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Unformatted text preview: k speed with limited connectivity (longhaul connectivity)
• Edge routers (access routers) – support wide range of low-speed
connections (this trafﬁc then aggregated and sent on to core) also wide
range of technologies (dial-up, DSL, cable, etc) with wide range of pricing
strategies. “Heuristically Optimal Topologies”
• Core routers – high bandwidth, low connectivity
• Edge routers – Many low bandwidth connections, aggregating
trafﬁc as close to edge as possible. (d) HOT net (selectively rewired PA net), (e) HOT net started from core
observed in real-world provider (Abilene), replacing non-Abilene nodes. Metrics (no clear connection to validation)
• Performance: maximum throughput of graph g , under gravity
model of trafﬁc.
• Likelihood: S (g ) = s(g )
smax , where s(g ) = edges wiwj . – degree-degree correlations
– s(g) similar to assortativity/dissortativity in ways. High s(g) means hubs
connected together and will form core. Empirical data, I
• Abilene network (Internet backbone for higher education use,
carries 1% of trafﬁc in North America).
• CENIC (California education network) “Validation” (a) (b) • (a) Qualitative agreement with HOT derived network
• (b) Observed routers sort of seem to segregate into core/edge
of their ﬁrst principles. Empirical data, II (a) (b) • (a) Anonymized ISP, (b) Rocketfuel sampled.
• “the point here is that even a heuristic process informed by a detailed understanding of router role and technology constraints can go a long way toward generating realistic
annotated router-level maps. While not conclusive, what is remarkable about these results
is that the simple assumptions for (ﬁxed) link bandwidths in Table I result in bandwidthdegree combinations that are not inconsistent with our understanding of heuristically
optimal network design.” Further points
• High variability could be due exclusively to edge. Variability
in link technologies (DSL, dial-up, cable) and user demands
• High variability may be due to errors in sampling approaches
• “Achilles’ Heel”
– hubs in core make networks vulnerable to targeted attack.
– hubs in periphery have little impact on connectivity.
– HOT networks more robust, even “damaged” HOT net better
than intact PA network. Comments
• Lacks objectivity (heavy self-citation)
• Matching the constraint-capacity performance curve does not
validate that their ﬁrst principles approach produces a true
• Speciﬁc to internet topology (which is their point) / ﬁrst
• See also: W. Willinger, D. Alderson, and J.C. Doyle. “Mathematics and
the Internet: A source of enormous confusion and great potential”, Notices
of the American Mathematical Society, 56(5):286-299, May 2009. Model Validation Lit Review: Conclusions
• New techniques being introduced (classiﬁers, PCA).
• Calls for necessity of validation (e.g., Mitzenmacher)
• Speciﬁcs may matter, constraint curves “ﬁrst principles”.
• Selection easier than validation!...
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This document was uploaded on 03/12/2014 for the course CSCI 289 at UC Davis.
- Winter '11