The Role of Design in the Internet and Other Complex Systems

David AldersonFebruary 10, 2004

Joint work with J. Doyle, W. Willinger, and L. Li

My challengeUse models of Internet topology as a case study to

illustrate many of the themes of this week– “How to make complex systems still complex but

experimentally accessible?”– Importance/interpretation of high variability in

complex systems– Modeling debate: design vs. randomness– Understanding the “robust, yet fragile” aspects of the

Internet– “Closing the loop” between modeling and analysis– Similarity to models in biology?

The Internet as a Case Study

• To the user, it creates the illusion of a simple, robust, homogeneous resource enabling endless varieties and types of technologies, physical infrastructures, virtual networks, and applications (heterogeneous).

• Its complexity is starting to approach that of simple biological systems

• Our understanding of the underlying technology together with the ability to perform detailed measurements means that most conjectures about its large-scale properties can be unambiguously resolved, though often not without substantial effort.

IP

TCP/AQM

Applications

Link

Source coding

FAST TCP/AQM

IP routing

HOT topology

A Theory for the Internet?

General Approach:Use an engineering design perspective

to understand, explainthe complex structure observed.

Take a single layer in isolation and assume thatthe other layers are handled near optimally.

IP

TCP/AQM

Applications

Link

A Theory for the Internet?

If TCP/AQM is the answer, what is the

question?

Primal/dual model of TCP/AQM congestion control…

cRx

xUs

ssxs

subject to

)( max0

gives

gives

??

IP

TCP/AQM

Applications

Link

A Theory for the Internet?

??If the current topology of the Internet is the answer,

what is the question?

The Internet hourglass

IP

Web FTP Mail News Video Audio ping napster

Applications

TCP SCTP UDP ICMP

Transport protocols

Ethernet 802.11 SatelliteOpticalPower lines BluetoothATM

Link technologies

IP

The Internet hourglass

Web FTP Mail News Video Audio ping napster

Applications

TCP

Ethernet 802.11 SatelliteOpticalPower lines BluetoothATM

Link technologies

The Internet hourglass

IP

Web FTP Mail News Video Audio ping napster

Applications

TCP

Ethernet 802.11 SatelliteOpticalPower lines BluetoothATM

Link technologies

Everythingon IP

IP oneverything

Network protocols.

HTTP

TCP

IP

Files

packetspacketspacketspacketspacketspackets

Sources

Links

Files

Sources

Links

Hosts

Routers

Sources

Links

Sources

Links

Hosts

Routers

packets

Modeling Network TopologyWhy does it matter?

1. Performance evaluation of protocols

2. Provisioning• Topology constrains the applications and services

that run on top of it

3. Understanding large-scale properties • Reliability and robustness to accidents, failures,

and attacks on network components

4. Insight into other network systems• To the extent that the network model is “universal”

Topology Modeling

• Direct inspection generally not possible

• Recent trend: generative models follow empirical measurement studies

• But…– So many things to measure– Incredible variability in so many aspects– How to determine what matters?

The Internet• Full of “high variability”

– Link bandwidth: Kbps – Gbps– File sizes: a few bytes – Mega/Gigabytes– Flows: a few packets – 100,000+ packets– In/out-degree (Web graph): 1 – 100,000+– Delay: Milliseconds – seconds and beyond

• How should we think about the incredible scaling ability of the Internet?

• Is there something “universal” about its structure?

Topology Modeling

• Direct inspection generally not possible

• Recent trend: generative models follow empirical measurement studies

• But…– So many things to measure– Incredible variability in so many aspects– How to determine what matters?

• We will focus on router-level topology

Router-Level Topology

Hosts

Routers

• Nodes are machines (routers or hosts) running IP protocol

• Measurements taken from traceroute experiments that infer topology from traffic sent over network

• Subject to sampling errors and bias

• Requires careful interpretation

Power Laws and Internet Topology

Source: Faloutsos et al (1999)

• How to account for high variability in node degree?• Can we develop an explanatory model for the current

network topology?

Most nodes have few connections

A few nodes have lots of connections

Power laws are ubiquitous• This is no surprise, and requires no “special”

explanation. • Gaussians (“Normal”) distributions are attractors

for averaging (e.g Central Limit Theorem) so are also ubiquitous.

• Power laws are attractors for averaging too, but are also the only distributions invariant under maximizing, marginalization, and mixtures.

• For high variability data subject to these operations, power laws should be expected (Power laws as “more normal than Normal”?)

20th Century’s 100 largest disasters worldwide

10-2

10-1

100

100

101

102

US Power outages (10M of customers)

Natural ($100B)

Technological ($10B)

Log(size)

Log(rank)

100

101

102

1

2

3

10

100

10-2

10-1

100

Log(size)

Log(rank)

100

101

102

20th Century’s 100 largest disasters worldwide

US Power outages (10M of customers,1985-1997)

Natural ($100B)

Technological ($10B)

Slope = -1(=1)

10-2

10-1

100

? 10

0

101

102 US Power outages

(10M of customers, 1985-1997)

10-2

10-1

100

Slope = -1(=1)

A large event is not inconsistent with statistics.

Our Perspective• Must consider the explicit design of the Internet

– Protocol layers on top of a physical infrastructure– Physical infrastructure constrained by technological

and economic limitations– Emphasis on network performance– Critical role of feedback at all levels

• We seek a theory for Internet topology that is explanatory and not merely descriptive.

• Consider the ability to match large scale statistics (e.g. power laws) as secondary evidence of having accounted for key factors affecting design

HOTHighly HeavilyHeuristically

Optimized Organized

Tolerance Tradeoffs

• Based on ideas of Carlson and Doyle• Complex structure (including power laws) of highly

engineered technology (and biological) systems is viewed as the natural by-product of tradeoffs between system-specific objectives and constraints

• Non-generic, highly engineered configurations are extremely unlikely to occur by chance

Heuristic Network DesignWhat factors dominate network design?

• Economic constraints – User demands – Link costs– Equipment costs

• Technology constraints – Router capacity– Link capacity

1e-1

1e-2

1

1e1

1e2

1e3

1e4

1e21 1e4 1e6 1e8

Rank (number of users)

Dial-up~56Kbps

BroadbandCable/DSL~500Kbps

Ethernet10-100Mbps

POS/Ethernet1-10Gbps

Con

nec

tion

Sp

eed

(M

bp

s)

most users have low speed

connections

a few users have very high speed

connections

high performancecomputing

academic and corporate

residential and small business

Internet End-User Bandwidths

How to build a network that

satisfies these end user demands?

Economic Constraints• Network operators have a limited budget to

construct and maintain their networks

• Links are tremendously expensive

• Tremendous drive to operate network so that traffic shares the same links– Enabling technology: multiplexing– Resulting feature: traffic aggregation at edges– Diversity of technologies at network edge (Ethernet,

DSL, broadband cable, wireless) is evidence of the drive to provide connectivity and aggregation using many media types

Heuristically Optimal Network

Hosts

Edges

CoresMesh-like core of fast,

low degree routers

High degree nodes are at the edges.

Heuristically Optimal NetworkClaim: economic considerations alone yield

• Mesh-like core of high-speed, low degree routers

• High degree, low-speed nodes at the edge

• Is this consistent with technology capability?

• Is this consistent with real network design?

Cisco 12000 Series Routers

Chassis Rack size SlotsSwitching Capacity

12416 Full 16 320 Gbps

12410 1/2 10 200 Gbps

12406 1/4 6 120 Gbps

12404 1/8 4 80 Gbps

• Modular in design, creating flexibility in configuration.

• Router capacity is constrained by the number and speed of line cards inserted in each slot.

Source: www.cisco.com

Cisco 12000 Series RoutersTechnology constrains the number and capacity of line cards that can be installed, creating a feasible region.

Cisco 12000 Series RoutersPricing info: State of Washington Master Contract, June 2002

(http://techmall.dis.wa.gov/master_contracts/intranet/routers_switches.asp)

$602,500

$381,500

$212,400

$128,500

$2,762,500

$1,667,500

$932,400

$560,500

bandwidth

degree1 16

10Gb

155Mb

256log/log

625Mb

2.5GbTechnically

feasible

160Gb

Technological advance

Technologically Feasible Region

0.01

0.1

1

10

100

1000

10000

100000

1000000

1 10 100 1000 10000

degree

Ban

dw

idth

(M

bp

s) cisco 12416

cisco 12410

cisco 12406

cisco 12404

cisco 7500

cisco 7200

cisco 3600/3700

cisco 2600

linksys 4-port router

uBR7246 cmts(cable)cisco 6260 dslam(DSL)cisco AS5850(dialup)

Edge Shared media(LAN, DSL,

Cable, Wireless,Dial-up)

Corebackbone

High-end gateways

Older/cheapertechnology

Sprint backbone

SOX

SFGP/AMPATH

U. Florida

U. So. Florida

Miss StateGigaPoP

WiscREN

SURFNet

Rutgers

MANLAN

NorthernCrossroads

Mid-AtlanticCrossroads

Drexel

U. Delaware

PSC

NCNI/MCNC

MAGPI

UMD NGIX

DARPABossNet

GEANT

Seattle

Sunnyvale

Los Angeles

Houston

Denver

KansasCity

Indian-apolis

Atlanta

Wash D.C.

Chicago

New York

OARNET

Northern LightsIndiana GigaPoP

MeritU. Louisville

NYSERNet

U. Memphis

Great Plains

OneNetArizona St.

U. Arizona

Qwest Labs

UNM

OregonGigaPoP

Front RangeGigaPoP

Texas Tech

Tulane U.

North TexasGigaPoP

TexasGigaPoP

LaNet

UT Austin

CENICUniNet

WIDE

AMES NGIX

OC-3 (155 Mb/s)OC-12 (622 Mb/s)GE (1 Gb/s)OC-48 (2.5 Gb/s)OC-192/10GE (10 Gb/s)

Abilene BackbonePhysical Connectivity(as of December 16, 2003)

PacificNorthwestGigaPoP

U. Hawaii

PacificWave

ESnet

TransPAC/APAN

Iowa St.

Florida A&MUT-SWMed Ctr.

NCSA

MREN

SINet

WPI

StarLight

IntermountainGigaPoP

Cisco 750X

Cisco 12008

Cisco 12410

dc1dc2

dc3

hpr

dc1

dc3

hpr

dc2dc1

dc1dc2

hprhpr

SACOAK

SVL

LAX

SDG

SLOdc1

FRGdc1

FREdc1

BAKdc1

TUSdc1

SOLdc1

CORdc1

hprdc1

dc2

dc3

hpr

OC-3 (155 Mb/s)OC-12 (622 Mb/s)GE (1 Gb/s)OC-48 (2.5 Gb/s)10GE (10 Gb/s)

CENIC Backbone (as of January 2004)

AbileneSunnyvale

AbileneLos Angeles

Backbone topology of both Abilene and CENIC are both built as a mesh of high speed, low degree routers.

As one moves from the core out toward the edge, connectivity gets higher, and speeds get lower.

dc1dc2

dc3

hpr

dc1

dc3

hpr

LAX

SDG

SLOdc1

BAKdc1

TUSdc1

hpr

Chaffey, Crafton Hills, Cypress, Fullerton CC,

Mt. San Jacinto, Rio Hondo, Riverside, San Bernardino CCD, San Bernardino Valley, N.

Orange Cty CCD, Santa Ana College

Chaffey Joint USD

LA USD

UC Irvine

UC San Diego

SDSC

UCLA

UC Riverside

San Diego CC, Soutwestern CC,

Grossmont, Cuyamaca, Imperial Valley, Mira Costa CC, Palomar

CollegeSan Diego COE Johnson & Johnson

CUDI Peer,ESNet Peer

LosNettos

LAAP

UCSSN(Las Vegas)

UC SantaBarbara

MonroviaUSD Gigaman

Antelope Valley CC, Cerritos, Citrus, College of

the Canyons, Compton, East LA, El Camino CC, Glendale, Long Beach City College, Pasadena

CC, Santa Monica, Ventura

College

LA CCD, LA City, LA Harbor, LA Mission, LA Pierce, LA Southwest, LA Trade Tech,

LA Valley, Moorpark, Mt. San Antonio, Oxnard

Los Angeles COE

San Bernardino CSS

Riverside COE

Orange COE

Caltech

Abilene

to Soledad

to Sunnyvale

to Sacramento

to Fremont

CENIC Backbone for Southern California

Heuristically Optimal Network• Mesh-like core of high-speed, low degree routers• High degree, low-speed nodes at the edge

• Claim: consistent with drivers of topology design– Economic considerations (traffic aggregation)

– End user demands

• Claim: consistent with technology constraints• Claim: consistent with real observed networks

Question: How could anyone imagine anything else?

Two opposite views of complexity

Physics:• Pattern formation by

reaction/diffusion• Edge-of-chaos• Order for free• Self-organized criticality• Phase transitions• Scale-free networks• Equilibrium, linear• Nonlinear, heavy tails as

exotica

Engineering and math:• Constraints• Tradeoffs• Structure • Organization• Optimality• Robustness/fragility• Verification• Far from equilibrium• Nonlinear, heavy tails as

tool

Models of Internet Topology• Random graphs [Waxman ’88]• Explicit hierarchy [Calvert/Zegura ’96]• Power laws [Faloutsos3 ’99]

Random NetworksTwo methods for generating random networks having

power law distributions in node degree• Preferential attachment (“scale-free” networks)

– Inspired by statistical physics– Barabasi et al.; 1999

• Power Law Random Graph (PLRG)– Inspired by graph theory– Aiello, Chung, and Lu; 2000

Common features:• Ignore all system-specific details• Central core of high-degree, hub-like nodes

Summary of Scale-Free Story• Fact: Scale-free networks have roughly power law

degree distributions• Claim:

– If the Internet has power law degree distribution– Then it must be scale-free (oops)– Therefore, it has the properties of a scale-free network

One ofthe most-read papers ever on

the Internet!

Scientists spot Achilles heel of the Internet

• "The reason this is so is because there are a couple of very big nodes and all messages are going through them. But if someone maliciously takes down the biggest nodes you can harm the system in incredible ways. You can very easily destroy the function of the Internet," he added.

• Barabasi, whose research is published in the science journal Nature, compared the structure of the Internet to the airline network of the United States.

Complexity Digest 2004.06 Feb. 09, 2004Archive: http://www.comdig.org

13. Accurately Modeling the Internet Topology , arXiv

Abstract: To model the behavior of a network it is crucial to obtain a good destopology because structure affects function. When studying the topological propInternet, we found out that there are two mechanisms which are necessary for thof the Internet: a nonlinear preferential growth, where the growth is describedpositive-feedback mechanism, and the appearance of new links between already exshow that the Positive-Feedback Preference (PFP) model, which is based on the areproduces topological properties of the Internet such as: degree distribution,(rich-club connectivity), shortest path length, neighbor clustering, network reand rectangle coefficient), disassortative mixing (nearest-neighbors average deinformation flow pattern (betweenness centrality). We believe that these growthfurther study because they provide a novel insight into the evolutionary dynamics ofnetworks.

* [38] Accurately Modeling the Internet Topology, Shi Zhou, Raul J. Mondragon, , 2004-02-05, arXiv

Key Points• The scale-free story is based critically on the implied

relationship between power laws and a network structure that has highly connected “central hubs”– Not all networks with power law degree distributions

have properties of scale free networks. (The Internet is just one example!)

– Building a model to replicate power law data is no more than curve fitting (descriptive, not explanatory)

• The scale-free models ignore all system-specific details in making their claims– Ignore architecture (e.g. hardware, protocol stack)

– Ignore objectives (e.g. performance)

– Ignore constraints (e.g. geography, economics)

End Result

The scale-free claims of the Internet are not merely wrong, they suggest properties that are the opposite

of the real thing.

Fundamental difference:

random vs. designed

Internet topologies

nodes=routersedges=links

25 interior routers818 end systems

High degree hub-like coreLow degree

mesh-like core

101

102

100

101

degree

rank

identical power-law degrees

How to characterize / compare these two networks?

“scale-rich” vs. scale-free

Network PerformanceGiven realistic technology constraints on routers, how

well is the network able to carry traffic?

Step 1: Constrain to be feasible

Abstracted Technologically Feasible Region

1

10

100

1000

10000

100000

1000000

10 100 1000

degree

Ban

dw

idth

(M

bp

s)

Bi

Bj

xij

Step 2: Compute traffic demand

kBxts

BBx

ijrkjikij

ji jijiij

,..

maxmax

:,

, ,

Step 3: Compute max flow

Network LikelihoodHow likely is a particular graph (having given node

degree distribution) to be constructed?

• Notion of likelihood depends on defining an appropriate probability space for random graphs.

• Many methods (all based on probabilistic preferential attachment) for randomly generating graphs having power law degree distributions:– Power Law Random Graph (PLRG) [Aiello et al.]

– Random rewiring (Markov chains)

In both cases, LogLikelihood (LLH) j

connectedji

idd,

Likelihood

HighLow

Fast

Slow

Performance

Why such strikingdifferences with same

node degree distribution?

1

10

100

1000

10000

100000

10 100

degree

Ban

dw

idth

(M

bp

s)

11

10

100

1000

10000

100000

10 100

degree1

Fast core

High-degree edge

Slow core

Slower edge

Performance LikelihoodLikelihood

HighLow

Fast

Slow

Scale-free• Core: Hub-like, high degree • Edge: Low degree• Robust to random • Fragile to “attack”

HOT scale-rich• Core: Mesh-like, low degree • Edge: High degree• Robust to random • Robust to “attack”

• High performance• Low link costs• Unlikely, rare, designed• Destroyed by rewiring• Similar to real Internet

• Low performance• High link costs• Highly likely, generic• Preserved by rewiring• Opposite of real Internet

+ objectives and constraints

HierarchicalScale-Free (HSF)

RandomHOT

Low LikelihoodLow Performance Most Likely

LikelihoodHighLow

Robust, Efficient

Fragile, Wasteful

scale-free, critical, SOC, edge-of-chaos

The only functional biological or technological networks are highly organized, robust, efficient, and very unlikely to arise by random.

HOT

Universal features of complex networks

HOT=Highly Organized/Optimized Tradeoffs/Tolerance

1 10 100

100

101

102

103

Number of reactions

Rank

Carriers

all metabolites

Reactions

Metabolites

58 133 190 240

33

65

78

132

152

184

204

236

251

313

Carriers

Catabolism

Amino acids

Nucleotides

Lipids & fatty acids

Cofactors

Precursors

H. Pylori

CarriersAmino acids

Nutrients

Precursors

Nucleotides

Fatty acidsAnd Lipids

Cofactors

Bowtie architecture

Catabolism

Biosynthesis

1 2

3 4

S ATP S ADP

S NADH S NAD

Stoichiometry

S1 S2

S3 S4

NADNADH

ADPATP

Substrate

Carrier

Reaction,Enzyme

StoichiometryMatrix

1

2

3

4

1 0

1 0

0 1

0 1

1 0

1 0

0 1

0 1

S

S

S

S

ATP

ADP

NADH

NAD

GLC

DPG

PGL

PGC RL5P

X5P

6PG

MAL

CIT

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PEP

R5P

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ACCOA PPI AMPATP NH3 AC THF

MTH H2S

PI NADNADH ADPATP NADPNADPH CO2 COAACCOA PPI AMPATP NH3 AC THFMTH H2S

Carriers

precursors amino acids

• WT is highly organized, structured

• Simple reactions• Long assembly lines• Universal common carriers• Precursors and carriers are universal common currenciesWild type

GLC

DPG

PGL

PGC RL5P

X5P

6PG

MAL

CIT

ICIT

SUCFUM

G6P

F6P

T3P

3PG

PEP

R5P

E4P

PYR

OA

AKG

SUCOA

PRPP

DAH DQT DHS SME S5P PSM CHO

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PPN HPP

BAPASS

HSE PHSDHD

PIP SAK SDP DPI MDP

PHP PPS

ASE

GLN

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SER

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ASP

TYR

THR

LYS

CYS

GLY

ASN

PI NADNADH ADPATP NADPNADPH CO2 COAACCOA PPI AMPATP NH3 AC THFMTH H2S

Carriers

precursors amino acids

GLC

DPG

PGL

PGC RL5P

X5P

6PG

MAL

CIT

ICIT

SUCFUM

G6P

F6P

T3P

3PG

PEP

R5P

E4P

PYR

OA

AKG

SUCOA

PRPP

DAH DQT DHS SME S5P PSM CHO

AN NAN CD5 IGP

PPN HPP

BAP

ASSHSE PHS

DHDPIP SAK SDP DPI MDP

PHP PPS

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GLN

GLU

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ASP

TYR

THR

LYS

CYS

GLY

ASN

PI NADNADH ADPATP NADPNADPH CO2 COAACCOA PPI AMPATP NH3 AC THFMTH H2S• Randomly rewire to get “scale-free” version• Preserve

• degree• carrier and enzyme

• Destroys structure• Only one useful pathway remains

Random

GLC

DPG

PGL

PGC RL5P

X5P

6PG

MAL

CIT

ICIT

SUCFUM

G6P

F6P

T3P

3PG

PEP

R5P

E4P

PYR

OA

AKG

SUCOA

PRPP

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ASE

GLN

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SER

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ASP

TYR

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LYS

CYS

GLY

ASN

PI NADNADH ADPATP NADPNADPH CO2 COAACCOA PPI AMPATP NH3 AC THFMTH H2S

Carriers

precursors amino acids

GLC

DPG

PGL

PGC RL5P

X5P

6PG

MAL

CIT

ICIT

SUCFUM

G6P

F6P

T3P

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PEP

R5P

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OA

AKG

SUCOA

PRPP

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AN NAN CD5 IGP

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ASSHSE PHS

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PHP PPS

ASE

GLN

GLU

SER

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ASP

TYR

THR

LYS

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GLY

ASN

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GLC

DPG

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6PG

MAL

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SUCFUM

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F6P

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LYS

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ACCOA PPI AMPATP NH3 AC THF

MTH H2S

Random Wild type

GLC

DPG

PGL

PGC RL5P

X5P

6PG

MAL

CIT

ICIT

SUCFUM

G6P

F6P

T3P

3PG

PEP

R5P

E4P

PYR

OA

AKG

SUCOA

PRPP

DAH DQT DHS SME S5P PSM CHO

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BAP

ASS

HSE PHSDHD

PIP SAK SDP DPI MDP

PHP PPS

ASE

GLN

GLU

SER

TRP

ASP

TYR

THR

LYS

CYS

GLY

ASN

PI NADNADH

ADPATP

NADPNADPH CO2 COA

ACCOA PPI AMPATP NH3 AC THF

MTH H2S

Modeling Analysis

ValidationMeasurement

“Closing the loop”

PreferentialAttachment

PLRG

HOT

PreferentialAttachment PLRG HOT

PreferentialAttachment PLRG HOT

1e6

1e5

1

1e1

1e2

1e3

1e4

1e11 1e2 1e3 1e4

Degree (number of connections)

Tot

al R

oute

r B

and

wid

th (

Mb

ps)

Core Routers

High-EndGateways

AccessEdge RoutersShared Media

OlderCheaper

Technology

AbstractedFeasible Region

Internet Routing Technologies

Degree (number of connections)

1e6

1e5

1

1e1

1e2

1e3

1e4

1e11 1e2 1e3 1e4

Tot

al R

oute

r B

and

wid

th (

Mb

ps)

Core Routers High-End

Gateways

AccessEdge RoutersShared Media

OlderCheaper

Technology

AbstractedFeasible Region

Internet Routing Technologies

Per link bandwidth

1e-1

1e-2

1

1e1

1e2

1e3

1e4

1e11 1e2 1e3 1e4

Degree (number of connections)

Ban

dw

idth

/ L

ink

(M

bp

s)

Dial-up~56Kbps

BroadbandCable

~500Kbps

DSL~500Kbps

Core Routers10Gbps Core/Edge

Routers1Gbps

Local AreaEthernet

10-100Mbps

Internet Link Speeds