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TCP: Competitive Adjustment with Extra Bandwidth and Time

Evaluating the competitiveness of TCP in adjusting bandwidth allocation over time for optimal performance. Results and proofs on fair share and efficiency in data flow. Consideration of system dynamics and fairness in bandwidth distribution.

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TCP: Competitive Adjustment with Extra Bandwidth and Time

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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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