The Science of Complex Networks
and the Internet:
Lies, Damned Lies, and Statistics
Walter Willinger
AT&T Labs-Research
walter@research.att.com
Outline
• The Science of Complex Networks (“Network Science”)
• What “Network Science” has to say about the Internet
• What “engineering” has to say about the Internet
• Engineered vs. random network models
• Implications
2
Acknowledgments
•
•
•
•
•
•
•
•
•
•
John Doyle (Caltech)
David Alderson (Naval Postgraduate School)
Steven Low (Caltech)
Yin Zhang (Univ. of Texas at Austin)
Matthew Roughan (U. Adelaide, Australia)
Anja Feldmann (TU Berlin)
Lixia Zhang (UCLA)
Reza Rejaie (Univ. of Oregon)
Mauro Maggioni (Duke Univ.)
Bala Krishnamurthy, Alex Gerber, Shubho Sen, Dan Pai
(AT&T)
• … and many of their students and postdocs
3
NETWORK SCIENCE
January, 2006
•“First, networks lie at the core of the economic, political, and
social fabric of the 21st century.”
•“Second, the current state of knowledge about the structure,
dynamics, and behaviors of both large infrastructure networks
and vital social networks at all scales is primitive.”
•“Third, the United States is not on track to consolidate the
information that already exists about the science of large,
complex networks, much less to develop the knowledge that
will be needed to design the networks envisaged…”
http://www.nap.edu/catalog/11516.html4
“Network Science” in Theory …
• What?
“The study of network representations of physical,
biological, and social phenomena leading to
predictive models of these phenomena.” (National
Research Council Report, 2006)
• Why?
“To develop a body of rigorous results that will
improve the predictability of the engineering design
of complex networks and also speed up basic
research in a variety of applications areas.” (National
Research Council Report, 2006)
• Who?
– Physicists (statistical physics), mathematicians
(graph theory), computer scientists (algorithm
design), etc.
5
Basic Questions ask by Network Scientists
Question 1
To what extent does there exist a “network structure” that is
responsible for large-scale properties in complex systems?
•
Performance
•
Robustness
•
Adaptability / Evolvability
•
“Complexity”
6
Basic Questions ask by Network Scientists (cont.)
Question 2
Are there “universal laws” governing the structure (and
resulting behavior) of complex networks? To what extent is
self-organization responsible for the emergence of system
features not explained from a traditional (i.e., reductionist)
viewpoint?
7
Basic Questions ask by Network Scientists (cont.)
Question 3
How can one assess the vulnerabilities or fragilities
inherent in these complex networks in order to avoid
“rare yet catastrophic” disasters? More practically,
how should one design, organize, build, and manage
complex networks?
8
Observation
• The questions motivating recent work in “Network
Science” are “the right questions”
– network structure and function
– technological, social, and biological
• The issue is whether or not “Network Science” in its
current form has been successful in providing
scientifically solid answers to these (and and other)
questions.
• Our litmus test for examining this issue
– Applications of the current “Network Science”
approach to real systems of interest (e.g., Internet)
9
As scientists, why should we care?
• “Network Science” as a new scientific discipline …
10
Publications in Network Science Literature by Discipline
(As recorded by the Web of Science1 on October 1, 2007; courtesy D. Alderson)
Journal Publications (cumulative)
"high impact"
physics
biology, chemistry, medicine
computer science
sociology, economics
engineering
complex systems
applied mathematics
earth science
business, management
1998 1999 2000 2001 2002 2003 2004 2005 2006 2007*
1
1
5
4
17
13
22
16
9
4
92
1
7
26
62 124 139 230 260 350
286 1485
0
1
4
16
22
31
67
80
94
77
392
0
1
2
7
10
22
47
61
64
19
233
0
1
2
6
7
11
14
22
15
16
94
0
0
1
2
7
4
13
15
22
12
76
0
1
1
2
3
7
11
13
18
22
78
0
0
0
0
2
6
6
10
29
21
74
0
1
1
2
7
4
6
11
11
0
43
0
0
0
1
2
1
4
6
9
1
24
2
13
42 102 201 238 420 494 621
458 2591
3000
2500
2000
1500
1000
500
"high impact"
physics
biology, chemistry, medicine
computer science
sociology, economics
applied mathematics
engineering
earth science
complex systems
business, management
0
1998 1999 2000 2001 2002 2003 2004 2005 2006 2007*
11
Most Cited Publications in Network Science Literature
(As recorded by the Web of Science1 on October 1, 2007; courtesy D. Alderson)
Article
1. Watts, DJ; Strogatz, SH. 1998. Collective dynamics of 'small-world' networks, NATURE 393(668).
2. Barabasi AL, Albert R. 1999. Emergence of scaling in random networks. SCIENCE 286 (543).
3. Albert R, Barabasi AL. 2002. Statistical Mechanics of Complex Networks. REV. OF MODERN PHYSICS 74 (1).
4. Newman MEJ. 2003. The structure and function of complex networks. SIAM REVIEW 45 (2).
5. Jeong H, Tombor B, Albert R, et al. 2000. The large-scale organization of metabolic networks. NATURE 407
(6804).
6. Strogatz, SH. 2001. Exploring complex networks, NATURE 410(6825).
7. Albert R, Jeong H, Barabasi AL. 2000. Error and attack tolerance of complex networks. NATURE 406 (6794).
8. Dorogovtsev SN, Mendes JFF. 2002. Evolution of networks. ADV IN PHYSICS 51 (4).
9. Giot, L; Bader, J.S.; Brouwer, C; Chaudhuri, A; Kuang, B; et al. 2003. A protein interaction map of Drosophila
melanogaster, SCIENCE, 302(5651).
10. Milo, R; Shen-Orr, S; Itzkovitz, S; Kashtan, N; Chklovskii, D; Alon, U. 2002. Network motifs: Simple building
blocks of complex networks, SCIENCE 298(5594).
11. Amaral LAN, et al. 2000. Classes of small-world networks. PROC. NAT. ACAD. SCI. 97 (21).
12. Ravasz, E; Somera, AL; Mongru, DA; Oltvai, ZN; Barbasi, AL. 2002. Hierarchical organization of modularity in
metabolic networks, SCIENCE 297(5586).
13. Pastor-Satorras, R; Vespignani, A. 2001. Epidemic spreading in scale-free networks, PHYS. REV. LETT. 86(14).
14. Tong, AHY, et al. 2004. Global mapping of the yeast genetic interaction network. SCIENCE 303(5659)
15. Barabasi, AL; Albert, R; Jeong, H. 1999. Mean-field theory for scale-free random networks, PHYSICA A 272.
cites
2244
2110
1972
960
903
884
747
636
550
489
475
457
440
412
364
1327912
As scientists, why should we care?
• “Network Science” as a new scientific discipline …
• “Network Science” for the masses …
13
The “New Science of Networks”
14
As scientists, why should we care?
• “Network Science” as a new scientific discipline …
• “Network Science” for the masses …
• “Network Science” for the (Internet) experts …
15
The “New Science of Networks”
16
As scientists, why should we care?
• “Network Science” as a new scientific discipline …
• “Network Science” for the masses …
• “Network Science” for the Internet experts …
• “Network Science” for undergraduate/graduate students
in Computer Science/Electrical Engineering
17
The “New Science of Networks”
• New course offerings
– http://www.cc.gatech.edu/classes/AY2010/cs8803
ns_fall/
– http://www.netscience.usma.edu/about.php
– http://nicomedia.math.upatras.gr/courses/mnets/in
dex_en.html
– http://wwwpersonal.umich.edu/~mejn/courses/2004/cscs535
/index.html
– http://www.phys.psu.edu/~ralbert/phys597_09-fall
18
As scientists, why should we care?
• “Network Science” as a new scientific discipline …
• “Network Science” for the masses …
• “Network Science” for the Internet experts …
• “Network Science” for undergraduate/graduate students
in Computer Science/Electrical Engineering
• … and most importantly, because we want to know how
serious a science “Network Science” is ….
19
The Main Points of this Talk …
I will show that in the case of the Internet …
The application of “Network Science” in its current form
has led to conclusions that are not controversial but simply
wrong.
I will deconstruct the existing arguments and generalize
the potential pitfalls common to “Network Science.”
I will also be constructive and illustrate an alternative
approach to “Network Science” based on
engineering considerations.
20
What does “Network Science” say about the Internet
• Illustration with a case study
– Problem: Internet router-level topology
– Approach: Measurement-based
– Result: Predictive models with far-reaching implications
• Textbook example for the power of “Network Science”
– Appears solid and rigorous
– Appealing approach with surprising findings
– Directly applicable to other domains
21
What does “Network Science” say about the Internet
• Measurement technique
– traceroute tool
– traceroute discovers compliant (i.e., IP) routers along
path between selected network host computers
22
Running traceroute: Basic Experiment
• Basic “experiment”
– Select a source and destination
– Run traceroute tool
• Example
– Run traceroute from my machine in Florham Park,
NJ, USA to www.duke.edu
23
Running “traceroute www.duke.edu” from NJ
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
1 fp-core.research.att.com (135.207.16.1) 2 ms 1 ms 1 ms
2 ngx19.research.att.com (135.207.1.19) 1 ms 0 ms 0 ms
3 12.106.32.1 1 ms 1 ms 1 ms
4 12.119.12.73 2 ms 2 ms 2 ms
5 tbr1.n54ny.ip.att.net (12.123.219.129) 4 ms 5 ms 3 ms
6 ggr7.n54ny.ip.att.net (12.122.88.21) 3 ms 3 ms 3 ms
7 192.205.35.98 4 ms 4 ms 8 ms
8 jfk-core-02.inet.qwest.net (205.171.30.5) 3 ms 3 ms 4 ms
9 dca-core-01.inet.qwest.net (67.14.6.201) 11 ms 11 ms 11 ms
10 dca-edge-04.inet.qwest.net (205.171.9.98) 11 ms 15 ms 11 ms
11 gw-dc-mcnc.ncren.net (63.148.128.122) 18 ms 18 ms 18 ms
12 rlgh7600-gw-to-rlgh1-gw.ncren.net (128.109.70.38) 18 ms 18 ms 18 ms
13 roti-gw-to-rlgh7600-gw.ncren.net (128.109.70.18) 20 ms 20 ms 20 ms
14 art1sp-tel1sp.netcom.duke.edu (152.3.219.118) 23 ms 20 ms 20 ms
15 webhost-lb-01.oit.duke.edu (152.3.189.3) 21 ms 38 ms 20 ms
24
traceroute-paths: (many) source-destination pairs
25
What does “Network Science” say about the Internet
• Measurement technique
– traceroute tool
– traceroute discovers compliant (i.e., IP) routers along
path between selected network host computers
• Available data: from large-scale traceroute experiments
– Pansiot and Grad (router-level, around 1995, France)
– Cheswick and Burch (mapping project 1997--, Bell-Labs)
– Mercator (router-level, around 1999, USC/ISI)
– Skitter (ongoing mapping project, CAIDA/UCSD)
– Rocketfuel (state-of-the-art router-level maps of
individual ISPs, UW Seattle)
– Dimes (ongoing EU project)
26
http://research.lumeta.com/ches/map/
27
http://www.isi.edu/scan/mercator/mercator.html
28
http://www.caida.org/tools/measurement/skitter/
29
http://www.cs.washington.edu/research/networking/rocketfuel/bb
30
http://www.cs.washington.edu/research/networking/rocketfuel/
31
What does “Network Science” say about the Internet (cont.)
• Inference
– Given: traceroute-based map (graph) of the routerlevel Internet (Internet service provider)
– Wanted: Metric/statistics that characterizes the
inferred connectivity maps
– Main metric: Node degree distribution
32
http://www.isi.edu/scan/mercator/mercator.html
33
What does “Network Science” say about the Internet (cont.)
• Inference
– Given: traceroute-based map (graph) of the routerlevel Internet (Internet service provider)
– Wanted: Metric/statistics that characterizes the
inferred connectivity maps
– Main metric: Node degree distribution
• Surprising finding
– Inferred node degree distributions follow a power law
– A few nodes have a huge degree, while the majority
of nodes have a small degree
34
Power Laws and Internet Topology
A few nodes have lots of connections
Source: Faloutsos et al (1999)
Most nodes have few connections
35
What does “Network Science” say about the Internet (cont.)
• Inference
– Given: traceroute-based map (graph) of the routerlevel Internet (Internet service provider)
– Wanted: Metric/statistics that characterizes the
inferred connectivity maps
– Main metric: Node degree distribution
• Surprising finding
– Inferred node degree distributions follow a power law
– A few nodes have a huge degree, while the majority
of nodes have a small degree
• Motivation for developing new network/graph models
– Dominant graph models: Erdos-Renyi random graphs
– But: Node degrees of Erdos-Renyi random graph
models follow a Poisson distribution
36
What does “Network Science” say about the Internet (cont.)
• New class of network models
– Preferential attachment (PA) growth model
•Incremental growth: New nodes/links are added
one at a time
•Preferential attachment: a new node is more
likely to connect to an already highly connected
node (p(k)  degree of node k)
– Captures popular notion of “the rich get richer”
– There exist many variants of this basic PA model
– Generally referred to as “scale-free” network models
• Key features of PA-type network models
– Randomness enters via attachment mechanism
– Exhibit power law node degree distributions
37
PA-type Networks
38
What does “Network Science” say about the Internet (cont.)
• Model validation
– The models “fit the data” because they reproduce
the observed node degree distributions
– The models are simple and parsimonious
• PA-type models have resulted in highly publicized claims
about the Internet and its properties
– High-degree nodes form a hub-like core
– Fragile/vulnerable to targeted node removal
– Achilles’ heel
– Zero epidemic threshold
39
Cover Story: Nature 406, 2000.
40
Beyond the Internet …
•
•
•
•
Social networks
Information networks
Biological networks
Technological networks
– U.S. electrical power grid (data source: FEMA)
41
42
U.S. Electrical Power Grid
43
Beyond the Internet …
•
•
•
•
Social networks
Information networks
Biological networks
Technological networks
– U.S. electrical power grid (data source: FEMA)
– Western U.S. power grid: 4921 nodes, 6594 links
– J.-W. Wang and L.-L. Rong, “Cascade-based attack vulnerability on the
US power grid,” Safety Science 47, 2009
– NYT article, April 18, 2010: “Academic paper in China sets off alarms
in U.S.”
• Interdependent networks (e.g., Internet and power grid)
– S.V. Buldyrev, R. Parshani, G. Paul, H.E. Stanley and S. Havlin,
“Catastrophic cascade of failures in interdependent networks”, Nature
464 (April 2010)
44
On the Impact of “Network Science” …
• On the scientific community as a whole
– General excitement (huge number of papers)
– The Internet story has been repeated in the context of
biological networks, social networks, etc.
– Renewed hope that large-scale complex networks
across the domains (e.g., engineering, biology, social
sciences) exhibit common features (universal
properties).
45
On the Impact of “Network Science” …
NYT 4/18/2010
46
On the Impact of “Network Science” …
• On the scientific community as a whole
– General excitement (huge number of papers)
– The Internet story has been repeated in the context of
biological networks, social networks, etc.
– Renewed hope that large-scale complex networks
across the domains (e.g., engineering, biology, social
sciences) exhibit common features (universal
properties).
• On domain experts (e.g., Internet researchers, biologists)
– General disbelief
– We “know” the claims are not true …
– Back to basics ….
47
Basic Question
Do the available Internet-related connectivity
measurements and their analysis support the sort
of claims that can be found in the existing complex
networks literature?
Key Issues
•What about data hygiene?
•What about statistical rigor?
•What about model validation?
48
On Data Hygiene
On Measuring Internet Connectivity
• No central agency/repository
• Economic incentive for ISPs to obscure network
structure
• Direct inspection is typically not possible
• Based on measurement experiments, hacks
• Mismatch between what we want to measure and can
measure
• Specific examples covered in this talk
– Physical connectivity (routers, switched, links)
50
Measurements: traceroute tool
• traceroute www.duke.edu
•
traceroute to www.duke.edu (152.3.189.3), 30 hops max, 60 byte packets
• 1 fp-core.research.att.com (135.207.16.1) 2 ms 1 ms 1 ms
• 2 ngx19.research.att.com (135.207.1.19) 1 ms 0 ms 0 ms
• 3 12.106.32.1 1 ms 1 ms 1 ms
• 4 12.119.12.73 2 ms 2 ms 2 ms
• 5 tbr1.n54ny.ip.att.net (12.123.219.129) 4 ms 5 ms 3 ms
• 6 ggr7.n54ny.ip.att.net (12.122.88.21) 3 ms 3 ms 3 ms
•7 192.205.35.98 4 ms 4 ms 8 ms
• 8 jfk-core-02.inet.qwest.net (205.171.30.5) 3 ms 3 ms 4 ms
• 9 dca-core-01.inet.qwest.net (67.14.6.201) 11 ms 11 ms 11 ms
•10 dca-edge-04.inet.qwest.net (205.171.9.98) 11 ms 15 ms 11 ms
•11 gw-dc-mcnc.ncren.net (63.148.128.122) 18 ms 18 ms 18 ms
•12 rlgh7600-gw-to-rlgh1-gw.ncren.net (128.109.70.38) 18 ms 18 ms 18 ms
•13 roti-gw-to-rlgh7600-gw.ncren.net (128.109.70.18) 20 ms 20 ms 20 ms
•14 art1sp-tel1sp.netcom.duke.edu (152.3.219.118) 23 ms 20 ms 20 ms
•15 webhost-lb-01.oit.duke.edu (152.3.189.3) 21 ms 38 ms 20 ms
51
Traceroute measurements revisited (1)
• traceroute is strictly about IP-level connectivity
– Originally developed by Van Jacobson (1988)
– Designed to trace out the route to a host
• Using traceroute to map the router-level topology
– Engineering hack
– Example of what we can measure, not what we want to
measure!
• Basic problem #1: IP alias resolution problem
– How to map interface IP addresses to IP routers
– Largely ignored or badly dealt with in the past
– New efforts in 2008 for better heuristics …
52
Interfaces 1 and 2 belong to the same router
53
Example: Abilene Network
IP Alias Resolution Problem for Abilene (thanks to Adam Bender)
55
Traceroute measurements revisited (2)
• traceroute is strictly about IP-level connectivity
• Basic problem #2: Layer-2 technologies (e.g., MPLS, ATM)
– MPLS is an example of a circuit technology that hides the
network’s physical infrastructure from IP
– Sending traceroutes through an opaque Layer-2 cloud results
in the “discovery” of high-degree nodes, which are simply an
artifact of an imperfect measurement technique.
– This problem has been largely ignored in all large-scale
traceroute experiments to date.
58
(a)
(b)
59
60
Traceroute measurements revisited (3)
• The irony of traceroute measurements
– The high-degree nodes in the middle of the network that
traceroute reveals are not for real …
– If there are high-degree nodes in the network, they can
only exist at the edge of the network where they will never
be revealed by generic traceroute-based experiments …
• Additional sources of errors
– Bias in (mathematical abstraction of) traceroute
– Has been a major focus within CS/Networking literature
– Non-issue in the presence of above-mentioned problems
61
Traceroute measurements revisited (4)
• Bottom line
– (Current) traceroute measurements are of little use for
inferring router-level connectivity
– It is unlikely that future traceroute measurements will be
more useful for the purpose of router-level inference
• Lessons learned
– Key question: Can you trust the available data?
– Critical role of Data Hygiene in the Petabyte Age
– Corollary: Petabytes of garbage = garbage
– Data hygiene is often viewed as “dirty/unglamorous” work
62
On Model Validation
Taking Model validation more serious …
• Criticism of conventional model validation
– For one and the same observed phenomenon, there
are usually many different explanations/models
– The ability to reproduce a few graph statistics does not
constitute “serious” model validation
– Model validation should be more than “data fitting”
• What constitutes “more serious” model validation?
– There is more to networks than connectivity …
– When “nodes” and “links” have specific meaning …
– What do real networks look like?
64
Cisco 12000 Series Routers
• Modular in design, creating flexibility in configuration.
• Router capacity is constrained by the number and speed of line
cards inserted in each slot.
Chassis
Rack size
Slots
Switching
Capacity
12416
Full
16
320 Gbps
12410
1/2
10
200 Gbps
12406
1/4
6
120 Gbps
12404
1/8
4
80 Gbps
Source: www.cisco.com
65
Router Technology Constraint
10
Cisco 12416 GSR, circa 2002
3
high BW
low degree
Bandwidth (Gbps)
Total Bandwidth
10
10
high degree
low BW
2
1
15 x 1-port 10 GE
10
0
15 x 3-port 1 GE
15 x 4-port OC12
15 x 8-port FE
Technology constraint
10
-1
10
0
10
1
Degree
10
2
66
Intermountain
GigaPoP
Front Range
GigaPoP
Northern Lights
U. Memphis
U. Louisville
Great Plains
U. Arizona
Merit
Iowa St.
U. Hawaii
Pacific
Northwest
GigaPoP
SURFNet
GEANT
TransPAC/APAN
NCNI/MCNC
Atlanta
(as of August 2004)
0.1-0.5 Gbps
0.5-1.0 Gbps
1.0-5.0 Gbps
5.0-10.0 Gbps
SOX
UT-SW
Med Ctr.
UMD NGIX
SFGP/
AMPATH
Texas
GigaPoP
UT Austin
Drexel U.
PSC
North Texas
GigaPoP
Texas Tech
Abilene Backbone
Physical Connectivity
MAGPI
Los Angeles
Houston
UniNet
DREN
Wash
D.C.
Sunnyvale
USGS
MANLAN
New York
ESnet
CENIC
SINet
Chicago
NISN
NREN
WPI
Indianapolis
Seattle
Pacific
Wave
Northern
Crossroads
StarLight
Kansas
City
Denver
NYSERNet
WiscREN
CHECS-NET
Oregon
GigaPoP
OARNET
OneNet
Qwest Labs
Arizona St.
Indiana GigaPoP
Jackson St.
Miss State
GigaPoP
LaNet
Tulane U.
Mid-Atlantic
Crossroads
U. Florida
DARPA
BossNet
U. So. Florida
Florida A&M
U. So. Miss.
67
CENIC Backbone (as of January 2004)
OC-3 (155 Mb/s)
OC-12 (622 Mb/s)
GE (1 Gb/s)
OC-48 (2.5 Gb/s)
10GE (10 Gb/s)
Abilene
Sunnyvale
Cisco 750X
COR
Cisco 12008
dc1
Cisco 12410
dc1
OAK dc2
dc2
SAC
hpr
dc1
hpr
FRG
dc2
dc3
dc1
dc1
hpr
SVL
The Corporation for
Education Network
Initiatives in California
(CENIC) acts as ISP for
the state's colleges and
universities
http://www.cenic.org
FRE
dc1
SOL
dc1
BAK
dc1
SLO
dc1
hpr
Abilene
Los Angeles
LAX hpr
dc2
dc3
dc1
TUS
SDG
dc1
hpr
Like Abilene, its backbone
is a sparsely-connected
mesh, with relatively low
connectivity and minimal
redundancy.
• no high-degree hubs?
• no Achilles’ heel?
dc3
dc1
68
69
Back to the Basic Question:
Do the available Internet-related connectivity measurements
and their analysis support the sort of claims that can be
found in the existing complex networks literature?
Short Answer: No!
Longer Answer:
• Real-world router-level topologies look nothing like PAtype networks
• The results derived from PA-type models of the Internet
are not “controversial” – they are simply wrong!
• “The tragedy of science – the slaying of a beautiful
hypothesis by an ugly fact.” (T. Huxley)
70
What Went Wrong?
• No critical assessment of available data
• Ignore all networking-related “details”
– Randomness enters via generic attachment mechanism
– Overarching desire to reproduce power law node degree
distributions
• Low model validation standards
– Reproducing observed node degree distribution
71
How to avoid such Fallacies?
• Know your data!
• Take model validation more serious!
• Apply an engineering perspective to engineered systems!
72
Internet Modeling: An Engineering Perspective
• Surely, the way an ISP designs its physical infrastructure is not
the result of a series of coin tosses …
– ISPs design their router-level topology for a purpose, namely
to carry an expected traffic demand
– Randomness enters in terms of uncertainty in traffic
demands
– ISPs are constrained in what they can afford to build, operate,
and maintain (technology, economics).
• Decisions of ISPs are driven by objectives (performance) and
reflect tradeoffs between what is feasible and what is desirable
(heuristic optimization)
– Constrained optimization as modeling language
– Power law node degrees are a non-issue!
73
Heuristically Optimized Topologies (HOT)
Given realistic technology constraints on routers, how well is
the network able to carry traffic?
Step 1: Constrain to
be feasible
Step 2: pick traffic demand model
Bj
Bandwidth (Mbps)
1000000
xij  Bi B j
xij
100000
10000
1000
100
Bi
Abstracted
Technologically
Feasible Region
Step 3: Compute max flow
max  xij  max  Bi B j

10
degree
1
10
100
1000
i, j
s.t.
i, j
x
i , j:krij
ij
 Bk , k
74
HOT Design Principles
Mesh-like core of fast,
Coresrouters
low degree
High
degree
Edges
nodes are at
the
edges.
Hosts
75
Preferential Attachment
102
node rank
HOT model
101
100
101
node degree
76
HOT- vs. PA-type Network Models
Features
HOT-type/ Internet PA-type models
Core nodes
Fast, low degree
Slow, high degree
High degree nodes
Edge
Core
Degree distribution
Highly Variable
Power law
Generation
Designed
Random
Performance
High throughput
Low throughput
Attack Tolerance
Robust
Fragile
Fragility
Hijack network
Attack hubs
77
Implications of this Engineering Perspective
• Important lessons learned
– Know your data! – they typically reflect what we can
measure rather than what we would like to measure
– Avoid the allure of PA-type network models! – there exist
more relevant, interesting, and rewarding network models
that await discovery
– Details do matter! – layers, protocols, feedback control, etc.
• Network resilience – more than “knocking out” nodes/links
– NYC 9/11/2001, Baltimore tunnel fire (July 2001)
– Eastern US/Canada blackout (August 2003)
– Taiwan earthquake (December 2006)
– Hijack BGP (“blackholing”, YouTube and Pakistan ISP, 2008)
78
And always keep in mind …
“When exactitude is elusive, it is better to be
approximately right than certifiably wrong.”
(B.B. Mandelbrot)
80
SOME RELATED REFERENCES
• L. Li, D. Alderson, W. Willinger, and J. Doyle, A first-principles approach to
understanding the Internet’s router-level topology, Proc. ACM SIGCOMM 2004.
• J.C. Doyle, D. Alderson, L. Li, S. Low, M. Roughan, S. Shalunov, R. Tanaka, and
W. Willinger. The "robust yet fragile" nature of the Internet. PNAS 102(41),
2005.
• D. Alderson, L. Li, W. Willinger, J.C. Doyle. Understanding Internet Topology:
Principles, Models, and Validation. ACM/IEEE Trans. on Networking 13(6),
2005.
• R. Oliveira, D. Pei, W. Willinger, B. Zhang, L. Zhang. In Search of the elusive
Ground Truth: The Internet's AS-level Connectivity Structure.
Proc. ACM SIGMETRICS 2008.
• B. Krishnamurthy and W. Willinger. What are our standards for validation of
measurement-based networking research? Proc. ACM HotMetrics Workshop
2008.
• W. Willinger, D. Alderson, and J.C. Doyle. Mathematics and the Internet: A
Source of Enormous Confusion and Great Potential. Notices of the AMS, Vol.
56, No. 2, 2009. Reprinted in: The Best Writing on Mathematics, Princeton
University Press, 2010.
• M. Roughan, W. Willinger, O. Maennel, D. Perouli, and R. Bush. 10 Lessons
from 10 years of measuring and modeling the Internet’s Autonomous Systems.
IEEE JSAC Special Issue on “Measurement of Internet topologies,” 2011. 81