PowerMLaw!and!ScaleMFree!Network!
Advanced!
Computer Networks
[WR13]!Willinger!and!Roughan,!“Internet!Topology!
Research!Redux,”!in!Haddadi!and!Bonaventure!(eds.),!!
Recent&Advances&in&Networking,!ACM!SIGCOMM!
eBook,!Ch.!1,!2013!
RouterMlevel!Topology!
Sanity!check:!routers!are!not!that!powerful,!even!
the!most!expensive!backbone!routers!cannot!handle!
hundreds!or!thousands!of!highMbandwidth!
connections!
Limitation!of!measurements:!!
1.  traceroute!cannot!recognize!multiple!IP!addresses!
belonging!to!the!same!router!
2.  opaque!layerM2!(ATM!or!MPLS)!clouds!
3.  limited!vantage!points:!measurement!bias!
As!related!to!Internet!topology:!
“.!.!.!we!expose!the!specious!nature!of!scaleMfree!
network!models!.!.!.”!
“.!.!.!no!bearing!on!Internet!topology!.!.!.”!
“.!.!.!wrong!claims!about!the!Internet!as!a!whole!.!.!.”!
“.!.!.!powerMlaw!scaling,!full!of!sound!and!fury,!
signifying!nothing!.!.!.”![StrogatzMWillingerRoughan]!
RouterMlevel!Topology!
“.!.!.!due!to!the!inherent!inability!of!traceroute!
to!(i)!reveal!unambiguously!the!actual!!connectivity!
(i.e.,!node!degree)!of!any!router,!and!(ii)!correctly!
identify!even!the!mere!absence!or!presence!of!
highMdegree!nodes!(let!alone!their!actual!values),!
statistical!statements!.!.!.!claiming!that!the!
Internet’s!router!connectivity!is!well!described!by!a!
powerMlaw!distribution!.!.!.!cannot!be!justified!with!
any!reasonable!degree!of!statistical!confidence.”!
Alternative!Approach!
Constraint!optimization!instead!of!model!fitting!
1. ISPs!design!their!network!for!a!purpose:!e.g.,!to!connect!
users!to!the!Internet!and!carry!their!traffic!most!
efficiently!and!effectively!
2. ISPs!trade!off!available!technology!against!cost,!
performance,!manageability,!etc.!
3. Robustness!in!an!uncertain!operating!environment!
Heuristically!Optimal!Topologies!
Observation:!individual!link!capacities!tend!to!
increase!while!the!degree!of!connectivity!tends!to!
decrease!as!one!moves!from!the!network!edge!to!
its!core!!
!
Topologies!are!optimal!not!in!a!mathematical!
sense!but!from!an!operational!point!of!view!
1. ISP’s!objective!cannot!be!fully!expressed!mathematically!
2. Efficiency!frontiers!impractical!to!compute!due!to!
bewildering!number!of!router!and!link!types!
3. Traffic!demand!models!are!at!best!imprecise!forecasts!
Heuristically!Optimal!Topologies!
For!a!single!ISP’s!physical!plant![WR13]:!
1. construct!a!loose!mesh!core!of!expensive,!powerful!
routers!with!a!small!number!of!highMspeed!links!
2. attach!hierarchical!treeMlike!structures!at!network!
edges!to!aggregate!traffic!with!cheaper,!highM
connectivity!but!lowMcapacity!routers!
3. add!connections!at!strategic!points!for!extra!
redundancy!and!robustness!
4. traffic!demand!matrix!determines!node!degree!
distribution!
Implications!for!Topology!Generation!
Generators!based!on!graphMtheoretic!models!
are!of!no!use!for!any!real!applications!
!
BUT:!
• HOTMtype!generators!require!detailed!input!in!terms!
of!endMuser!geographic!dispersion,!traffic!matrix,!
design!objectives!and!constraints!
• Need!to!understand!how!ISPs!react!to!changes!in!
environment,!technology,!economy!
• No!more!“generic,”!blackMbox!routerMlevel!topology!
Overall!Internet!Topology!
Given!routerMlevel!topology!of!individual!ISPs!
Interconnect!them!at!common!locations!to!
form!the!ASMlevel!topology!
But!the!detailed!routerMlevel!topologies!must!be!collapsed!into!
their!corresponding!PoPMlevel!maps!which!serve!as!glue!between!
the!detailed!
routerMlevel!
topologies!and!
an!ASMlevel!
topology!of!the!
Internet!
BGP!Routing!
BGP!path!vectors!indicate!reachability!not!
connectivity!
Path!vectors!used!for!loop!detection,!often!abused!
for!traffic!engineering!and!do!not!have!to!be!the!
same!as!data!path!
BGP!doesn’t!transmit!every!path,!e.g.,!backMup!
paths:!35KM45K!peering!links!found,!whereas!one!IXP!
already!supports!50K!peering!links!
BGP!only!transmit!“best”!path:!measurement!bias!
ASMLevel!Topology!
BottomMline:!we!don’t!know!how!to!generate!
“realistic”!ASMlevel!topology!
!
Difficulties:!
• What!is!an!AS?!Multiple!ASes!per!administrative!domain,!
multiple!administrations!per!AS!
• No!ISPMequivalent!who!“owns”!the!AS!structure!
• ASes!are!not!“nodes”!
• Routing!and!connectivity!
between!ASes!are!not!the!
same!as!those!between!routers!
What!Qualifies!as!AS!Adjacency?!
Business!relationship!
Physical!(layerM1)!connectivity:!multiM!and!hyperMgraph!
LayerM2!connectivity:!network!virtualization!makes!it!
potentially!different!from!layerM1!connectivity!
BGP!reachability!
Policy!routing:!directed!multiMgraph!with!regional!
differences!
Traffic!flow!
PoPMlevel!Topology!
Conclusion!
PoP:!point!of!presence!
“Details”!in!the!form!of!protocols,!architecture,!
functionality,!and!purpose!matter!
• physical!building!where!routers!of!an!ISP!are!located!
• market!where!an!ISP!has!service!
PoPMlevel!topology!is!the!same!as!routerMlevel!topology!if!
there!is!only!one!router!per!PoP!
Goldilock!topology!for!network!modeling?!
• reasonable!network!size!
• internal!design!templated!
• network!changes!less!frequently!than!routerMlevel!topology!
• less!dependent!on!details!of!protocol!implementation,!router!
models,!etc.!
Most!promising!direction!for!Internet!topology!research?!
Examine!the!“hygiene”!of!the!available!measurements!
Treat!network!modeling!as!an!exercise!in!reverseM
engineering!and!not!as!an!exercise!in!modelMfitting!!
Beware!of!M.L.!Mencken’s!quote,!“For!every!complex!
problem!there!is!an!answer!that!is!clear,!simple,!and!
wrong”!