Abstract
Routing policies or path inflation can give rise to violations of the Triangle Inequality with respect to delay (RTTs) in the Internet. In network coordinate systems, such Triangle Inequality Violations (TIVs) will introduce inaccuracy, as nodes in this particular case could not be embedded into any metric space. In this paper, we consider these TIVs as an inherent and natural property of the Internet; rather than trying to remove them, we consider characterizing them and mitigating their impact on distributed coordinate systems.
In a first step, we study TIVs existing in the Internet, using different metrics in order to quantify various levels of TIVs’ severity. Our results show that path lengths do have an effect on the impact of these TIVs. In particular, the shorter the link between any two nodes is, the less severe TIVs involved in are.
In a second step, we do leverage our study to reduce the impact of TIVs on coordinate systems. We focus on the particular case of the Vivaldi coordinate system and we explore how TIVs may impact its accuracy and stability. In particular, we observed correlation between the (in)stability and high effective error of nodes’ coordinates with respect to their involvement in TIVs situations. We finally propose a Two-Tier architecture opposed to a flat structure of Vivaldi that do mitigate the effect of TIVs on the distances predictions.
Chapter PDF
Similar content being viewed by others
References
Rowstron, A., Drusche, P.: Pastry: Scalable, distributed object location and routing for large-scale peer-to-peer systems. In: Guerraoui, R. (ed.) Middleware 2001. LNCS, vol. 2218, pp. 329–350. Springer, Heidelberg (2001)
Chu, Y.h., Rao, S.G., Zhang, H.: A case for end system multicast. In: Proc. the ACM SIGMETRICS, Santa Clara (June 2000)
Rewaskar, S., Kaur, J.: Testing the scalability of overlay routing infrastructures. In: Proc the PAM Conference, Sophia Antipolis, France (April 2004)
Ng, T.S.E., Zhang, H.: Predicting Internet network distance with coordinates-based approaches. In: Proc. IEEE INFOCOM, New York, NY, USA (June 2002)
Dabek, F., Cox, R., Kaashoek, F., Morris, R.: Vivaldi: A decentralized network coordinate system. In: Proc. ACM SIGCOMM, Portland, OR, USA (August 2004)
Zheng, H., Lua, E.K., Pias, M., Griffin, T.: Internet Routing Policies and Round-Trip-Times. In: Proc. the PAM Conference, Boston, MA, USA (April 2005)
Ledlie, J., Gardner, P., Seltzer, M.I.: Network coordinates in the wild. In: Proc NSDI, Cambridge (April 2007)
Mendel, M., Bartal, Y., Linial, N., Naor, A.: On metric ramsey-type phenomena. In: Proc. the Annual ACM Symposium on Theory of Computing (STOC), San Diego, CA (June 2003)
Wang, G., Zhang, B., Ng, T.S.E.: Towards network triangle inequality violation aware distributed systems. In: Proc. the ACM/IMC Conference, San Diego, CA, USA, October 2007, pp. 175–188 (2007)
A simulator for peer-to-peer protocols, http://www.pdos.lcs.mit.edu/p2psim/index.html
Wong, B., Slivkins, A., Sirer, E.: Meridian: A lightweight network location service without virtual coordinates. In: Proc. the ACM SIGCOMM, August (2005)
Gummadi, K.P., Saroiu, S., Gribble, S.D.: King: Estimating latency between arbitrary Internet end hosts. In: Proc the SIGCOMM Internet Measurement Workshop, Marseille, France (November 2002)
Savage, S., Collins, A., Hoffman, E., Snell, J., Anderson, T.: The end-to-end effects of Internet path selection. In: Proc. of ACM SIGCOMM 1999, Cambridge, MA, USA (September 1999)
Lee, S., Zhang, Z., Sahu, S., Saha, D.: On suitability of euclidean embedding of internet hosts. SIGMETRICS 34(1), 157–168 (2006)
Min, S., Holliday, J., Cho, D.: Optimal super-peer selection for large-scale p2p system. In: Proc. the ICHIT Conference, Washington, DC, USA, November 2006, pp. 588–593 (2006)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 IFIP International Federation for Information Processing
About this paper
Cite this paper
Kaafar, M.A., Gueye, B., Cantin, F., Leduc, G., Mathy, L. (2008). Towards a Two-Tier Internet Coordinate System to Mitigate the Impact of Triangle Inequality Violations. In: Das, A., Pung, H.K., Lee, F.B.S., Wong, L.W.C. (eds) NETWORKING 2008 Ad Hoc and Sensor Networks, Wireless Networks, Next Generation Internet. NETWORKING 2008. Lecture Notes in Computer Science, vol 4982. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79549-0_35
Download citation
DOI: https://doi.org/10.1007/978-3-540-79549-0_35
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-79548-3
Online ISBN: 978-3-540-79549-0
eBook Packages: Computer ScienceComputer Science (R0)