Network Design

IS250Spring 2010

John Chuang

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Questions

What does the Internet look like?- Why do we care?

Are there any structural invariants?

Can we develop models of network formation and growth?

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What does the Internet Look Like?

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What does the Internet Look Like?Full Internet map (Router Level) as of 18 Feb 1999

99664 edges, 88107 nodes (42443 leaves)Burch and Cheswick

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Why do we care?

Top-down topology design of 1969 replaced by bottom-up evolution of modern Internet - The Internet and the WWW are probably the only engineered systems whose structures are unknown to their designers

Performance of network protocols and algorithms dependent on underlying topology- Researchers and engineers need realistic models of network topology to calibrate/validate their design

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Personal Example Chuang-Sirbu Scaling Law (1998)

- Normalized multicast tree cost scales with number of receivers at an exponent of 0.8

Lm/Lu = Nk

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Topologies to Use

Get topologies of real networks

Generate synthetic graphs

Erdos-Renyi Random Graph

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Faloutsos, Faloutsos, Faloutsos (1999)

Power Law observed in degree distribution of Internet topology- Many low-degree nodes, few high-degree nodes

log(

d v)

log(rv)

Y=a*Xb

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Power Law Networks Engineered systems

- Internet (Faloutsos et al. 1999)- WWW (Lawrence & Giles 1998, Broder et al. 2000, Kleinberg &

Lawrence 2001)- Electric power grid (Watts & Strogatz 1998)

Biological systems- neural network of Caenorhabditis elegans (Watts and Strogatz

1998)

Social networks- Scientific publication citation (Redner 1998)- actor collaboration (Barabasi and Albert 2002)

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Node Degree Distribution isn’t Everything

Li, Alderson, Willinger, Doyle. A First-Principles Approach to Understanding the Internet’s Router-level Topology (2004)

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The Internet is not Random!

Okay, so the Internet cannot be modeled as a random graph- Erdos-Renyi random graphs do not exhibit power law

What other structural invariants might there be?- We know that the Internet has small diameter, and also high degree of local clustering…

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Small World Networks

Watts-Strogatz Small World Model- High degree of clustering- Small diameter- But no power-law degree distribution

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Barabasi-Albert Model

Incremental Growth and Preferential Attachment- Probability of receiving new edge dependent on current degree

Properties- Small diameter- Power law degree distribution

- But no clusteringhttp://en.wikipedia.org/wiki/BA_model

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Other Models

HOT: Highly Optimized Tolerance (Carlson & Doyle, 1999)- Design based on explicit optimization of performance metrics, yet still exhibiting power laws

Jellyfish (Siganos, Tauro, Faloutsos, 2004)- Incorporates hierarchical nature of Internet

Do we still have time?

No -- Time for Course Eval

Yes -- A paradox just for fun

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Braess’ Paradox(Selfish Routing and the Price of Anarchy)

Initial Network

Delay = 1.5

x

x1

1 x

x1

1

0

Improved Network

Delay = 2

See http://en.wikipedia.org/wiki/Braess%27s_paradox for real world examples!