1. Network Design IS250 Spring 2010 John Chuang

2. 2 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?

3. John Chuang3 What does the Internet Look Like?

4. John Chuang4 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

5. John Chuang5 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

6. John Chuang6 Personal Example  Chuang-Sirbu Scaling Law (1998) -Normalized multicast tree cost scales with number of receivers at an exponent of 0.8 L m /L u = N k

7. John Chuang7 Topologies to Use  Get topologies of real networks  Generate synthetic graphs Erdos-Renyi Random Graph

8. John Chuang8 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(r v ) Y=a*X b

9. John Chuang9 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)

10. John Chuang10 Node Degree Distribution isn’t Everything  Li, Alderson, Willinger, Doyle. A First-Principles Approach to Understanding the Internet’s Router-level Topology (2004)

11. John Chuang11 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…

12. John Chuang12 Small World Networks  Watts-Strogatz Small World Model -High degree of clustering -Small diameter -But no power-law degree distribution

13. John Chuang13 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 clustering http://en.wikipedia.org/wiki/BA_model

14. John Chuang14 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

15. Do we still have time? No -- Time for Course Eval Yes -- A paradox just for fun

16. John Chuang16 Braess’ Paradox (Selfish Routing and the Price of Anarchy)  Initial Network  Delay = 1.5 x x 1 1 x x 1 1 0  Improved Network  Delay = 2 See http://en.wikipedia.org/wiki/Braess%27s_paradox for real world examples!