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Network Design

Network Design. IS250 Spring 2010 John Chuang. 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?. What does the Internet Look Like?. What does the Internet Look Like?.

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Network Design

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  1. Network Design IS250 Spring 2010 John Chuang

  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? John Chuang

  3. What does the Internet Look Like? John Chuang

  4. 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 John Chuang

  5. 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 John Chuang

  6. 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 John Chuang

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

  8. log(dv) log(rv) Faloutsos, Faloutsos, Faloutsos (1999) • Power Law observed in degree distribution of Internet topology • Many low-degree nodes, few high-degree nodes Y=a*Xb John Chuang

  9. 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) John Chuang

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

  11. 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… John Chuang

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

  13. 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 John Chuang

  14. 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 John Chuang

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

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

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