With Extra Bandwidth and Time for Adjustment

TCP is Competitive

J. Edmonds, S. Datta, and P. Dymond

TCP (Transport Control Protocol)

• Email

• Web

• Telnet

Bytes on the Internet

TCP

Other

•Arrival time

•File Size

Input: Set of Sender/Jobs

•Many Packets Data Flow

•Fixed Path

General Network

Adjustments

Bottleneck Capacity and Adjustments

B

b ,t

b ,t

B

(not buffer or time delay)

TCP Protocol

Time

A=1 c=½

b ,t

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

A Paradigm Shift

Computation TaskFile to Transfer

??? Speed up

# ProcessorsBottleneck Capacity

Processor AllocationBandwidth Allocation b ,t

Work Size & TimesFile Size & Times ca ,,

Network

User Perceived LatencyFlow Time

(c - a )AVG

J = { , , , , , , … , , }

Bad(J) =

…Good(J) =

……

Bad(J)Good(J) (c - a )AVG= n Long

(n-1) + Long n

ca

ca

Comparison with other Schedulers

BTCP

BEQUI

ShortestRemainingWork First

B

•[CJ] TCP EQUI

•Optimal

Knowledge of Scheduler

Non-Clairvoyant: ?

Online: ?Future

Distributed: ?

Optimal: All KnowingAll Powerful

TCP

Not Competitive

Competitive

Adj

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) (n½)

aa aa a

Previous Results (Upper Bounds)

BAL1+(J)OPT1(J) O(1/)[KP]

[E] EQUI2+(J)OPT1(J) O(1/)

[EP] BROADCAST4+(J)OPT1(J) O(1/)

?

TCP[Cor] A c1

TCP

B-TCP

New Results

CorollaryA c1

A=1 c=½

New

New Future Work

O(1)OPT(J)TCP(J)

New Results

AdjAdj Adj

q q

OPT1(J)TCPO(1)(J)

OPT1(J) + AdjTCPO(1)(J)

[E] EQUI2+(J)OPT1(J) O(1)

Proof: Reduction

New ResultsRandom Asynchronous Early Marking

•“Drops”packets before cap reached

•No packets actually dropped

!

b ,t

•“Drops” individual random packets•Smooth total transmission

•Challenge#

# packets to drop

?

TCP: Fair ??

New Results

mTCPO(m3)(J)

OPT1(J) O(m)

TCP2+(J)OPT1(J) O(1/)

(Free Market & Locally)

f f

A c1

A=1 c=½

[F] say no

hope

Open: Dynamical System •converges? •bounded?

Proof Sketches

TCP EQUI

[CJ] global measure

BTCP

BEQUI

•TCP EQUI

New: Job by job comparison

Proof Sketch

b ,t

Unadjusted Adjusted

Time

A=1 c=½

UnadjustedAdjusted

b ,t

At , Total B

Total Adjusted (1-cq) B

After q , Total Unadjusted cq B

Proof Sketch

Proof Sketch

Time

A=1 c=½

UnadjustedAdjusted

b ,t

Total Adjusted (1-cq) Bhas fair share Adjusted

After q , at ,

= (1-cq) EQUIb ,tBb ,t (1-cq) nTCP

Proof Sketch

c=½b ,tTCP

EQUI b ,t

After q , at ,

TCP (1-cq) EQUIb ,t b ,t

TCPO(1) b ,t

b ,tTCPO(1) EQUI b ,t

Proof Sketch

AdjAdj Adj

q q

TCPO(1) b ,t

EQUI b ,t

Less Adj

Less Less Less

Proof Sketch

EQUI

After q , at , b ,tTCPO(1) EQUI b ,t

Proof Sketch

EQUI

Less

Adjq

Proof Sketch

AdjAdj Adj

q q

TCPO(1) b ,t

EQUI b ,t

Less Adj

Less Less Less

O(1)OPT(J)TCP(J)

New Results

AdjAdj Adj

q q

OPT1(J)TCPO(1)(J)

OPT1(J) + AdjTCPO(1)(J)

Proof Sketch

O(1)OPT1(J)

TCPO(1)(J) EQUI2+(J’)OPT1(J’ )

Adj+ OPT1(J’ )+

J

TCPO(1) b ,t

EQUI b ,t

J’Less

Proof Sketch

O(1)OPT1(J)

TCPO(1)(J) EQUI2+(J’)OPT1(J’ )

Adj+ OPT1(J’ )+

J

TCPO(1) b ,t

EQUI b ,t

J’Less

Less Done

TCP: Fair ??

New Results

mTCPO(m3)(J)

OPT1(J) O(m)

TCP2+(J)OPT1(J) O(1/)

(Free Market & Locally)

f f

A c1

A=1 c=½

[F] say no

hope

Open: Dynamical System •converges? •bounded?

TCP2+(J)OPT1(J) O(1/)

f f

Proof Sketch

•Each charges f for its bandwidth

TCP Free Market Fair

•Allocates , so all charged the same.

fff

• supply & demand cost for bandwidthf

Proof Sketch

TCP Locally Fair•Allocates , so locally fair at each

mTCPO(m3)(J)

OPT1(J) O(m)

Conclusion

TCP is Competitive