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Topology Modeling: First-Principles Approach

Topology Modeling: First-Principles Approach. Aditya Akella Supplemental Slides 03/30/2007. Evaluate performance of protocols Protect Internet Resource provisioning Understand large scale networks. Challenges. Why Topology Modeling. Large Size

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Topology Modeling: First-Principles Approach

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  1. Topology Modeling: First-Principles Approach Aditya Akella Supplemental Slides 03/30/2007

  2. Evaluate performance of protocols Protect Internet Resource provisioning Understand large scale networks Challenges Why Topology Modeling • Large Size • Real topologies are not publicly available • Incredible variability in many aspects

  3. 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

  4. 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

  5. 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 • 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)

  6. 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

  7. Li et al. • Consider the explicit design of the Internet • Annotated network graphs (capacity, bandwidth) • Technological and economic limitations • Network performance • 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

  8. 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

  9. core technologies approximate aggregate feasible region older/cheaper technologies edge technologies Aggregate Router Feasibility

  10. 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)

  11. Hosts Heuristically Optimal Topology Mesh-like core of fast, low degree routers Cores High degree nodes are at the edges. Edges

  12. 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)

  13. 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 Metrics for Comparison: Network Performance Given realistic technology constraints on routers, how well is the network able to carry traffic?

  14. 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

  15. 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?

  16. 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

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