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

A First-Principles Approach to Understanding the Internet’s Router-level Topology. Lun Li David Alderson Walter Willinger John C. Doyle 2004 ACM SIGCOMM Portland, OR. Evaluate performance of protocols Protect Internet Resource provisioning Understand large scale networks. Challenges.

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

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  1. A First-Principles Approachto Understanding the Internet’s Router-level Topology Lun Li David Alderson Walter Willinger John C. Doyle 2004 ACM SIGCOMM Portland, OR

  2. 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

  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

  6. 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)

  7. 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

  8. 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

  9. 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

  10. 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

  11. core technologies approximate aggregate feasible region older/cheaper technologies edge technologies Aggregate Router Feasibility Source: Cisco Product Catalog, June 2002

  12. 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)

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

  14. 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)

  15. 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)

  16. 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?

  17. Same Degree Distribution PA

  18. Same Degree Distribution PLRG

  19. Same Degree Distribution HOT

  20. PA PLRG/GRG HOT Abilene-inspired Sub-optimal

  21. 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?

  22. 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

  23. 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?

  24. 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

  25. 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

  26. Points to Emphasize • Same Degree distribution can have different core structures • Same Core structure can have different degree distributions

  27. 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.

  28. 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

  29. Future Work • Validation • rely on cooperative ISPs to validate router technology constraints • combine with heuristics and supplementary measurements • develop annotated prototype ISP topology generator

  30. A Tier 1 Router Bandwidth-Degree (Courtesy: Matt Roughan)

  31. 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>

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