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Outline. TCP-AQM TCP-AQM/IP Fairness-throughput tradeoff. with Jiantao Wang, Lun Li and John Doyle. HOT (Doyle et al) Minimize user response time Heavy-tailed file sizes. WWW, Email, Napster, FTP, …. Applications TCP/AQM. Duality model (Kelly, Low et al) Maximize aggregate utility.

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  1. Outline • TCP-AQM • TCP-AQM/IP • Fairness-throughput tradeoff with Jiantao Wang, Lun Li and John Doyle

  2. HOT (Doyle et al) • Minimize user response time • Heavy-tailed file sizes WWW, Email, Napster, FTP, … Applications TCP/AQM Duality model (Kelly, Low et al) • Maximize aggregate utility IP Shortest-path routing • Minimize path costs Transmission Power control • Maximize channel capacity Ethernet, ATM, POS, WDM, … Protocol Decomposition

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

  4. F1 G1 FN GL Network model x y Rf(s) Network AQM TCP q p Rb’(s)

  5. Equilibrium • Performance • Throughput, loss, delay • Fairness Dynamics • Local stability • Global stability Methodology Protocol (Reno, Vegas, RED, REM/PI…)

  6. Result[L 00]:(x*,p*) primal-dual optimal iff Summary: duality model • Flow control problem [Kelly, Malloo, Tan 98] • Primal-dual algorithm Reno, Vegas RED, REM/PI, AVQ • TCP/AQM • Maximize utility with different utility functions

  7. Example utility functions [Mo, Walrand ’00]

  8. KMT’s primal algorithm • Dynamic source • Static link Theorem[Kelly, Mauloo, Tan ’98] • Global asymptotic stability in absence of delay

  9. Delay stability • Dynamic source • Static link • Delay model

  10. Delay stability • Dynamic source • Static link Theorem[Vinnicombe ‘00] • Local asymptotic stability if See also: [Johari, Tan ‘01] [Massoulie ’00]

  11. LL’s dual algorithm • Static source • Dynamic link Theorem[L, Lapsley ’99] • Global asymptotic stability in absence of delay • Global asymptotic stability in presence of delay and other asynchronism, provided g small

  12. Delay stability • Static source • Dynamic link Theorem[Paganini, Doyle, L ‘01] • Locally asymptotically stable for arbitrary delay and capacity if

  13. Recap Primal Dual Dynamics source link Fairness arbitrary limited Utilization low high Global stability no delay no delay Local stability small delay arbitrary delay

  14. IPAM Workshop 2002 • Add slow link dynamics to primal • Kunniyur, Srikant 2000, 2002 • Vinnicombe 2002 • Add slow source dynamics to dual • Paganini, et al 2002 • Choe, Low 2002

  15. KK’s primal-dual algorithm • Dynamic source • Dynamic link (AVQ) Theorem [Kunniyur, Srikant ’00, ’03] • Global asymptotic stability without delay • Local asymptotic stability if, in addition,

  16. Paganini’s primal-dual algorithm • Static source • Dynamic link Theorem[Paganini, et al ’02] • Locally asymptotically stable if, in addition,

  17. x y Rf(s) F1 G1 Network AQM TCP FN GL q p Rb’(s) Theorem(Choe & L, ’02) Provided R is full rank, feedback loop is locally stable if Stability: Stabilized Vegas

  18. x y Rf(s) F1 G1 Network AQM TCP FN GL q p Rb’(s) Stability: Stabilized Vegas Application • Stabilized TCP with current routers • Queueing delay as congestion measure has right scaling • Incremental deployment with ECN

  19. arbitrary high small Recap Primal Dual Dynamics source link Fairness arbitrary limited Utilization low high Global stability no delay no delay Local stability small delay arbitrary delay

  20. Flow level: Reno, HSTCP, STCP, FAST • Commonflow level dynamics! window adjustment control gain flow level goal = • Different gain k and utility Ui • They determine equilibrium and stability • Different congestion measure pi • Loss probability (Reno, HSTCP, STCP) • Queueing delay (Vegas, FAST)

  21. FAST algorithm Theorem (Jin, Wei, Low ‘03) In absence of delay, for single link: • Mapping from w(t) to w(t+1) is contraction • Global exponential convergence • Full utilization after finite time • Utility function: ai log xi (proportional fairness)

  22. New development • FAST TCP • Cheng Jin • David Wei • Global stability with delay • John Wen, Murat Arcak • Antonis Papachristodoulou, John Doyle • Zhikui Wang, Fernando Paganini • Sankar Kunniyur, R. Srikant • Stochastic models • Peerapol Tinnakornsrisuphap, Armand Makowski

  23. Outline • TCP-AQM • TCP-AQM/IP • Wang, Li, Low, Doyle, Infocom ‘03 • Fairness-throughput tradeoff

  24. HOT (Doyle et al) • Minimize user response time • Heavy-tailed file sizes WWW, Email, Napster, FTP, … Applications TCP/AQM Duality model (Kelly, Low et al) • Maximize aggregate utility IP Shortest-path routing • Minimize path costs Transmission Power control • Maximize channel capacity Ethernet, ATM, POS, WDM, … Protocol Decomposition

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

  26. Motivation

  27. Shortest path routing! Motivation Can TCP/IP maximize utility?

  28. Proof Reduce integer partition to primal problem Given: integers {c1, …, cn} Find: set A s.t. TCP-AQM/IP Theorem(Wang, et al 03) Primal problem is NP-hard

  29. TCP-AQM/IP Theorem(Wang, et al 03) Primal problem is NP-hard • Achievable utility of TCP/IP? • Stability? • Duality gap? Conclusion: Inevitable tradeoff between • achievable utility • routing stability

  30. destination routing price static apl(0) apl(1) TCP/AQM IP … … r(t),r(t+1), r(0) r(1) Ring network • Single destination • Instant convergence of TCP/IP • Shortest path routing • Link cost = a pl(t) + b dl r

  31. destination apl(0) apl(1) TCP/AQM IP … … r(t),r(t+1), r(0) r(1) Ring network • Stability:ra? • Utility: Va ? r* : optimal routing V* : max utility r

  32. destination Ring network • Stability:ra? • Utility: Va ? link cost = a pl(t) + b dl Theorem(Infocom 2003) • “No” duality gap • Unstable if b = 0 starting from anyr(0), subsequent r(t) oscillates between 0 and 1 r

  33. destination r Ring network • Stability:ra? • Utility: Va ? link cost = a pl(t) + b dl Theorem(Infocom 2003) • Solve primal problem asymptotically as

  34. destination r Ring network • Stability:ra? • Utility: Va ? link cost = a pl(t) + b dl Theorem(Infocom 2003) • a large: globally unstable • a small: globally stable • a medium: depends on r(0)

  35. random graph 20 nodes, 200 links Achievable utility General network Conclusion: Inevitable tradeoff between • achievable utility • routing stability

  36. Outline • TCP-AQM • TCP-AQM/IP • Fairness-throughput tradeoff • Tang, Wang, Low, Allerton ‘03

  37. Example utility functions [Mo, Walrand ’00]

  38. Fairness [Mo, Walrand ’00] Definition An allocation is fair if a is large

  39. Efficiency Definition An allocation is efficient if is large

  40. New development • FAST TCP • Cheng Jin • David Wei • Global stability with delay • John Wen, Murat Arcak • Antonis Papachristodoulou, John Doyle • Zhikui Wang, Fernando Paganini • Sankar Kunniyur, R. Srikant • Stochastic models • Peerapol Tinnakornsrisuphap, Armand Makowski • Fairness-throughput tradeoff • Jiantao Wang, Kevin Tang, SL

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