long-run behavior of equation-based rate control: theory and its empirical validation

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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

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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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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


=> 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


=> no, mostly overshoots

)r̂,p̂(f

x̂

TCPTCP

TCP

TCPp̂


experiment

=> not alwaysTCP

TFRC

p̂

p̂

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=> yes

Lab experiments with RED (cont’d)

(pkts/s) x̂TCP

(pkts/s) x̂TFRC


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Lab experiments with DropTail (100 pkts)

(C) Is the control conservative ?

)r̂,p̂(f

x̂

TFRCTFRC

TFRC

TFRCp̂

=> yes


=> no)r̂,p̂(f

x̂

TCPTCP

TCP

TCPp̂


=> 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)


(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

long-run behavior of equation-based rate control: theory and its empirical validation

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