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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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With Extra Bandwidth and Time for AdjustmentTCP is Competitive

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


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

  • Email

  • Web

  • Telnet


  • File Size

  • Arrival time

  • Many Packets » Data Flow

Input: Set of Sender/Jobs


Adjustments

B

b

b

,t

,t

(not buffer

or time delay)

Bottleneck Capacity and Adjustments

å£

B


b

,t

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

A=1

c=½

Multiplicative

decrease

Additive

increase

Time


  • 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


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


TCP

  • [CJ] TCP ÞEQUI

EQUI

B

B

B

Shortest

Remaining

Work First

  • Optimal

Comparison with other Schedulers


All Knowing

All Powerful

Optimal:

?

Future

Online:

?

Non-Clairvoyant:

TCP

?

Distributed:

Knowledge of Scheduler


Not Competitive


Competitive


a

EQUI(J)

[MPT]

£ 2

OPT(J)

[ECBD]

£ 3.73

Previous Results(Batch)


a

a

a

a

a

EQUI(J)

[MPT]

³W(n)

OPT(J)

NonClair(J)

³W(n½)

OPT(J)

Previous Results(Lower Bounds)


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)


£ O(1)

Adj

Adj

Adj

TCPO(1)(J) - Adj

TCPO(1)(J)

TCP(J)

q

q

OPT(J)

OPT1(J)

OPT1(J)

New Results


EQUI2+e(J)

[E]

£ O(1)

OPT1(J)

Reduction

Proof Sketch


TCP

  • TCP ÞEQUI

EQUI

B

B

TCP Þ EQUI

[CJ] global measure

New: Job by job comparison


b

,t

Proof Sketch

Unadjusted

Adjusted


b

A=1

c=½

,t

Time

Unadjusted

Adjusted

TCP³ (1-cq) EQUI

b

b

,t

,t

at ,

After q ,

Proof Sketch


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


Proof Sketch

EQUI


Proof Sketch

EQUI


TCPO(1)(J)

TCPO(1)(J)

TCP(J)

£ O(1)

OPT(J)

OPT1(J)

OPT1(J) + Adj

New Results


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


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


TCPO(1)

EQUI

Less

Less

Less

Adj

Adj

Adj

q

q

b

b

,t

,t

Less£ Adj

Proof Sketch


Less

Adj

q

Less£ Adj

Proof Sketch

EQUI


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


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


RecentResult

Conclusion

TCP is Competitive


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