[PPT] - Understanding Router-level Topology: Principles, Models, and PowerPoint Presentation

SLIDE 1

Understanding Router-level Topology: Principles, Models, and Validation

David Alderson California Institute of Technology ISMA Workshop on Internet Topology May 10, 2006

SLIDE 2

D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 2

Acknowledgments

Primary Coauthors

John Doyle (Caltech)
Walter Willinger (AT&T Labs-Research)
Lun Li (Caltech)

Contributions

Reiko Tanaka (RIKEN, Japan)
Matt Roughan (U. Adelaide, Australia)
Steven Low (Caltech)
Ramesh Govindan (USC)
Neil Spring (U. Maryland)
Stanislav Shalunov (Abilene)
Heather Sherman (CENIC)

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 3

On modeling

“All models are wrong, but some models are useful.”

G. P. E. Box

“When exactitude is elusive, it is better to be approximately right than certifiably wrong.”

B. B.

Mandelbrot

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 4

the Internet as an inspiration for the development of elegant mathematical models of networks wanting to say “something meaningful” about the Internet (something about which decision makers are concerned)

vs

what is the MESSAGE? what “MATTERS”? and TO WHOM? who has RESPONSIBILTY for the message?

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 5

The application of graph theory and statistics to the study of Internet topology without the details of system architecture and engineering can lead to incorrect (and possibly misleading) conclusions. Let’s consider the router-level Internet

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 6

The Router-Level Internet

my computer router router web server

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 7

The Internet is a LAYERED Network HTTP TCP IP LINK

my computer router router web server

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 8

The Internet is a LAYERED Network HTTP TCP IP LINK

my computer router router web server

packet packet packet packet packet packet

The perception of the Internet as a simple, user-friendly, and robust system is enabled by FEEDBACK and

ther CONTROLS that operate both

WITHIN LAYERS and ACROSS LAYERS. These ARCHITECTURAL DETAILS (protocols, interfaces, etc.) are MOST ESSENTIAL to the nature of the Internet.

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 9

Internet structure can be viewed as a solution to a DESIGN problem

physical constraints on components

– distance/delay, capacity

functional constraints on the system as a whole

– “X-ities”: functionality, maintainability, adaptability, evolvability, etc. design approach: modularity

simplify the problem by breaking it up
but still with provable properties as if it were an

integrated whole

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 10

Internet Architecture: Dual Decomposition HTTP TCP IP LINK

my computer router router web server

Vertical decomposition Protocol Stack

Benefits:

Each layer can evolve

independently

Substitutes, complements

Requirements:

1. Each layer follows the rules
2. Every other layer does “good

enough” with its implementation

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 11

networks and their properties are different at each layer

IP TRANSMISSION TCP

virtual physical static dynamic

APPLICATION

Router-level connectivity IP-level connectivity Autonomous System (AS) graph Web graph Email graph P2P graph and many others …

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 12

Internet Architecture: Dual Decomposition HTTP TCP IP LINK

my computer router router web server

Horizontal decomposition

Each level is decentralized and asynchronous Benefit: Individual components can fail (provided that they “fail off”) without disrupting the network.

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 13

The Router-Level Internet

my computer router router web server

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 14

Bigger Picture: Internet Architecture

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 15

Bigger Picture: Internet Architecture

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 16

Bigger Picture: Internet Architecture

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 17

Autonomous System (AS) Graphs = Business Relationships

AS 1 AS 3 AS 4 AS 2

Nodes = ASes Links = peering relationships

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 18

AS graphs obscure topology!

The AS graph may look like this. Reality may be closer to this…

Courtesy Tim Griffin

see talks by Hyunseok Chang and others on Thursday AM for more

n AS topology modeling

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 19

MESSAGE #1: specify WHICH aspect of Internet topology

There is no “generic” Internet topology
Router-level, IP-level, AS-level, application-level, …
Details of each make a big difference

PITFALL: Lack of specificity causes confusion – Albert, Jeong, and Barabasi (2000) study robustness properties of the Internet by equating AS-level topology with router-level topology ⇒Knocking out nodes in the AS graph?? – Berger, Borgs, Chayes, and Saberi (2005) study the spread

f viruses on the Internet by equating the Web graph with

the router-level topology. ⇒Virus propagation on the Web graph??

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 20

Unfortunately, direct inspection of Internet topology is generally NOT possible

Economic incentive for ISPs to obscure network structure
Recent trend

– Empirical measurement studies – Generative models

Obstacles

– Mismatch between what we want to measure and can measure – Imperfect measurements – What macro/microscopic statistics characterize a topology? – How to determine what matters? Remainder of talk: focus on router-level topology

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 21

considerable progress in measuring router-level topology…

traceroute tool

– Discovers compliant (i.e., IP) routers along path between selected network host computers

Large-scale traceroute experiments

– Pansiot and Grad (router-level map from around 1995) – Cheswick and Burch (mapping project 1997--) – Mercator (router-level maps from around 1999 by R. Govindan and H. Tangmunarunkit) – Skitter (ongoing mapping project by CAIDA folks) – Rocketfuel (state-of-the-art router-level maps of individual ISPs by UW folks)

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 22 http://research.lumeta.com/ches/map/

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 23 http://www.isi.edu/scan/mercator/mercator.html

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 24 http://www.caida.org/tools/measurement/skitter/

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 25 http://www.cs.washington.edu/research/networking/rocketfuel/bb

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 26

…but considerable drawbacks to existing approaches

traceroute-based measurements are ambiguous

– traceroute is strictly about IP-level connectivity – traceroute cannot distinguish between high connectivity nodes that are for real and that are fake and due to underlying Layer 2 (e.g., Ethernet, ATM) or Layer 2.5 technologies (e.g., MPLS)

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 27 http://www.caida.org/tools/measurement/skitter/

www.savvis.net managed IP and hosting company founded 1995

ffering “private

IP with ATM at core”

Possible that this “node” is an entire network! (not just a router)

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 28

…but considerable drawbacks to existing approaches

traceroute-based measurements are ambiguous

– traceroute is strictly about IP-level connectivity – traceroute cannot distinguish between high connectivity nodes that are for real and that are fake and due to underlying Layer 2 (e.g., Ethernet, ATM) or Layer 2.5 technologies (e.g., MPLS)

traceroute-based measurements are inaccurate

– Requires some guesswork in deciding which IP addresses/interface cards refer to the same router (“alias resolution” problem)

traceroute-based measurements are incomplete/biased

– IP-level connectivity is more easily/accurately inferred the closer the routers are to the traceroute source(s) – Node degree distribution is inferred to be of the power- law type even when the actual distribution is not see talk by Aaron Clauset et al. on Thu AM for more on this…

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 29

MESSAGE #2: Idiosyncracies of network measurements require careful interpretation

Each technique is typically specific to network of interest

(e.g., traceroute for IP-level, BGP tables for AS-level)

Even best-of-breed measurement data is ambiguous,

inaccurate, and incomplete PITFALL: Taking (someone else’s) data at face value may provide a false basis for results – example: use of MERCATOR data to support claims of power-law degree distribution for router-level Internet ⇒Are routers with >1000 connections plausible??

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 30

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Noncumulative Size-Frequency Binned Size-Frequency Size-Rank (log-log scale) Size-Rank (log-linear scale)

raw MERCATOR data a common reporting technique without 2 largest nodes without 2 largest nodes exponential in tail… plausible data?

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 31

Observation Modeling Approach

Real networks are not

random, but have obvious hierarchy.

Structural models

(GT-ITM Calvert/Zegura, 1996)

Long-range links are

expensive

Random graph models

(Waxman, 1988)

Internet topologies exhibit

power law degree distributions (Faloutsos et al., 1999)

Degree-based models

replicate power-law degree sequences (e.g. scale-free networks, 1999-2004)

It is difficult to know what “matters” when it comes to representing router-level topology

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 32

Node Degree (d)

Source: Faloutsos et al. (1999) Rank: R(d) = P (D>d) x #nodes

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Node Degree (d) Node Rank

Power Laws and Internet Topology

Node Degree: d = # connections Router-Level Graph Autonomous System (AS) Graph

A random variable X is said to follow a power law with index α >

0 if

Led to active research in degree-based network models

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 33

Degree-Based Network Models

Basic Idea: traditional random graphs [Erdös & Renyí, 59] do

not produce power laws, so develop new models that explicitly attempt to match the observed (power law) distribution in node degree

Preferential Attachment

– Incremental growth + new nodes attach to high-degree nodes – “Rich get richer”—power laws in asymptotic limit – Scale-free networks [Barabási & Albert, 99] – Generators: Inet, GPL, AB, BA, BRITE, CMU power-law generator

Expected Degree Sequence

– Based on random graph models that skew probability distribution to produce power laws in expectation – Power law random graph (PLRG) [Aiello et al., 00] – Generalized random graph (GRG) [Chung & Lu, 03]

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 34

“Error tolerance” = Loss of random node has little effect “Attack vulnerability” = Targeted loss of hub fragments network

“Scale-free” networks and the “Achilles’ heel” of the Internet

Reference: R. Albert, H. Jeong, and A.-L. Barabási. Attack and error tolerance of complex

networks. Nature 406, 378-382,

2000.

node degree

101 101 102 100

node rank

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 35

The literature on Scale-Free Networks claims broad implications for the Internet and other networks

Power laws in network connectivity… ⇔ Are necessary and sufficient for “scale-free structure” ⇔ Imply critically connected “hubs” ⇒ Create an Achilles’ heel vulnerability ⇒ Yield a zero epidemic threshold for contagion ⇒Are evidence of fundamental self-organization in networks ⇒This self-organization is believed by some to be a universal feature of technological, biological, social and business networks ⇒Efforts to protect complex networks should focus on the most highly-connected components

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 36

node degree

101 101 102 100

node rank

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 37

Low degree core
Result of design
High performance and

robustness

High degree central

“hubs”

From random construction
Poor performance and

robustness

MESSAGE #3: networks with the same statistical features can be OPPOSITES in terms

f engineering

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 38

Trends in Topology Modeling

Observation Modeling Approach

Real networks are not

random, but have obvious hierarchy.

Structural models

(GT-ITM Calvert/Zegura, 1996)

Long-range links are

expensive

Random graph models

(Waxman, 1988)

Internet topologies exhibit

power law degree distributions (Faloutsos et al., 1999)

Degree-based models

replicate power-law degree sequences (scale-free networks, 1999-2004)

Degree-based models

are fundamentally inconsistent with engineering reality

Optimization-driven models

yield topologies consistent with design tradeoffs of network engineers (SIGCOMM’04)

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 39

HTTP TCP IP LINK

my computer router router web server

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 40

Who builds real router-level topologies?
How do technology and cost influence deployment?
How does one evaluate a “good” design?
What drives their structure?
What about power laws?

LINK

some form of an (implicit) OPTIMIZATION problem, although actual “design” may be decentralized and heuristic the “decision makers” are individual ISPs network PERFORMANCE can be measured in terms of tra they provide CONSTRAINTS on what the ISP can do a mere consequence of the inputs to the optimization prob

Our Perspective

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 41

Cisco 12000 Series Routers

80 Gbps 4 1/8 12404 120 Gbps 6 1/4 12406 200 Gbps 10 1/2 12410 320 Gbps 16 Full 12416 Switching Capacity Slots Rack size Chassis

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

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 42

10 10

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Degree

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Bandwidth (Gbps)

15 x 1-port 10 GE 15 x 3-port 1 GE 15 x 4-port OC12 15 x 8-port FE Technology constraint

Total Bandwidth

Router Technology Constraint

Cisco 12416 GSR, circa 2002 high BW low degree high degree low BW

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 43

bandwidth degree

1 16 10Gb 155Mb 256

log/log

625Mb 2.5Gb

Technically feasible

160Gb

Technologica l advance

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 44

1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 Router Degree Total BW Cisco 12416 GSR (c.2002) Cisco 7600 WAN Agg. Aggregated DSL Broadband Cable Aggregated Dialup

Abstracted Technologically Feasible Region

router models specialize by “role”

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 45

Hosts Edges Core

Heuristically Optimal Topology

High degree nodes are at the edges. Sparse, mesh-like core of fast, low-degree routers. High cost of links drives traffic aggregation at network edge Relatively uniform connectivity within core. Possibly high variability in connectivity at edge.

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 46

SOX

U. Florida
U. So. Florida

Miss State GigaPoP WiscREN SURFNet MANLAN Northern Crossroads Mid-Atlantic Crossroads Drexel U. NCNI/MCNC MAGPI UMD NGIX

Seattle Sunnyvale Los Angeles Houston Denver Kansas City Indian- apolis Atlanta Wash D.C. Chicago New York

OARNET Northern Lights Indiana GigaPoP Merit

U. Louisville

NYSERNet

U. Memphis

Great Plains OneNet

U. Arizona

Qwest Labs CHECS-NET Oregon GigaPoP Front Range GigaPoP Texas Tech Tulane U. Texas GigaPoP LaNet UT Austin CENIC UniNet NISN Pacific Northwest GigaPoP

U. Hawaii

Pacific Wave TransPAC/APAN Iowa St. Florida A&M UT-SW Med Ctr. SINet WPI Star- Light Intermountain GigaPoP

Abilene Backbone Physical Connectivity

(as of August 2004) 0.1-0.5 Gbps 0.5-1.0 Gbps 1.0-5.0 Gbps 5.0-10.0 Gbps DREN Jackson St. NREN USGS

U. So. Miss.

PSC DARPA BossNet SFGP/ AMPATH Arizona St. ESnet GEANT North Texas GigaPoP

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 47

Cisco 750X Cisco 12008 Cisco 12410

dc1 dc2 dc3 hpr dc1 dc3 hpr dc2 dc1 dc1 dc2 hpr hpr

SAC OAK SVL LAX SDG SLO

dc1

FRG

dc1

FRE

dc1

BAK

dc1

TUS

dc1

SOL

dc1

COR

dc1 hpr dc1 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)

Abilene Los Angeles Abilene Sunnyvale

The Corporation for Education Network Initiatives in California (CENIC) acts as ISP for the state's colleges and universities http://www.cenic.org Like Abilene, its backbone is a sparsely- connected mesh, with relatively low connectivity and minimal redundancy.

no high-degree hubs?
no Achilles’ heel?

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 48

Router Deployment: Abilene and CENIC

1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+00 1.E+01 1.E+02 1.E+03 Router Degree Total BW (Mbps)

Abilene T640s Juniper T640 Feasible Region CENIC 12410s Cisco 12410 Feasible Region CENIC 12008s Cisco 12008 Feasible Region CENIC 750Xs Cisco 750X Feasible Region

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 49

AT&T Router Deployment (c.2003)

1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 Router Degree Total Bandwidth

ISP 'Core' Routers Core Router Config Region ISP 'High Speed Access' Routers ISP 'Low Speed Access' Routers Access Router Config Region

core routers “low speed” access routers “high speed” access routers

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 50

Hosts Edges Core

Heuristically Optimal Topology

High degree nodes are at the edges. Sparse, mesh-like core of fast, low-degree routers. High cost of links drives traffic aggregation at network edge Relatively uniform connectivity within core. Possibly high variability in connectivity at edge.

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 51

A Closer Look Router-Level Measurement Data

Rocketfuel Project: Higher fidelity maps of individual ISPs
Shows that core routers do not follow a power law distribution

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Node Degree Node Rank

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Node Degree Node Rank Node Degree Distribution for AS 7018

Source: Rocketfuel

Pansiot and Grad data in Faloutsos (1999)

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 52

4

Source: Rocketfuel all routers access routers backbone routers

Node Degree Distribution for AS 7018

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A Closer Look Router-Level Measurement Data

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Node Degree Node Rank

Again, traceroute measurement data requires careful scrutiny

Rocketfuel Project: Higher fidelity maps of individual ISPs
Shows that core routers do not follow a power law distribution

Nonetheless, power laws in aggregate connectivity are plausible.

High variability is toward the network edge.

Pansiot and Grad data in Faloutsos (1999)

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 53

Rocketfuel: Interpretation, Validation, Augmentation

application of “first principles” (e.g. router technology)
alias resolution: discovery of duplicate nodes
new graph annotation methods

AS 7018 9261 total nodes 640 core nodes 156 duplicates (24%) 484 unique core nodes AS 1239 7043 total nodes 673 core nodes 215 duplicates (32%) 458 unique core nodes

AS 7018: Austin, TX

ISP Points of Presence (POPs) have highly

rganized structure

(simplicity, hierarchy, redundancy)

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 54

node degree

101 101 102 100

node rank

Preferential Attachment

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 55

SOX SFGP/ AMPATH

U. Florida
U. So. Florida

Miss State GigaPoP WiscREN SURFNet Rutgers U. MANLAN Northern Crossroads Mid-Atlantic Crossroads Drexel U.

U. Delaware

PSC NCNI/MCNC MAGPI UMD NGIX DARPA BossNet GEANT

Seattle Sunnyvale Los Angeles Houston Denver Kansas City Indian- apolis Atlanta Wash D.C. Chicago New York

OARNET Northern Lights Indiana GigaPoP Merit

U. Louisville

NYSERNet

U. Memphis

Great Plains OneNet Arizona St. U. Arizona Qwest Labs UNM Oregon GigaPoP Front Range GigaPoP Texas Tech Tulane U. North Texas GigaPoP Texas GigaPo P LaNet UT Austin CENIC UniNet WIDE AMES NGIX Pacific Northwest GigaPoP

U. Hawaii

Pacific Wave ESnet TransPAC/APAN Iowa St. Florida A&M UT-SW Med Ctr. NCSA MREN SINet WPI StarLight Intermountain GigaPoP

Abilene Backbone Physical Connectivity

0.1-0.5 Gbps 0.5-1.0 Gbps 1.0-5.0 Gbps 5.0-10.0 Gbps

Abilene-inspired

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 56

Network Performance

Given 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

Bandwidth (Mbps)

k B x t s B B x

ij

r k j i k ij j i j i j i ij

∀ ≤ =

∑ ∑ ∑

∈

, . . max max

: , , ,

α

Step 3: Compute max flow

Bi Bj

xij

Step 2: Compute traffic demand

j i ij

B B x ∝

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 57

PA Heuristically Optimized

Structure Determines Performance

P(g) = 1.19 x 1010 P(g) = 1.13 x 1012

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Abilene-inspired

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 58

Structural Metric

Introduced in SIGCOMM’04
Easily computed for any graph
Depends on the structure of the graph, not the generation

mechanism

Measures how “hub-like” the network core is

j connected j i id

d g s

∑

=

,

) (

Define the metric (di = degree of node i)

max

) ( ) ( s g s g S =

We can renormalize so that 0 ≤ S(g) ≤ 1 where smax has the largest value of s(g) among all graphs g having the same degree distribution.

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 59

Properties of the S(g) metric

Captures all of the information in degree correlation

statistics [Dorogovtsev and Mendes, 2003]

Closely related to notion of assortativity [Newman, 2002]
Graphs with high-S(g) have certain self-similar

properties as defined by notions of rewiring, coarse graining, trimming

For graphs resulting from probabilistic construction (e.g.

PLRG/GRG), LogLikelihood (LLH) ∝ S(g)

Relevant Interpretation: How likely is a particular graph (having given degree sequence) to arise at random? For details:

L. Li, D. Alderson, J.C. Doyle, W. Willinger. Toward a

Theory of Scale-Free Networks: Definition, Properties, and Implications. Internet Mathematics, In Press (2006). see also the talk by Lun Li on Thurs P

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 60

PA PLRG Heuristically Optimal Abilene-inspired Sub-optimal

Networks with the Same Degree Sequence

102 101

Rank

100 100 101

Degree

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 61

PA PLRG/GRG HOT Abilene-inspired Sub-optimal

smax S(g) = 1 P(g) = 1.08 x 1010

0.2 0.4 0.6 0.8 1

Relative Likelihood

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12

Perfomance (bps)

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 62

PA PLRG/GRG HOT Abilene-inspired Sub-optimal

smax S(g) = 1 P(g) = 1.08 x 1010

???

0.2 0.4 0.6 0.8 1

Relative Likelihood

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Perfomance (bps)

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 63

PA HOT Worst case = low- degree core router Worst case = high degree central hub

Response to router attack

real Tier-1 ISPs typically only ~10% loaded

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 64

MESSAGE #4: importance of model validation

Descriptive modeling that replicates statistical

features is no more than an exercise in “data fitting”

Emphasis on “closing the loop” (using

complementary measurements and domain expertise)

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D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 65

The “nodes” and “links” are physical things that have

hard constraints (technology).

ISPs are constrained in what they can afford to build,
perate, and maintain (economics).
Decisions of ISPs are driven by objectives

(performance) and reflect tradeoffs between what is feasible and what is desirable (heuristic optimization)

Many important questions (robustness) only make

sense in the context of the broader system (protocol stack) PITFALL: Emphasis on power laws – “Full of sound and fury, signifying nothing?” (Strogatz) – Power laws as “more normal than Normal” (ask

Summary: What “Matters” For Router-Level Topologies?

SLIDE 66

D. Alderson, Caltech

2006 ISMA Workshop on Internet Topology 66

http://hot.caltech.edu/topology.html

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