H.V., Isdal, T., Piatek, M., Dixon, C., Anderson, T., Krishnamurthy, A., Venkataramani, A.: iPlane: An information plane for distributed services. In: USENIX OSDI (2006)Google Scholar
  18. 18.
    RouteViews: Routeviews (2008),
  19. 19.
    Madhyastha, H.V., Anderson, T., Krishnamurthy, A., Spring, N., Venkataramani, A.: A structural approach to latency prediction. In: IMC (2006)Google Scholar
  20. 20.
    Yang, X., Wetherall, D.: Source selectable path diversity via routing deflections. In: ACM SIGCOMM (2006)Google Scholar
  21. 21.
    Spring, N., Mahajan, R., Anderson, T.: Quantifying the causes of path inflation. In: ACM SIGCOMM (2002)Google Scholar
  22. 22.
    Gao, L.: On inferring autonomous system relationships in the Internet. IEEE/ACM Transactions on Networking 9(6), 733–745 (2001)CrossRefGoogle Scholar
  23. 23.
    Dimitropoulos, X., Krioukov, D., Fomenkov, M., Huffaker, B., Hyun, Y., kc claffy, R.G.: As relationships: inference and validation. SIGCOMM CCR 37(1), 29–40 (2007)CrossRefGoogle Scholar
  24. 24.
    Clark, D.D., Wroclawski, J., Sollins, K.R., Braden, R.: Tussles in cyberspace: Defining tomorrow’s Internet. IEEE/ACM Transactions on Networking 13(3), 462–475 (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Cristian Lumezanu
    • 1
  • Randy Baden
    • 1
  • Neil Spring
    • 1
  • Bobby Bhattacharjee
    • 1
  1. 1.University of MarylandUSA

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