Transcript Overview

The Role of Design in the Internet
and Other Complex Systems
David Alderson
February 10, 2004
Joint work with
J. Doyle, W. Willinger, and L. Li
My challenge
Use 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.
A Theory for the Internet?
Applications
Source coding
General Approach:
Use an engineering design perspective
TCP/AQM
TCP/ to understand,FAST
explain
AQM
the complex structure observed.
routing
Take IP
a single layer in isolationIPand
assume that
the other layers are handled near optimally.
Link
HOT topology
A Theory for the Internet?
Applications
TCP/
AQM
?
If TCP/AQM is the
answer, what is the
question?
max
xs  0
subject to
U ( x )
s
s
s
Rx  c
IP
Primal/dual model of TCP/AQM
congestion control…
Link
A Theory for the Internet?
Applications
TCP/
AQM
IP
?
Link
If the current topology of
the Internet is the answer,
what is the question?
The Internet hourglass
Applications
Web
FTP
Mail
News
Video
Audio
ping
napster
Transport protocols
TCP SCTP UDP
ICMP
IP
Ethernet 802.11
Power lines ATM
Optical
Link technologies
Satellite Bluetooth
The Internet hourglass
Applications
Web
FTP
Mail
News
Video
Audio
ping
napster
TCP
IP
Ethernet 802.11
Power lines ATM
Optical
Link technologies
Satellite Bluetooth
The Internet hourglass
Applications
Web
FTP
Mail
News
Video Audio
Everything
on IP
ping
napster
TCP
IP
Ethernet 802.11
IP on
Power lines ATM Optical
everything
Link technologies
Satellite Bluetooth
Network protocols.
Files
HTTP
Files
TCP
IP
packets
packets
packets
packets
packets
packets
Links
Sources
Links
Sources
Routers
Links
Sources
Hosts
Links
Sources
Routers
packets
Hosts
Modeling Network Topology
Why 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
Routers
Hosts
• 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
A few nodes have lots of connections
Source: Faloutsos et al (1999)
Most nodes have few connections
• How to account for high variability in node degree?
• Can we develop an explanatory model for the current
network topology?
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
2
10
Technological ($10B)
Log(rank)
Natural ($100B)
1
10
US Power outages
(10M of customers)
0
10
-2
10
-1
0
10
10
Log(size)
2
100
10
Log(rank)
1
10
10
3
2
0
1
10
-2
10
-1
0
10
10
Log(size)
20th Century’s 100 largest disasters worldwide
2
10
Technological ($10B)
Natural ($100B)
1
10
US Power outages
(10M of customers,
1985-1997)
Slope = -1
(=1)
0
10
-2
10
-1
10
0
10
2
US Power outages
(10M of customers,
1985-1997)
10
Slope = -1
(=1)
1
10
0
10
?
A large event is not
inconsistent with statistics.
-2
10
-1
10
0
10
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
HOT
Highly
Heavily
Heuristically
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 systemspecific objectives and constraints
• Non-generic, highly engineered configurations are
extremely unlikely to occur by chance
Heuristic Network Design
What factors dominate network design?
• Economic constraints
– User demands
– Link costs
– Equipment costs
• Technology constraints
– Router capacity
– Link capacity
Connection Speed (Mbps)
Internet End-User Bandwidths
1e4
1e3
POS/Ethernet
1-10Gbps
academic
and corporate
1e2
1e1
1
1e-1
high
performance
computing
Ethernet
10-100Mbps
a few users have
very high speed
connections
most users
have low speed
connections
residential and
small business
Broadband
Cable/DSL
~500Kbps
How to build a
network
that
1e-2
1e6
1e4
satisfies 1these end1e2
user demands? Rank (number of users)
Dial-up
~56Kbps
1e8
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
Mesh-like core of fast,
Coresrouters
low degree
High
degree
Edges
nodes are at
the
edges.
Hosts
Heuristically Optimal Network
Claim: 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
• 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
Cisco 12000 Series Routers
Technology constrains the number and capacity of line cards
that can be installed, creating a feasible region.
Cisco 12000 Series Routers
Pricing info: State of Washington Master Contract, June 2002
(http://techmall.dis.wa.gov/master_contracts/intranet/routers_switches.asp)
$2,762,500
$1,667,500
$932,400
$560,500
$602,500
$381,500
$212,400
$128,500
Technological
advance
160Gb
bandwidth
10Gb
Technically
feasible
2.5Gb
625Mb
155Mb
log/log
1
16
256
degree
Technologically Feasible Region
Core
backbone
Bandwidth (Mbps)
1000000
High-end
gateways
100000
cisco 12416
cisco 12410
10000
cisco 12406
1000
cisco 12404
100
cisco 7500
10
cisco 7200
cisco 3600/3700
1
1
10
0.1
0.01
Older/cheaper
technology
100
degree
1000
10000
cisco 2600
linksys 4-port router
Edge
Shared media
(LAN, DSL,
Cable, Wireless,
Dial-up)
uBR7246 cmts
(cable)
cisco 6260 dslam
(DSL)
cisco AS5850
(dialup)
Sprint backbone
Intermountain
GigaPoP
Front Range
GigaPoP
Northern Lights
U. Memphis
Indiana GigaPoP
U. Louisville
Great Plains
Merit
OARNET
Qwest Labs
Arizona St.
WiscREN
OneNet
NCSA
U. Arizona
Iowa St.
StarLight
MREN
Oregon
GigaPoP
Pacific
Northwest
GigaPoP
NYSERNet
Pacific
Wave
UNM
Denver
Kansas
City
WPI
Indianapolis
Chicago
Northern
Crossroads
Seattle
SINet
U. Hawaii
New York
ESnet
AMES NGIX
Wash
D.C.
Sunnyvale
WIDE
CENIC
SURFNet
Rutgers
Los Angeles
MANLAN
UniNet
Houston
TransPAC/APAN
Abilene Backbone
Physical Connectivity
(as of December 16, 2003)
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)
North Texas
GigaPoP
SFGP/
AMPATH
Texas
GigaPoP
Miss State
GigaPoP
UT Austin
UT-SW
Med Ctr.
Atlanta
SOX
Texas Tech
LaNet
Tulane U.
GEANT
Florida A&M
U. So. Florida
MAGPI
PSC
DARPA
BossNet
UMD NGIX
Mid-Atlantic
Crossroads
Drexel
U. Florida
U. Delaware
NCNI/MCNC
CENIC Backbone (as of January 2004)
Backbone topology of
both Abilene and
CENIC are both built
as a mesh of high
speed, low degree
routers.
OC-3 (155 Mb/s)
OC-12 (622 Mb/s)
GE (1 Gb/s)
OC-48 (2.5 Gb/s)
10GE (10 Gb/s)
Cisco 750X
COR
Cisco 12008
dc1
Cisco 12410
dc1
OAK
Abilene
Sunnyvale
dc2
hpr
SAC
hpr
dc1
dc2
FRG
dc2
dc1
hpr
dc1
SVL
dc3
FRE
dc1
SOL
dc1
BAK
dc1
As one moves from
the core out toward the
edge, connectivity gets
higher, and speeds get
lower.
SLO
dc1
hpr
hpr
LAX
dc2
Abilene
Los Angeles
dc1
dc3
TUS
SDG
dc1
hpr
dc3
dc1
CENIC Backbone for
Southern California
to Sunnyvale
to Fremont
to Soledad
SLO
dc1
LA CCD, LA City, LA Harbor,
LA Mission, LA Pierce, LA
Southwest, LA Trade Tech, LA
UC Santa
Valley, Moorpark, Mt. San
Barbara
Antonio, Oxnard
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
to Sacramento
BAK
hpr
dc1
Caltech
UCLA
LAX
dc2
Los
Nettos
Abilene
hpr
UC Irvine
dc1
UCSSN
(Las Vegas)
dc3
LAAP
San Bernardino CSS
Riverside COE
dc1
CUDI Peer,
ESNet Peer
UC Riverside
SDG
Orange COE
TUS
Monrovia
USD Gigaman
Los Angeles COE
San Diego CC,
Soutwestern CC,
Grossmont, Cuyamaca,
Imperial Valley, Mira
Costa CC, Palomar
College
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
hpr
dc3
dc1
San Diego COE
SDSC
UC San Diego
LA USD
Johnson & Johnson
Chaffey Joint USD
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:
Engineering and math:
• 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
•
•
•
•
•
•
•
•
•
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 Networks
Two 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 of
the 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, 2004
Archive: 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 des
topology because structure affects function. When studying the topological prop
Internet, we found out that there are two mechanisms which are necessary for th
of the Internet: a nonlinear preferential growth, where the growth is described
positive-feedback mechanism, and the appearance of new links between already ex
show that the Positive-Feedback Preference (PFP) model, which is based on the a
reproduces topological properties of the Internet such as: degree distribution,
(rich-club connectivity), shortest path length, neighbor clustering, network re
and rectangle coefficient), disassortative mixing (nearest-neighbors average de
information flow pattern (betweenness centrality). We believe that these growth
further study because they provide a novel insight into the evolutionary dynamics of
networks.
* [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=routers
edges=links
25 interior routers
818 end systems
“scale-rich” vs. scale-free
rank
1
10
Low degree
mesh-like core
0
10
High degree hublike core
identical
power-law
degrees
1
2
degree these
How to characterize 10
/ compare
two networks?
10
Network Performance
Given realistic technology constraints on routers,
how well is the network able to carry traffic?
Step 1: Constrain to
be feasible
Step 2: Compute traffic demand
Bj
Bandwidth (Mbps)
1000000
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
Network Likelihood
How 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)
d
d

In both cases, LogLikelihood (LLH) 
i
i, j
connected
j
Why such striking
differences with same
node degree distribution?
Fast
Performance
Slow
Low
High
Likelihood
Fast
Slow
Low
High
Likelihood
Performance
Likelihood
Bandwidth (Mbps)
Fast core
100000
100000
10000
10000
1000
1000
100
100
High-degree
edge
10
Slow
core
Slower
edge
10
1
1
1
10
100
degree
1
10
100
degree
HOT scale-rich
•
•
•
•
Core: Mesh-like, low degree
Edge: High degree
Robust to random 
Robust to “attack”
Scale-free
•
•
•
•
Core: Hub-like, high degree
Edge: Low degree
Robust to random 
Fragile to “attack”
+ objectives and constraints
•
•
•
•
•
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
HOT
Low Likelihood
Low Performance
Random
Hierarchical
Scale-Free (HSF)
Most Likely
Universal features of complex networks
The only functional biological or technological
networks are highly organized, robust, efficient,
and very unlikely to arise by random.
Robust,
Efficient
HOT
scale-free,
critical, SOC,
edge-of-chaos
Fragile,
Wasteful
Low
High
Likelihood
HOT=Highly Organized/Optimized Tradeoffs/Tolerance
Carriers
Metabolites
3
Catabolism
Precursors
10
Rank
all metabolites
33
65
78
2
10
Amino acids
132
152
Carriers
Nucleotides
1
10
Lipids &
fatty acids
0
184
204
236
251
10
1
10
Number of reactions
100
Cofactors
313
58
133
190
240
1 8 0
1 8 0
1 6 0
1 6 0
1 4 0
5
4
3
2
1
0
1 2 0
H. Pylori
1 0 0
8 0
6 0
4 0
carriers
carriers
carriers
carriers
carrier
carrier
1 4 0
5
4
3
2
1
0
1 2 0
1 0 0
8 0
6 0
4 0
2 0
Reactions
0
1
2
3
4
5
6
7
8
2 0
0
1
2
3
4
5
6
7
8
carr
carr
carr
carr
carr
carr
Bowtie architecture
Carriers
Amino acids
Nucleotides
Nutrients
Catabolism
Precursors
Fatty acids
And Lipids
Cofactors
Biosynthesis
S1  ATP  S2  ADP
S3  NADH  S4  NAD
Carrier
ADP
ATP
NAD
NADH
S1
S2
Substrate
S3
S4
Reaction,
Enzyme



Stoichiometry
S1  1 0 
S 2  1 0 
S3  0 1


S4  0 1 
ATP  1 0 


ADP  1 0 
NADH  0 1


NAD  0 1 
Stoichiometry
Matrix
GLC
PI
G6P
NAD
NADH
ADP
ATP
NADP
NADPH
CO2
COA
ACCOA
PPI
AMP
ATP
NH3
AC
THF
MTH
H2S
PGL
PGC
RL5P
F6P
X5P
6PG
PRPP
AN
NAN
R5P
DAH
DQT
DHS
SME
S5P
PSM
CD5
IGP
TRP
CHO
E4P
PPN
HPP
TYR
T3P
CYS
PEP
DPG
3PG
ASE
PHP
PPS
SER
PYR
MAL
OA
GLY
ASP
ASN
BAP
ASS
CIT
HSE
PHS
THR
DHD
PIP
FUM
SUC
SAK
SDP
DPI
MDP
LYS
SUCOA
GLN
ICIT
AKG
GLU
amino acids
precursors
NAD
NADH
PI
GLC
ADP
ATP
Carriers
NADP
NADPH
CO2
COA
ACCOA
PPI
AMP
ATP
NH3
THF
MTH
AC
H2S
• WT is highly organized,
structured
G6P
PGL
PGC
RL5P
PRPP
AN
R5P
F6P
X5P
DAH
DQT
DHS
SME
S5P
PSM
E4P
6PG
NAN
CD5
IGP
PPN
HPP
TYR
T3P
CYS
PEP
DPG
3PG
ASE
PHP
PPS
SER
GLY
ASP
ASN
PYR
OA
MAL
TRP
CHO
BAP
ASS
CIT
HSE
THR
PHS
DHD
PIP
FUM
SUC
ICIT
SAK
SDP
DPI
MDP
LYS
SUCOA
AKG
Wild type
GLN
GLU
• Simple reactions
• Long assembly lines
• Universal common carriers
• Precursors and carriers
are universal common
currencies
GLC
NAD
NADH
PI
G6P
ADP
ATP
NADP
NADPH
CO2
COA
ACCOA
PPI
AMP
ATP
NH3
THF
MTH
AC
H2S
PGL
PGC
RL5P
F6P
X5P
6PG
PRPP
AN
NAN
R5P
DAH
DQT
DHS
SME
S5P
PSM
CD5
IGP
E4P
PPN
HPP
TYR
T3P
CYS
PEP
DPG
3PG
ASE
PHP
PPS
SER
PYR
MAL
TRP
CHO
OA
GLY
ASP
ASN
BAP
ASS
CIT
HSE
PHS
THR
DHD
PIP
FUM
SUC
SAK
SDP
DPI
MDP
LYS
Carriers
SUCOA
GLN
ICIT
AKG
precursors
GLU
amino acids
• Randomly rewire to get
“scale-free” version
• Preserve
• degree
• carrier and enzyme
• Destroys structure
• Only one useful pathway
remains
NAD
NADH
PI
GLC
ADP
ATP
NADP
NADPH
CO2
COA
ACCOA
PPI
AMP
ATP
NH3
AC
PRPP
AN
NAN
CD5
THF
MTH
H2S
G6P
PGL
PGC
RL5P
R5P
F6P
X5P
6PG
DAH
DQT
DHS
SME
S5P
PSM
IGP
E4P
PPN
HPP
TYR
T3P
CYS
PEP
DPG
3PG
ASE
PHP
PPS
SER
PYR
MAL
TRP
CHO
OA
GLY
ASP
ASN
BAP
ASS
HSE
CIT
PHS
THR
DHD
PIP
FUM
SUC
ICIT
SAK
SDP
DPI
MDP
LYS
SUCOA
AKG
Random
GLN
GLU
GLC
NAD
NADH
PI
G6P
ADP
ATP
NADP
NADPH
CO2
COA
ACCOA
PPI
AMP
ATP
NH3
THF
MTH
AC
H2S
PGL
PGC
RL5P
F6P
X5P
6PG
PRPP
AN
NAN
R5P
DAH
DQT
DHS
SME
S5P
PSM
CD5
IGP
TRP
CHO
E4P
PPN
HPP
TYR
T3P
CYS
PEP
DPG
3PG
ASE
PHP
PPS
SER
PYR
MAL
OA
GLY
ASP
ASN
BAP
ASS
CIT
HSE
PHS
THR
DHD
PIP
FUM
SUC
SAK
SDP
DPI
MDP
LYS
Carriers
SUCOA
GLN
ICIT
AKG
GLU
amino acids
precursors
NAD
NADH
PI
ADP
ATP
NADP
NADPH
CO2
COA
ACCOA
PPI
AMP
ATP
NH3
THF
MTH
AC
H2S
NAD
NADH
PI
GLC
ADP
ATP
NADP
NADPH
CO2
COA
ACCOA
PPI
AMP
ATP
NH3
AC
PRPP
AN
NAN
CD5
THF
MTH
H2S
G6P
GLC
PGL
PGC
RL5P
PRPP
AN
R5P
F6P
X5P
DAH
DQT
DHS
SME
S5P
PSM
CD5
IGP
PGC
PPN
HPP
3PG
PHP
PPS
OA
DQT
DHS
SME
S5P
PSM
IGP
DPG
E4P
3PG
PPN
HPP
TYR
CYS
ASE
PHP
PPS
SER
PYR
GLY
ASP
ASN
ASS
CIT
HSE
THR
PHS
MAL
TRP
CHO
PEP
GLY
ASP
ASN
BAP
DAH
T3P
SER
PYR
MAL
X5P
6PG
ASE
R5P
F6P
CYS
PEP
RL5P
TYR
T3P
DPG
TRP
CHO
E4P
6PG
NAN
G6P
PGL
OA
BAP
ASS
DHD
PIP
SAK
SDP
DPI
MDP
HSE
CIT
LYS
PHS
THR
DHD
PIP
FUM
SUC
ICIT
SAK
SDP
DPI
MDP
LYS
SUCOA
AKG
Wild type
GLN
FUM
SUC
SUCOA
GLU
ICIT
AKG
Random
GLN
GLU
NAD
NADH
PI
GLC
ADP
ATP
NADP
NADPH
CO2
COA
ACCOA
PPI
AMP
ATP
NH3
THF
MTH
AC
H2S
G6P
PGL
PGC
RL5P
PRPP
AN
R5P
F6P
X5P
DAH
DQT
DHS
SME
S5P
PSM
CD5
IGP
PPN
HPP
TYR
T3P
CYS
PEP
DPG
3PG
ASE
PHP
SER
PPS
GLY
ASP
ASN
PYR
OA
MAL
TRP
CHO
E4P
6PG
NAN
BAP
ASS
CIT
HSE
THR
PHS
DHD
PIP
FUM
SUC
SAK
SDP
DPI
MDP
LYS
SUCOA
GLN
ICIT
AKG
GLU
“Closing the loop”
Modeling
Measurement
Analysis
Validation
PLRG
Preferential
Attachment
HOT
Preferential
Attachment
PLRG
HOT
Preferential
Attachment
PLRG
HOT
Total Router Bandwidth (Mbps)
Internet Routing Technologies
1e6
Core
Routers
1e5
High-End
Gateways
1e4
Older
Cheaper
Technology
1e3
Access
Edge Routers
Shared Media
1e2
Abstracted
Feasible Region
1e1
1
1
1e1
1e2
1e3
Degree (number of connections)
1e4
Total Router Bandwidth (Mbps)
Internet Routing Technologies
1e6
Core
Routers High-End
Gateways
1e5
Per link
bandwidth
1e4
Older
Cheaper
Technology
1e3
Access
Edge Routers
Shared Media
1e2
Abstracted
Feasible Region
1e1
1
1
1e1
1e2
1e3
Degree (number of connections)
1e4
Bandwidth / Link (Mbps)
Internet Link Speeds
Core
Routers
10Gbps
1e4
1e3
1e2
Core/Edge
Routers
1Gbps
Local Area
Ethernet
10-100Mbps
1e1
Broadband
Cable
~500Kbps
1
1e-1
DSL
~500Kbps
Dial-up
~56Kbps
1e-2
1
1e1
1e2
1e3
Degree (number of connections)
1e4