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Long-Run Behavior of Equation-Based Rate Control: Theory and its Empirical Validation. Milan Vojnović. Joint work with Jean-Yves Le Boudec Lab and Internet measurements with C. Laetsch, T. Müller. Seminar on Theory of Communication Networks, ETHZ, Zürich, May 6, 2003. My thesis. - PowerPoint PPT Presentation
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Long-Run Behavior of Equation-Based Rate
Control:Theory and its Empirical Validation
Milan Vojnović
Seminar on Theory of Communication Networks, ETHZ, Zürich, May 6, 2003
Joint work with Jean-Yves Le BoudecLab and Internet measurements with C. Laetsch, T.
Müller
2
My thesis
equation-based rate control -- is it TCP friendly ?
increase-decrease controls -- e.g. TCP-- fairness in bandwidth sharing
expedited forwarding-- queueing bounds for diffserv EF
input-queued switch-- scheduler latency
This talk:
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Problem we study TCP -- Internet predominant transport protocol;
implements a window-based transmission control Equation-based rate control -- rate-based
transmission control (e.g. for media streaming)-- TFRC (TCP-Friendly Rate Control)
Floyd et al (2000), an IETF internet-draft Controls need to be TCP-friendly -- an axiom
established by part of Internet research community (mid-nineties)
TCP TCP
Internetnon-TCP
non-TCP
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Problem we study (cont’d)TCP characterized by:
TCP throughput = f(loss-event rate)Basic control law of equation-based
rate control: loss-event rate estimated on-line
(call the estimator ) at some instants
send rate = Where is the problem ?
f is non-linear, loss is random
sampling bias-- rate set at special points in time )p̂(f
p̂
])p̂[E(f)]p̂(f[E
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Problem we study (cont’d)
In long-run, is the control TCP-friendly ?
(TCP-f) Throughput TCP throughput
throughput = time-average send rate (e.g. pkts/sec)
Note: ideally, (TCP-f) with (almost) equality
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Outline of the talk
Parts I and II take from: M. Vojnovic, J.-Y. Le Boudec, ACM SIGCOMM 2002 M. Vojnovic, J.-Y. Le Boudec, ITC-17, 2001,
Best Student Paper Award
Is the control conservative ?
)p(fThroughput )C( p = loss-event rate of this protocol
Part I
Part II Other factors
Part IIIEmpirical study of the factors-- lab and Internet measurements
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Ln 3n 2n1n
Part IIs the control conservative ?
)p̂(fX nn
)t(X rate Send
t
...
n
n ˆ1
p̂
L
1llnln wˆ
nT1nT 3nT LnT Loss events:
Loss intervals:
Additional control laws exist, not in slides (see papers)
n1nn TTS
2nT ...... ...
Basic control law:
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Assumptions loss events
-- a stationary ergodic point process on R, with finite non-null intensity
system stable -- for any initial value, there exists convergence of the send rate to unique stationary ergodic process
2101 TT0TT
)]0(X[E ds)s(Xt1
lim Throughputt
0t
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When (C) holds ?
Throughput:
=> joint probability law of mattersL,,10,
])ˆ/1(f
[E
][E)]0(X[E
0
0
0
(mean-value formula - ‘cycle formula’, ‘Palm inversion’)-- formula quantifies stochastic bias (importance of viewpoint)
-- it is different from a naive guess )]ˆ/1(f[E)]0(X[E 0
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Viewpoint matters ! (Feller’s, Bus stop paradox-like)
)]S[E]X[E]S,Xcov[
1](X[E)]0(X[E eess00
000
a random observer
3X
)t(X
t3T2T0T
0S
1T ...
...
02T 1T
...
(convention: 0 an arbitrary fixed point)
an observer sampling at the points
]X[E eess 0
2X1X0X
1X
2X
falls more likely into a large Sn
if Xn is positively correlated to Sn, then it sees more than E[X0]
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When (C) holds? (cont’d)
(F1) x->1/f(1/x) convex
0]ˆ,cov[ 00 (C1) => (C), that is,
conservative
]ˆ,cov[)p(fp)p('f
1
1)p(fE[X(0)]
00
3
Follows from:
)]
)ˆ/1(f[E
][E)]0(X[E(
0
0
0
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)x/1(f
x
When (F1) is true?
c1, c2, c3 = positive-valued constantsr = round-trip timeq = TCP retransmit timeout (typically, q=4r)
PFTK-standard:
)p32p](pc,1min[qprc1
)p(f 321
PFTK-simplified:
)p32p(qcprc1
)p(f2/72/3
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SQRT
PFTK-
prc1
)p(f1
SQRT:
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(F1) true for SQRT and PFTK-simplified
)x/1(f1
PFTK-SQRT
x
For PFTK-standard(F1) holds almost,-- deviation from convexity negligible
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i.i.d. => (C1) true nn)(
autocorrelation of mattersnn)(
n̂
],cov[w]ˆ,cov[ lnn
L
1llnn
From def.of
When (C1) holds ?)0]ˆ,(cov[ 00
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Claim 1Assume and negatively
or lightly correlatedConsider x->1/f(1/x) in an interval
where takes its valuesn n̂
1) the more convex x->1/f(1/x) is, the more conservative is
2) the more variable is, the more conservative is
n̂
n̂
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SQRT
Claim 1, numerical example
PFTK-simplified the larger p is, the more convex x->1/f(1/x) is=> more conservative
PFTK more convex than SQRT => effect stronger
i.i.d., has generalized exponential density
nn)( 0
PFTK-
SQRT
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Claim 1, numerical example (cont’d)
SQRT
PFTK-simplified
the more variable is, the more conservative is
n̂
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ns-2 example for Claim 1Setting: a RED queue shared by equal number of TFRC and TCP
flows, PFTK-simplified
)p̂(f
x̂
TFRC
TFRC
TFRCp̂
the larger p is, the more convex
x->1/f(1/x) is=> more
conservative
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Recap
sufficient conditions for the control to be conservative [(C) holds] x->f(1/x)
-- SQRT => conservative -- PFTK => overly conservative
loss process -- condition on second-order statistics
by-product: explained TFRC throughput-drop-- due to stochastic + convexity bias
Next, another set of conditions-- identifies a control for which (C) not true
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Second set of conditions for (C) to hold, or not
=> (C) holds, conservative
=> (C) not holds, non-conservative
(F2) x->f(1/x) concave(C2) 0]S,Xcov[ 00
(F2’) x->f(1/x) convex(C2’) (V) not a fixed constant
n̂0]S,Xcov[ 00
veconservati )p(f)]0(X[E (C) ,recall
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When is the control non-conservative ?
SQRT: x->f(1/x) concave PFTK formulae
x->f(1/x) convex for small x, else, concave
Example: (PFTK)
0]S,Xcov[ 00 )]ˆ/1(f[E)]0(X[E 0
Audio source packet send rate fixed, packets lengths varied
Networkpackets dropped independently of their length (e.g. RED in packet-mode)
)x/1(f
x
SQRT
PFTK-
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When is the control non-conservative ? -- ns-2
example
L=8 (not shown), the same qualitative observations, but less pronounced (the last part of the claim)
for PFTK, not conservative
recall, x->f(1/x) is convex for PFTK for small x (large p)
)p̂(f
x̂
TFRC
TFRC
TFRCp̂
Setting: a rate control with fixed packet send rate, variable packet lengths, packets dropped with a fixed probability, L=4
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(TCP-f) Is control TCP-friendly ?
not TCP-friendly ! even though it is conservative
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Part IIOther factors
(P) Is loss-event rate no better than TCP’s ?
TCPpp
(F) Does TCP conform to its formula ?
)p(fthroughput TCP TCP
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(P) Is loss-event rate better than TCP’s ?
Sources may see different loss-event rates, another artifact of importance of viewpoint
Claim 3: in many-sources regime
PTCP ppp
seen by TCP seen by equation-based rate control
seen by a non-adaptive sender
(Poisson)many-sources regime = state of the network evolves
independently of a single source
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(P) Is loss-event rate better than TCP’s ? (cont’d)
made formal by Palm calculus (see paper)
Intuition non-adaptive sender (Poisson) would
see time-average loss-event rate an adaptive source samples ‘bad’
states less frequently the more adaptive the source is,
the smaller loss-event rate it would see
TCP would be more adaptive than an equation-based rate control
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ns-2 example for Claim 3
s)connection of(number N
estimated loss-event rates
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(F) Does TCP conform to its formula ?
TCP Sack1
TFRCx̂
)p̂(f
=> not always
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(TCP-f) Is control TCP-friendly ?
The observed non TCP-friendliness is because TCP does not conform to its formula-- it is not an intrinsic problem of the control
Ignoring this might lead a designer to try to“improve” her protocol -- wrongly so
Guideline: check the factors separately !
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Part IIIEmpirical study of the factors
Check the factors separately Internet measurements lab experiments
Conclusion
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Internet measurements
TCP TFRC
Background
Circles = PCs, Linux (FreeBSD, not in slides)
• TCP = Sack/Fack, D-Sack, timestamps, Linux-specific
• TFRC = experimental code (ICIR, 2000), we adapted to conform to TFRC spec
• Background = equal # of TCPs and TFRCs
• R = UMASS, INRIA, Melbourne, Caltech, KTH, Hong Kong
Setting:
100 Mb/s
10 or 100 Mb/s
Internet
R
Slides: R = UMASSAccess at R = 100 Mb/s
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Internet measurements: EPFL -> UMASS
(C) Is the control conservative ?
)r̂,p̂(f
x̂
TFRCTFRC
TFRC
TFRCp̂
=> yes
(F) Does TCP conform to its formula ?
=> not always
)r̂,p̂(f
x̂
TCPTCP
TCP
TCPp̂
(P) Is loss-rate no better than TCP’s ?
experiment
=> not alwaysTCP
TFRC
p̂
p̂
33(pkts/s) x̂TCP
(pkts/s) x̂TFRC => no
(TCP-f) Is the control TCP-friendly ?
Internet measurements: EPFL -> UMASS
both, (P) and (F) not true
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Lab experiments
TCP TFRC
10 Mb/s
Background
qdisc = RED, Droptail
delay= 50 ms
Circles = PCs, Linux kernel 2.4.18
Setting:
• TCP, TFRC, Background = same as with lab experiments
• Delay = emulated by NIST Net100 Mb/s
100 Mb/s
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Lab experiments with RED (cont’d)(C) Is the control conservative ?
)r̂,p̂(f
x̂
TFRCTFRC
TFRC
TFRCp̂
=> yes
(F) Does TCP conform to its formula ?
=> no, mostly overshoots
)r̂,p̂(f
x̂
TCPTCP
TCP
TCPp̂
(P) Is loss-rate no better than TCP’s ?
experiment
=> not alwaysTCP
TFRC
p̂
p̂
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=> yes
Lab experiments with RED (cont’d)
(pkts/s) x̂TCP
(pkts/s) x̂TFRC
(TCP-f) Is the control TCP-friendly ?
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Lab experiments with DropTail (100 pkts)
(C) Is the control conservative ?
)r̂,p̂(f
x̂
TFRCTFRC
TFRC
TFRCp̂
=> yes
(F) Does TCP conform to its formula ?
=> no)r̂,p̂(f
x̂
TCPTCP
TCP
TCPp̂
(P) Is loss-rate no better than TCP’s ?
=> yesTCP
TFRC
p̂
p̂
experiment
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(pkts/s) x̂TCP
(pkts/s) x̂TFRC
=> not alwaysif yes, mostlyexcessively
Lab experiments with DropTail (100 pkts)
(TCP-f) Is the control TCP-friendly ?
(P) true, but large discrepancy
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Separate factors ! (C) conditions for either conservative
or non-conservative control-- TFRC throughput-drop explained-- a control with PFTK and fixed packet send rate intrinsically non-conservative for large loss-event rate
(P) in many-sources regime, expect loss-event rate be larger than TCP sees-- other regimes exist where (P) is not true
(F) TCP may deviate from PFTK formula
Conclusion
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variability of round-trip time, its correlation with loss process -- do they matter ?
conservativeness -- seek for realistic cases when the control is non-conservative
loss-event rate-- when and why it is smaller (or larger) than TCP’s ?
Further work