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Internet Protocols

Internet Protocols. Steven Low CS/EE netlab. CALTECH .edu October 2004 with J. Doyle, L. Li, A. Tang, J. Wang. p l (t). x i (t). Internet Protocols. Selects user criteria, web layout, utility. Application. Selects source transmission rates . TCP/AQM IP.

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Internet Protocols

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  1. Internet Protocols Steven Low CS/EE netlab.CALTECH.edu October 2004 with J. Doyle, L. Li, A. Tang, J. Wang

  2. pl(t) xi(t) Internet Protocols Selects user criteria, web layout, utility Application Selects source transmission rates TCP/AQM IP Selects paths from sources to dests Link Selects topology, capacities, power,…

  3. pl(t) xi(t) Internet Protocols • Protocols determines network behavior • Critical, yet difficult, to understand and optimize • Local algorithms, distributed spatially and vertically  global behavior • Designed separately, deployed asynchronously, evolves independently Application TCP/AQM IP Link

  4. pl(t) xi(t) Internet Protocols • Protocols determines network behavior • Critical, yet difficult, to understand and optimize • Local algorithms, distributed spatially and vertically  global behavior • Designed separately, deployed asynchronously, evolves independently Need to reverse engineer … to forward engineer new largenetworks Application TCP/AQM IP Link

  5. pl(t) xi(t) Internet Protocols • Protocols determines network behavior • Critical, yet difficult, to understand and optimize • Local algorithms, distributed spatially and vertically  global behavior • Designed separately, deployed asynchronously, evolves independently Need to reverse engineer … much easier than biology with full specs Application TCP/AQM IP Link

  6. pl(t) xi(t) Internet Protocols Minimize response time (web layout) Application Maximize utility (TCP/AQM) TCP/AQM IP Minimize path costs (IP) Link Minimize SIR, max capacities, …

  7. Application Application TCP/AQM IP Link IP Link Internet Protocols • Each layer is abstracted as an optimization problem • Operation of a layer is a distributed solution • Results of one problem (layer) are parameters of others • Operate at different timescales

  8. Applications TCP/ AQM IP Link Outline Chiang: X-ities?? General Approach: 1) Understand a single layer in isolation and assume other layers are designed nearly optimally. 2) Understand interactions across layers 3) Incorporate additional layers, with the ultimate goal of viewing entire protocol stack as solving one giant optimization problem (where individual layers are solving parts of it). Utility maximization Utility maximization Chiang: Wireless issues ??

  9. Link Outline Applications TCP/ AQM • Utility maximization • Some implications IP

  10. x y R F1 G1 Network AQM TCP GL FN q p RT Reno, Vegas IP routing DT, RED, … Network model

  11. Reno, Vegas DT, RED, … IP routing Network model - example TCP Reno: currently deployed TCP AI MD TailDrop

  12. Reno, Vegas DT, RED, … IP routing Network model - example TCP FAST: high speed version of Vegas

  13. Reno, Vegas, FAST DT, RED, REM/PI, AVQ Duality model • Flow control problem (Kelly, Malloo, Tan 98) • Primal-dual algorithm • TCP/AQM • Maximize utility (& solve Dual) with different utility functions • (L 03):(x*,p*) primal-dual optimal iff

  14. a = 1 : Vegas, FAST, STCP • a = 1.2: HSTCP (homogeneous sources) • a = 2 : Reno (homogeneous sources) • a = infinity: XCP (single link only) Duality model Historically • Packet level implemented first • Flow level understood as after-thought • But flow level design determines • performance, fairness, stability (Mo & Walrand 00)

  15. Duality model Historically • Packet level implemented first • Flow level understood as after-thought • But flow level design determines • performance, fairness, stability Now: can forward engineer Given (application) utility functions, can generate provably scalable TCP algorithms

  16. TCP-AQM Link Protocol decomposition Applications TCP/ AQM IP TCP-AQM: • TCP algorithms maximize utility with different utility functions Congestion prices coordinate across protocol layers

  17. TCP-AQM TCP-AQM Link Protocol decomposition Applications IP TCP/ AQM IP TCP/IP: • TCP algorithms maximize utility with different utility functions • Shortest-path routing is optimal using congestion prices as link costs Congestion prices coordinate across protocol layers

  18. TCP-AQM TCP-AQM Link Protocol decomposition Applications IP TCP/ AQM IP TCP/IP (with fixed c): • Equilibrium of TCP/IP exists iff zero duality gap • NP-hard, but subclass with zero duality gap is LP • Equilibrium, if exists, can be unstable • Can stabilize, but with reduced utility Inevitable tradeoff bw utility max & routing stability

  19. TCP-AQM TCP-AQM Link Protocol decomposition Applications Link IP IP TCP/ AQM IP TCP/IP with optimal c: • With optimal provisioning, static routing is optimal using provisioning cost a as link costs TCP/IP with static routing in well-designed network

  20. Link Outline Applications TCP/ AQM • Utility maximization • Some implications IP

  21. Implications • Is fair allocation always inefficient ? • Does raising capacity always increase throughput ? Intricate and surprising interactions in large-scale networks … unlike at single link

  22. Implications • Is fair allocation always inefficient • Does raising capacity always increase throughput

  23. Fairness (Mo, Walrand 00) • Identify allocation with a • An allocation is fairer if its a is larger

  24. Fairness (Mo, Walrand 00) • a = 0: maximum throughput • a = 1: proportional fairness • a = 2: min delay fairness (Reno) • a = infinity: maxmin fairness

  25. Efficiency • Unique optimal rate x(a) • An allocation is efficient if T(a) is large

  26. Conjecture Conjecture T(a) is nonincreasing i.e. a fair allocation is always inefficient

  27. max throughput proportional fairness maxmin fairness 1/(L+1) 1/2 0 1 L/L(L+1) 1/2 Example 1 Conjecture T(a) is nonincreasing i.e. a fair allocation is always inefficient

  28. Intuition “The fundamental conflict between achieving flow fairness and maximizing overall system throughput….. The basic issue is thus the trade-off between these two conflicting criteria.” Luo,etc.(2003), ACM MONET

  29. Results • Theorem: Necessary & sufficient condition for general networks (R, c) provided every link has a 1-link flow • Corollary 1: true if N(R)=1

  30. Counter-example • There exists a network such that dT/da > 0 for almost all a>0 • Intuition • Largea favors expensive flows • Long flows may not be expensive • Max-min may be more efficient than proportional fairness long expensive

  31. Counter-example • Theorem: Given any a0>0, there exists network where • Compact example

  32. Implications • Is fair allocation always inefficient ? • Does raising capacity always increase throughput ? Intricate and surprising interactions in large-scale networks … unlike at single link

  33. Throughput & capacity • Intuition: Increasing link capacities always raises throughput T • Theorem: Necessary & sufficient condition for general networks (R, c) • Corollary: For all a, increasing • a link’s capacity can reduce T • all links’ capacities equally can reduce T • all links’ capacities proportionally raises T

  34. TCP-AQM Protocol decomposition Link IP • TCP algorithms maximize utility with different utility functions • IP shortest path routing is optimal using congestion prices as link costs,with given link capacities c • With optimal provisioning, static routing is optimal using provisioning cost a as link costs Congestion prices coordinate across protocol layers

  35. TCP-AQM Some implications TCP/AQM: • TCP maximizes aggregate utility (not throughput) • Fair bandwidth allocation is not always inefficient • Increasing capacity does not always raise throughput Intricate network interactions  paradoxical behavior

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