[CAIDA] answer: The topology/reachability data we have collected
suggests that half of all `backbone' routers
(i.e., those routers in the
largest bi-directionally connected component of the Internet as
observed through a month of skitter data, 21nov-18dec 00,
from 17 skitter monitors)
[if you're lost by now, just go look at the pretty pictures
below]
have no connections to other ASes than their own.
Another 1/3 have connections to one AS.
8.5% connect to 2 ASes;
The remaining 8% connect to more than 2 ASes.
In our observable Internet topology (including the backbone, see above `observable by skitter' definition), the number of ASes to which an IP address is connected is distributed like:
AS outegree #IPs Exceed
1 271640 30749
2 19363 11386
3 4781 6605
4 2309 4296
5 1302 2994
6 810 2184
7 511 1673
8 373 1300
9 234 1066
10 183 883
...................
84 1 2
101 1 1
108 1 0
# Total IPs 302389
Most of these IP addresses (90%) connect to only one AS,
and for a huge majority it will be their own AS.
(i.e., NOT a peer).
[CAIDA] answer: We recognize that the notions of Tier 1 and Tier 2 typically involve phrases such as `transit-free' or `settlement-free', although we have not observed consensus on the exact definition. (There's been a bit of "I know it when I see it" in this space.)
In seeking more objective taxonomy, for most any connectivity measure of AS size, one can see gaps on a logarithmic scale, meaning that ASes naturally split into groups separated by a factor larger than 1.4 (40% difference). These `AS constellations' change from one measure to another, although the top players remain more or less the same. In addition, constellations are sometimes more numerous than just three tiers of providers, so one cannot immediately map them to such tiers.
Example below of how many times a given AS appeared as transit versus originating a prefix.
Figure 1: scatterplot of ASes on UOregon Route View data,
x-axis: number of times this AS appeared as transit
for a path.
y-axis: number of times this AS served as origin AS
for a path.
ASes with large transit count are individually marked
in their own color symbol (upper right)
The other color symbols identify density (number of
ASes characterized by that (x,y) value), which
is present mostly at 0 transit count, i.e., stub ASes.
Note the 3 groups (tiers) of ASes that naturally emerge:
1 AS way up high (the red square on upper right);
10 a binary order of magnitude below that one;
followed by a gap on the transit x-axis scale.
note also that obviously we have all AS names for
the 'big guys' below
but not sure folks want those published
so we anonymize it.
CAIDA's topology measurements (which reveal far more comprehensive coverage than the best available routing table data) also yield compelling tier-ing of ASes just based on quantitative empirical assessment of observed indegree, outdegree, origin vs transit prefix count, etc, using skitter (topology) data with RouteViews to assist with mapping of IP addresses to ASes.
Figure 3 shows gaps between AS groups on a plot that compares coverage of UO RouteViews route table vs skitter topology data. (point: in general, 17 skitter monitors obtain a lot more connectivity information than even 40 diverse core routing tables)
Yet another cool example of natural `tiering' of AS data, but with different metric, we use the number of inbound AS paths (a generalization of indegree) in the figure below.
This graph only uses 16-AS-hop-count path lengths (including self-intersecting paths); the y-axis shows a deviation from the geometric progression, if we compute the same metric for higher (17) hop count paths. (If you didn't understand this paragraph, just note that you could make remarkably good guesses as to the identity of the few ASes on the lower right of the graph.)
if you're not sick of this kind of stuff yet
you also might like
stub AS analysis
(underlying motivation: does every stub AS really need its own AS number?)
andre broido and kc