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1 GLOCOM Review 8:4 (76-1) 2003 Center for Global Communications 1

2 2

3 GLOCOM Review 8:4 (76-1) Recent research has been providing more support for the idea that Internet layers are formed along Power Law lines. Network systems, which follow Power Law principles, show scale-freeness and unequal distributions, and examining them can deepen our understanding of the Internet itself. The present paper focuses on the most basic levels of the Internet backbone, to determine whether or not it's network structure is governed by the Power Law. The analysis is based on data for IIJ, which is believed to have parameters representative of domestic information systems. IIJ is a rapidly expanding network, and it follows the Power Law, which can be inferred to be the case for the Internet backbone as a whole. Taking a closer look at IIJ's growth processes revels that following the geographic stabilization of NOCs and the rapid increase in circuit volume in 1998, there was a numerical increase in Power Law Indexes (Zipf Indexes) and also an increasing concentration of site hubs in Tokyo. It is true that the early years of do not show stabilized Power Law distribution, and 1995, the year in which the Telehodai system went into effect, shows untypical figures. On the whole, however, applying Power Law Indexes to network analysis has shed light on the network structure of and growth process of backbone circuiting. Keywords; Internet backbone circuiting, Power Laws, Power Law Indexes, Tokyo-based centralization, Regional IX, IIJ, "hubs" 3

4 Web WWW 3 4 IXInternet exchange 4

5 5 GLOCOM Review 8:4 (76-1) 1 2 2

6 5 6 A y x 1 y = bx 1 xr2 1 x = ar 2 2 x R 3 R = a 1/ x 1/ 3 N r 3 r = ( A / N ) x 1/ A = a 1/ 3 6

7 GLOCOM Review 8:4 (76-1) x p 3 4 x p [] = 1( A / N ) x 1/ p ' ( A / N) x 1/ 5 11 log y = log blog x 1 x 3 7

8 IIJ IIJ 8

9 GLOCOM Review 8:4 (76-1) 21NOC A-Bone IIJ ISP 12 NOCNOC NOCNOC NOCNOC NOC NOC NOC NOC21 21NOC 4,800Mbps 2,700Mbps1,200Mbps 4 TREE

10 NOC 62002IIJNOC 26,763Mbps9,692Mbps2,700Mbps 2,001MbpsNOC NOC NOCNOC NOC

11 GLOCOM Review 8:4 (76-1) 11

12 IIJ NOC NOC19958 NOC NOC8517 NOC1996 3NOC NOC IIJ Mbps200247,866Mbps IIJ NOC NOC

13 GLOCOM Review 8:4 (76-1) 13

14 NTT 1994 NetscapeWebWindows 95TCP/IP PC JPIXKDDMEXIIJ OCNODNDIONISP Bekkoame RIMNETISP IIJIIJ 14

15 GLOCOM Review 8:4 (76-1) 12 IIJ NOC 1NOC NOC NetscapeWebWindows 95 TCP/IPPC JPIXKDDMEXIIJ ISPBekkoameISP 15

16 1 M.Takayasu,and H.Takayasu [1993] "Fractals 1." NTT1997Web Web 3 =2002NHK pp IX 5 Auerbach.F [1913] "Das Gesets der Bevolkerungsknzentration." Petermann's Mitteilungen, 59, pp <http://linkage.rockefeller.edu/wli/zipf/> 7 Lada A. Adamic "Zipf, Power-laws, and Pareto - a ranking tutorial" Xerox Palo Alto Research Center <http://ginger.hpl.hp.com/shl/papers/ranking/ranking.html> x x R R = Ax =2002NHK

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