With Extra Bandwidth and Time for Adjustment TCP is Competitive
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Transcript of With Extra Bandwidth and Time for Adjustment TCP is Competitive
With Extra Bandwidth and Time for Adjustment
TCP is Competitive
J. Edmonds, S. Datta, and P. Dymond
TCP (Transport Control Protocol)
• 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