a first principles approach to understanding the internet s router level topology l.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
A First-Principles Approach to Understanding the Internet’s Router-level Topology PowerPoint Presentation
Download Presentation
A First-Principles Approach to Understanding the Internet’s Router-level Topology

Loading in 2 Seconds...

play fullscreen
1 / 34

A First-Principles Approach to Understanding the Internet’s Router-level Topology - PowerPoint PPT Presentation


  • 420 Views
  • Uploaded on

A First-Principles Approach to Understanding the Internet’s Router-level Topology 2004 ACM SIGCOMM Portland, OR Evaluate performance of protocols Protect Internet Resource provisioning Understand large scale networks Challenges Why Topology Large Size

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'A First-Principles Approach to Understanding the Internet’s Router-level Topology' - jaden


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
a first principles approach to understanding the internet s router level topology

A First-Principles Approachto Understanding the Internet’s Router-level Topology

2004 ACM SIGCOMM

Portland, OR

challenges
Evaluate performance of protocols

Protect Internet

Resource provisioning

Understand large scale networks

Challenges

Why Topology

  • Large Size
  • Real topologies are not publicly available
  • Incredible variability in many aspects
trends in topology modeling
Observation

Modeling Approach

  • Random graph models (Waxman, 1988)
  • Long-range links are expensive
  • Real networks are not random, but have obvious hierarchy.
  • Structural models (GT-ITM Calvert/Zegura, 1996)
  • Internet topologies exhibit power law degree distributions (Faloutsos et al., 1999)
  • Degree-based models replicate power-law degree sequences
Trends in Topology Modeling
slide4

Power Laws and Internet Topology

Most nodes have few connections

A few nodes have lots of connections

Source: Faloutsos et al. (1999)

Rank R(d)

R(d) = P (D>d) x #nodes

Degree d

  • Router-level graph & Autonomous System (AS) graph
  • Led to active research in degree-based network models
degree based models of topology
Degree-Based Models of Topology
  • Preferential Attachment
    • Growth by sequentially adding new nodes
    • New nodes connect preferentially to nodes having more connections
    • Examples: Inet, GPL, AB, BA, BRITE, CMU power-law generator
degree based models of topology7
Degree-Based Models of Topology
  • Preferential Attachment (PA)
    • Growth by sequentially adding new nodes
    • New nodes connect preferentially to nodes having more connections
    • Examples: 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
    • Examples: Power Law Random Graph (PLRG), Generalized Random Graph (GRG)
features of degree based models
Features of Degree-Based Models

Preferential Attachment

Expected Degree Sequence

  • Degree sequence follows a power law (by construction)
  • High-degree nodes correspond to highly connected central “hubs”, which are crucial to the system
  • Achilles’ heel: robust to random failure, fragile to specific attack
  • “scale-free” in complex networks
our approach
Our Approach
  • Consider the explicit design of the Internet
    • Annotated network graphs (capacity, bandwidth)
    • Technological and economic limitations
    • Network performance
    • Heuristic optimized tradeoffs (HOT)
  • Seek a theory for Internet topology that isexplanatoryand not merely descriptive.
    • Explain high variability in network connectivity
    • Ability to match large scale statistics (e.g. power laws) is only secondary evidence
trends in topology modeling11
Observation

Modeling Approach

  • Random graph models (Waxman, 1988)
  • Long-range links are expensive
  • Real networks are not random, but have obvious hierarchy.
  • Structural models (GT-ITM Calvert/Zegura, 1996)
  • Internet topologies exhibit power law degree distributions (Faloutsos et al., 1999)
  • Degree-based models replicate power-law degree sequences
  • Physical networks have hard technological (and economic) constraints.
  • Optimization-driven models topologies consistent with design tradeoffs of network engineers
Trends in Topology Modeling
router technology constraint

3

10

high BW low degree

high degree low BW

2

10

1

10

Bandwidth (Gbps)

15 x 10 GE

15 x 3 x 1 GE

0

10

15 x 4 x OC12

15 x 8 FE

Technology constraint

-1

10

0

1

2

10

10

10

Degree

Router Technology Constraint

Cisco 12416 GSR, circa 2002

Total Bandwidth

Bandwidth per Degree

aggregate router feasibility

core technologies

approximate

aggregate

feasible region

older/cheaper

technologies

edge technologies

Aggregate Router Feasibility

Source: Cisco Product Catalog, June 2002

variability in end user bandwidths

high

performance

computing

academic

and corporate

residential and

small business

Variability in End-User Bandwidths

1e4

Ethernet

1-10Gbps

1e3

1e2

Ethernet

10-100Mbps

Connection Speed (Mbps)

a few users have very high speed connections

1e1

Broadband

Cable/DSL

~500Kbps

1

1e-1

Dial-up

~56Kbps

most users

have low speed connections

1e-2

1e6

1

1e2

1e4

1e8

Rank (number of users)

slide15

Hosts

Heuristically Optimal Topology

Mesh-like core of fast, low degree routers

Cores

High degree nodes are at the edges.

Edges

slide16

Intermountain

GigaPoP

U. Memphis

Indiana GigaPoP

WiscREN

OARNET

Great Plains

Front Range

GigaPoP

U. Louisville

NYSERNet

StarLight

Arizona St.

NCSA

Iowa St.

Qwest Labs

U. Arizona

UNM

Oregon

GigaPoP

WPI

Pacific

Wave

Pacific

Northwest

GigaPoP

SINet

SURFNet

ESnet

MANLAN

U. Hawaii

GEANT

Rutgers U.

WIDE

MREN

UniNet

MAGPI

CENIC

Northern

Crossroads

0.1-0.5 Gbps

0.5-1.0 Gbps

1.0-5.0 Gbps

5.0-10.0 Gbps

TransPAC/APAN

AMES NGIX

Tulane U.

LaNet

SOX

North Texas

GigaPoP

U. Delaware

Drexel U.

DARPA

BossNet

Texas

GigaPoP

Mid-Atlantic

Crossroads

Texas Tech

SFGP/

AMPATH

Miss State

GigaPoP

UT Austin

NCNI/MCNC

U. Florida

UMD NGIX

UT-SW

Med Ctr.

U. So. Florida

Florida A&M

Northern Lights

Merit

OneNet

Kansas

City

Indian-

apolis

Denver

Chicago

Seattle

New York

Wash

D.C.

Sunnyvale

Los Angeles

Atlanta

Houston

PSC

Abilene Backbone

Physical Connectivity

(as of December 16, 2003)

corporation for education network initiatives in california cenic

CENIC Backbone (as of January 2004)

Cisco 750X

Cisco 12008

Cisco 12410

COR

OC-3 (155 Mb/s)

OC-12 (622 Mb/s)

GE (1 Gb/s)

OC-48 (2.5 Gb/s)

10GE (10 Gb/s)

dc1

dc1

dc2

OAK

dc2

SAC

CENIC Router Configurations, Jan. 2004

hpr

dc1

hpr

FRG

dc2

dc1

hpr

dc1

dc3

SVL

FRE

dc1

SOL

dc1

BAK

dc1

SLO

hpr

dc1

Abilene

Los Angeles

Abilene

Sunnyvale

hpr

LAX

dc2

dc3

dc1

TUS

dc1

SDG

hpr

dc3

dc1

Corporation for Education Network Initiatives in California (CENIC)
two different perspectives
Two Different Perspectives
  • Degree-based perspective
    • Match aggregate statistics
    • Suggest high-degree central hubs
  • First principles perspective
    • Technology and economic constraints
    • Performance
    • Suggest fast, low-degree core routers
    • Consistent with physical design of real networks

How to reconcile these two perspectives?

slide22

PA

PLRG/GRG

HOT

Abilene-inspired

Sub-optimal

network performance

Step 1: Constrain to be feasible

Step 2: Compute traffic demand

1000000

100000

10000

Bj

Abstracted Technologically Feasible Region

1000

Bandwidth (Mbps)

100

Step 3: Compute max flow

xij

10

degree

1

10

100

1000

Bi

Network Performance

Given realistic technology constraints on routers, how well is the network able to carry traffic?

structure determines performance
Structure Determines Performance

HOT

PA

PLRG/GRG

P(g) = 1.13 x 1012

P(g) = 1.19 x 1010

P(g) = 1.64 x 1010

likelihood related metric
Likelihood-Related Metric

Define the metric

(di = degree of node i)

  • Easily computed for any graph
  • Depends on the structure of the graph, not the generation mechanism
  • Measures how “hub-like” the network core is

For graphs resulting from probabilistic construction (e.g. PLRG/GRG),

LogLikelihood (LLH)  L(g)

Interpretation: How likely is a particular graph (having given node degree distribution) to be constructed?

slide26

12

10

11

10

10

10

0

0.2

0.4

0.6

0.8

1

l(g) = Relative Likelihood

PA

Abilene-inspired

Sub-optimal

PLRG/GRG

HOT

P(g)

Perfomance (bps)

Lmax

l(g) = 1

P(g) = 1.08 x 1010

slide27

12

10

11

10

10

10

0

0.2

0.4

0.6

0.8

1

l(g) = Relative Likelihood

PA

Abilene-inspired

Sub-optimal

PLRG/GRG

HOT

P(g)

Perfomance (bps)

Lmax

l(g) = 1

P(g) = 1.08 x 1010

points to emphasize
Points to Emphasize
  • Same Degree distribution can have different core structures
  • Same Core structure can have different degree distributions
slide30

2

2

2

10

10

10

Node Rank

Node Rank

Node Rank

1

1

1

10

10

10

0

0

0

10

10

10

0

1

2

0

1

2

0

1

2

10

10

10

10

10

10

10

10

10

Node Degree

Node Degree

Node Degree

Abilene-inspired core

Uniform high BW users

Low variability deg dist.

Abilene-inspired core

High variability at edges

Power-law deg distribution

Abilene-inspired core

Uniform low BW users

low variability deg dist.

conclusions
Conclusions
  • Probabilistic degree-based generation mechanisms are likely to produce networks that have poor performance and are very unlikely to generate realistic networks.
  • Models of router-level topology should consider inherent technological and economic tradeoffs in network design, and they should consider issues such as performance over simple connectivity.
  • Realistic router-level topology generators will require additional work to incorporate other key features (e.g. geography, population density) into the framework
future work
Future Work
  • Validation
    • rely on cooperative ISPs to validate router technology constraints
    • combine with heuristics and supplementary measurements
    • develop annotated prototype ISP topology generator
future work34
Future Work
  • Validation
    • rely on cooperative ISPs to validate router technology constraints
    • combine with heuristics and supplementary measurements
    • develop annotated prototype ISP topology generator
    • Contact: David Alderson<alderd@cds.caltech.edu>
  • HOT-inspired framework for protocol stack
    • consider layering as optimization decomposition
    • study properties of `natural' decompositions
    • Contact: Lun Li<lun@cds.caltech.edu>