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

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

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

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

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

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

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

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

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

Not Competitive

Competitive

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

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

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/  )

 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

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

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

Proof Sketch b,t Unadjusted Adjusted

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

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

Proof Sketch EQUI

Proof Sketch EQUI

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

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

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  

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

Proof Sketch EQUI Less Adj q Less  Adj

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 

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

Conclusion TCP is Competitive Recent Result