Abstract
In this paper we focus on the trend of the average path length of the AS-level Internet, which is one of the most important parameters to measure the efficiency of the Internet. The conclusion drawn by the power-law and small world models is that the average path length of network scales as ln(n) or ln(ln(n)), n is the number of nodes in network. But through analyzing the data of BGP tables in recent 5 years, we find that the average path length of the Internet is descending and the descending rate is about 0.00025 which is much different from the result induced from the theories. We anatomize the reason and find many factors will affect the value of path length, like multi-homing, commercial relationships and so on. Besides, the trend of the average path length is also drawn with mathematics.
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References
The National Laboratory for Applied Network Research (NLANR), sponsored by the National Science Foundation, http://moat.nlanr.net/
The Cooperative Association for Internet Data Analysis (CAIDA), located at the San Diego Supercomputer Center, http://www.caida.org/home/
Topology project, Electric Engineering and Computer Science Department, University of Michigan, http://topology.eecs.umich.edu/
SCAN project at the Information Sciences Institute, http://www.isi.edu/div7/scan/
Faloutsos, M., Faloutsos, P., Faloutsos, C.: Comput. Commun. Rev. 29, 251 (1999)
Govindan, R., Tangmunarunkit, H.: In: Proceedings of IEEE INFOCOM, Tel-Aviv, Israel, March 2000, pp. 1371–1380 (2000)
Broido, A., Claffy, K.C.: San Diego Proceedings of SPIE International Symposium on Convergence of IT and Communication, Denver, Colorado (2001)
Caldarelli, G., Marchetti, R., Pietronero, L.: Europhys. Lett. 52, 386 (2000)
Pastor-Satorras, R., Vázquez, A., Vespignani, A.: Phys. Rev. Lett., 258701 (2001); Vázquez, A., Pastor-Satorras, R., Vespignani, A.: Phys. Rev. E 65, 066130 (2002)
Chen, Q., Chang, H., Govindan, R., Jamin, S., Shenker, S.J., Willinger, W.: In: Proceedings of IEEE INFOCOM 2002, New York (2002)
Medina, A., Matta, I.: Boston University, Technical Report No. BU-CS-TR-2000-005 (2000)
Jin, C., Chen, Q., Jamin, S.: EECS Department, University of Michigan, Technical Report No. CSE-TR-433-00 (2000)
Siganos, G., Faloutsos, M., Faloutsos, P., Faloutsos, C.: Power-laws and the AS-level Internet topology. IEEE/ACM Trans. on Networking 11, 514–524 (2003)
Faloutsos, M., Faloutsos, P., Faloutsos, C.: On Power Law Relationships of the Internet Topology. In: ACM SIGCOMM, September 1-3, Cambridge MA, pp. 251–262 (1999)
Goh, K.-I., Kahng, B., Kim, D.: Phys. Rev. Lett. 87, 278701 (2001)
Adamic, L.A., Lukose, R.M., Puniyani, A.R., Huberman, B.A.: Phys. Rev. E 64, 046135 (2001)
Albert, R., Barabasi, A.-L.: Rev. Mod. Phys. 74, 47 (2002)
Newman, M.E.J.: SIAM Review 45, 167 (2003)
Newman, M.E.J.: J. Stat. Phys. 101, 819 (2000)
Calvert, K., Zegura, E., Doar, M.: Modeling Internet topology. IEEE Trans. on Communication, 160–163 (December 1997)
Medina, A., Matta, I., Byers, J.: On the origin of powerlaws in Internet topologies. ACM SIGCOMM Computer Communication Review 30(2), 18–34 (2000)
Bollobás, B., Riordan, O.: The diameter of a scale-free random graph, Department of Mathematical Sciences, University of Memphis (preprint, 2002)
Barrat, A.: Comment on Small-world networks: Evidence for crossover picture, cond-mat/9903323 (preprint, 1999)
Newman, M.E.J., Moore, C., Watts, D.J.: Mean field solution of the small-world network model. Phys. Rev. Lett. 84, 3201–3204 (2000)
Barabási, A.L., Albert, R.: Science 286, 509 (1999)
Routeviews Project, http://bgp.potaroo.net/as1221/bgp-active.html
Albert, R., Barabasi, A.-L.: Statistical mechanics of complex networks. Reviews of Modern Physics 74 (January 2002)
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Zhao, J., Zhu, P., Lu, X., Xuan, L. (2008). Does the Average Path Length Grow in the Internet?. In: Vazão, T., Freire, M.M., Chong, I. (eds) Information Networking. Towards Ubiquitous Networking and Services. ICOIN 2007. Lecture Notes in Computer Science, vol 5200. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89524-4_19
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DOI: https://doi.org/10.1007/978-3-540-89524-4_19
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