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With Extra Bandwidth and Time for Adjustment TCP is Competitive

With Extra Bandwidth and Time for Adjustment TCP is Competitive. J . Edmonds, S . Datta, and P . Dymon d. TCP (Transport Control Protocol). Email Web Telnet. Many Packets » Data Flow. Input: Set of Sender/Jobs. File Size. Arrival time. Fixed Path. General Network. Adjustments.

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With Extra Bandwidth and Time for Adjustment TCP is Competitive

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  1. With Extra Bandwidth and Time for AdjustmentTCP is Competitive J. Edmonds, S. Datta, and P. Dymond

  2. TCP (Transport Control Protocol) • Email • Web • Telnet

  3. Many Packets » Data Flow Input: Set of Sender/Jobs • File Size • Arrival time • Fixed Path

  4. General Network

  5. Adjustments B Î b b ,t ,t (not buffer or time delay) Bottleneck Capacity and Adjustments å£ B

  6. b ,t TCP Protocol A=1 c=½ Multiplicative decrease Additive increase Time

  7. Throughput & packet loss rate - arrival ) (completion AVG • “User Perceived Latency” or “Flow Time” Evaluating TCP • Good observed performance • Simulation of approximate models • Few theoretical results • [KKPS] 20 Questions to “guess” allocation • Fair to all Users • [CJ] Single-bottleneck:TCP fair • [F] Multi-bottleneck: TCP not fair

  8. File to Transfer Computation Task Bottleneck Capacity # Processors Bandwidth Allocation Processor Allocation , File Size & Times Work Size & Times Network c a , b ??? ,t Speed up A Paradigm Shift

  9. a a c c , , , , … , , , , J = { } - a ) - a ) (c (c AVG AVG Bad(J) Good(J) User Perceived LatencyFlow Time Bad(J) = … Good(J) = … … n Long n » » = (n-1)e + Long

  10. TCP • [CJ] TCP ÞEQUI EQUI B B B Shortest Remaining Work First • Optimal Comparison with other Schedulers

  11. All Knowing All Powerful Optimal: ? Future Online: ? Non-Clairvoyant: TCP ? Distributed: Knowledge of Scheduler

  12. Not Competitive

  13. Adj Competitive

  14. a EQUI(J) [MPT] £ 2 OPT(J) [ECBD] £ 3.73 Previous Results(Batch)

  15. a a a a a EQUI(J) [MPT] ³W(n) OPT(J) NonClair(J) ³W(n½) OPT(J) Previous Results(Lower Bounds)

  16. TCP BAL1+e(J) [KP] £ O(1/e) OPT1(J) B-TCP EQUI2+e(J) [E] £ O(1/e) OPT1(J) BROADCAST4+e(J) [EP] £ O(1/e) OPT1(J) AÞ¥ cÞ1 ? [Cor] TCP Previous Results (Upper Bounds)

  17. A=1 c=½ AÞ¥ cÞ1 New Results New New Future Work

  18. Adj =å Adj Adj EQUI2+e(J) [E] £ O(1) OPT1(J) Proof: Reduction TCPO(1)(J) TCPO(1)(J) TCP(J) q q £ O(1) OPT1(J) OPT(J) OPT1(J) + Adj New Results

  19. “Drops” individual random packets • Smooth total transmission • Challenge å # » # packets to drop ? ! Î b ,t New ResultsRandom Asynchronous Early Marking • “Drops”packets before cap reached • No packets actually dropped

  20. Open: Dynamical System • converges? • bounded? hope AÞ¥ cÞ1 A=1 (Free Market & Locally) c=½ » f f TCP2+e(J) £ O(1/e) OPT1(J) TCPO(m3)(J) £ O(m) OPT1(J) £ m New Results TCP: Fair ?? [F] say no

  21. Proof Sketches

  22. TCP • TCP ÞEQUI EQUI B B TCP Þ EQUI [CJ] global measure New: Job by job comparison

  23. b ,t Proof Sketch Unadjusted Adjusted

  24. Proof Sketch b A=1 c=½ ,t Time Unadjusted Adjusted B B After q , Total Unadjusted£ cq B At , Total = Total Adjusted³ (1-cq)

  25. b A=1 c=½ ,t Time Unadjusted Adjusted B B has ³ fair share Adjusted b b ,t at , After q , TCP ³ (1-cq) ,t = (1-cq) EQUI n Proof Sketch Total Adjusted³ (1-cq)

  26. TCPO(1) EQUI c=½ TCP b b b b b b b ,t ,t ,t ,t at , After q , ,t ,t ,t TCPO(1) ³EQUI Proof Sketch TCP³ (1-cq) EQUI

  27. TCPO(1) EQUI Less Less Less Adj =å =å Adj Adj q q b b ,t ,t Proof Sketch Less£ Adj

  28. b b ,t ,t at , After q , TCPO(1) ³EQUI Proof Sketch EQUI

  29. Less Adj q Proof Sketch EQUI

  30. TCPO(1) EQUI Less Less Less Adj =å =å Adj Adj q q b b ,t ,t Proof Sketch Less£ Adj

  31. Adj =å Adj Adj TCPO(1)(J) TCPO(1)(J) TCP(J) q q £ O(1) OPT(J) OPT1(J) OPT1(J) + Adj New Results

  32. TCPO(1) EQUI Less J’ £ TCPO(1)(J) EQUI2+e(J’) £ £ O(1) OPT1(J’) OPT1(J’ ) b b Adj OPT1(J) + + ,t ,t Proof Sketch J

  33. TCPO(1) EQUI Less J’ TCPO(1)(J) EQUI2+e(J’) £ £ O(1) OPT1(J’) OPT1(J’ ) b b Adj OPT1(J) + + ,t ,t ³ ³ Less = Proof Sketch J Done

  34. Open: Dynamical System • converges? • bounded? hope AÞ¥ cÞ1 A=1 (Free Market & Locally) c=½ » f f TCP2+e(J) £ O(1/e) OPT1(J) TCPO(m3)(J) £ O(m) OPT1(J) £ m New Results TCP: Fair ?? [F] say no

  35. Proof Sketch • » supply & demand cost for bandwidth f • Each charges ffor its bandwidth • Allocates , so all charged the same. » f f TCP2+e(J) £ O(1/e) f f f OPT1(J) TCP Free Market Fair

  36. Proof Sketch • Allocates , so locally fair at each TCPO(m3)(J) £ O(m) OPT1(J) £ m TCP Locally Fair

  37. Conclusion TCP is Competitive

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