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

2. Email Web Telnet TCP (Transport Control Protocol) AIMD (Additive Increase, Multiplicative Decrease)

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

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

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

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

7. User Perceived Latency Flow Time (c - a ) AVG J = {,,,,,, …,, } Bad(J) Good(J) (c - a ) AVG =  n Long (n-1)  + Long n  Good(J) = … … c a Bad(J) = … c a

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

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

10. Not Competitive

11. Competitive

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

13. Previous Results (Lower Bounds) EQUI(J) OPT(J)   (n) [MPT] NonClair(J) OPT(J)   (n ½ ) aaaaa

14. Previous Results (Upper Bounds) BAL 1+  (J) OPT 1 (J)  O(1/  ) [KP] [E] EQUI 2+  (J) OPT 1 (J)  O(1/  ) [EP] BROADCAST 4+  (J) OPT 1 (J)  O(1/  )

15.  O(1) OPT(J) TCP(J) New Results OPT 1 (J) TCP O(1) (J) Adj  qq OPT 1 (J) TCP O(1) (J) - Adj

16. Proof Sketch [E] EQUI 2+  (J) OPT 1 (J)  O(1) Reduction

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

18. Proof Sketch b,t Unadjusted Adjusted

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

20. Proof Sketch c= ½ b,t TCP EQUI b,t at, b,t After q, TCP  (1-c q ) EQUI b,t TCP O(1) b,t b TCP O(1)  EQUI b,t

21. Proof Sketch EQUI

22. Proof Sketch EQUI

23.  O(1) OPT(J) TCP(J) New Results OPT 1 (J) TCP O(1) (J) OPT 1 (J) + Adj TCP O(1) (J)

24. Proof Sketch  O(1) OPT 1 (J) TCP O(1) (J) EQUI 2+  (J’) OPT 1 (J’ )  Adj + OPT 1 (J’ ) + J  TCP O(1) b,t EQUI b,t J’ Less

25. Proof Sketch  O(1) OPT 1 (J) TCP O(1) (J) EQUI 2+  (J’) OPT 1 (J’ )  Adj + OPT 1 (J’ ) + J TCP O(1) b,t EQUI b,t J’ Less  Less  

26. Proof Sketch TCP O(1) b,t EQUI b,t Adj  qq Less  Adj Less 

27. Proof Sketch EQUI Less Adj q Less  Adj

28. Proof Sketch  O(1) OPT 1 (J) TCP O(1) (J) EQUI 2+  (J’) OPT 1 (J’ )  Adj + OPT 1 (J’ ) + J TCP O(1) b,t EQUI b,t J’ Less  Less 

29. Proof Sketch  O(1) OPT 1 (J) TCP O(1) (J) EQUI 2+  (J’) OPT 1 (J’ )  Adj + OPT 1 (J’ ) + J TCP O(1) b,t EQUI b,t J’ Less Done

30. Conclusion TCP is Competitive Recent Result