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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) AIMD (Additive Increase, Multiplicative Decrease). Email Web Telnet. File Size. Arrival time. Many Packets » Data Flow.

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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)AIMD (Additive Increase, Multiplicative Decrease) • Email • Web • Telnet

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

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

  5. b ,t TCP (Transport Control Protocol)AIMD (Additive Increase, Multiplicative Decrease) A=1 c=½ Multiplicative decrease Additive increase Time

  6. 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

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

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

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

  10. Not Competitive

  11. Competitive

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

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

  14. BAL1+e(J) [KP] £ O(1/e) OPT1(J) EQUI2+e(J) [E] £ O(1/e) OPT1(J) BROADCAST4+e(J) [EP] £ O(1/e) OPT1(J) Previous Results (Upper Bounds)

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

  16. EQUI2+e(J) [E] £ O(1) OPT1(J) Reduction Proof Sketch

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

  18. b ,t Proof Sketch Unadjusted Adjusted

  19. b A=1 c=½ ,t Time Unadjusted Adjusted TCP³ (1-cq) EQUI b b ,t ,t at , After q , Proof Sketch

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

  21. Proof Sketch EQUI

  22. Proof Sketch EQUI

  23. TCPO(1)(J) TCPO(1)(J) TCP(J) £ O(1) OPT(J) OPT1(J) OPT1(J) + Adj New Results

  24. 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

  25. 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

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

  27. Less Adj q Less£ Adj Proof Sketch EQUI

  28. 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 Less = Proof Sketch J

  29. 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 Done

  30. RecentResult Conclusion TCP is Competitive

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