ARC TCP Workshop, ENS, Paris, November 5-7, 2003

Equation-Based Rate Control: Is it TCP-friendly ?

Milan Vojnovic

Joint work with Jean-Yves Le Boudec

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The Axiom: TCP-friendliness

Requires adaptive sources to obey to TCP in the following sense:

TCP-friendliness (late 1990’s)

“A flow that is not TCP-friendly is one whose long-term arrival rate exceeds that of any conformant TCP in the same circumstances.” Floyd and Fall, 1999

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Equation-Based Rate Control: Basic Control

Estimator of 1/p:

Send rate:

Example Protocol: TFRC (RFC 3448, IETF proposed standard, Jan 2003)

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Is Equation-Based Rate Control a TCP Friend ?

We deduce: the Engineering Intuition

Problem: When the Intuition is True and when Not ?

p -> f(p) is TCP loss-throughput formulaSo, it must be that

if I adjust the send rate at loss-events to f(), evaluated at the on-line estimated loss-event

rate, my new protocol will be TCP-friendly

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Outline

1. Breakdown the TCP-friendliness into sub-conditions, study the sub-conditions separately Why the common evaluation practice to verify TCP-friendliness is not good ?

2. TCP-friendliness is difficult to verify Counterexamples to TCP-friendliness

3. Conservativeness is easier Sufficient conditions for conservativeness Or bounded non-conservativeness

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1. Common Evaluation Practice

Non-TCP

Common Practice:

TCP

Why the common evaluation practice is NOT GOOD ?

- hides a cause of the observed throughput deviation- may lead a protocol designer to an improper adjustment

measured throughputs

x

x’

Test: TCP-friendly iff x <= x’

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Breakdown the TCP-Friendliness Condition

(I) Does the source verify x <= f(p,r) ?

(II) Does the source attain the same loss-event rate as TCP ?

(III) Does the source see the same average round-trip time as TCP ?

(IV) Does TCP verify its throughput formula ?

Important to BREAKDOWN the TCP-friendliness condition into sub-conditions, and study them separately !

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Breakdown the TCP-Friendliness Condition (Cont’d)

(I) Conservativeness x <= f(p, r)

(II) Loss-Event Rates p >= p’

(III) Round-Trip Times r >= r’

(IV) Obedience of TCP to the Formula x’ >= f(p’, r’)

If (I), (II), (III), and (IV) hold, that implies TCP-friendliness.

TCPEquation-Based Rate Control

(x, p, r) (x’, p’, r’)

throughput loss-event rate average RTT

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2)b1(4

p'p

2. Counterexample to TCP-Friendliness:AIMD experiences larger loss rate than

EBRC

EBRC

)b1(2r)b1(a

p 2

r

Ass. EBRC uses f(p) in (1)AIMD

(a,b)

'p1

)b1(2)b1(a

'x

)b1(ra2

'p 22

r

(1)

TCP-like (b=1/2)p’/p=16/9 (approx. 1.7778)

Ob: p’ > p <=> non-TCP-friendliness

Example 1: Either One AIMD or One EBRC over a Link

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Convergence for One EBRC over a Linkslope K2/2

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Convergence for One EBRC over a Link (Cont’d)

Can be seen as Jacobi iterative solving of:

The equilibrium point:

If stable:

Remarks

both AIMD and EBRC are rate-based both AIMD and EBRC are fluid, no packetization effects

=> the deviation of the loss-event rates is intrinsic to the very nature of the dynamics of the two controls

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Validation by ns-2 Simulation

b pakets

TFRC

b pakets

TCP

x/x’

x/f(p,r) p’/p r’/r x’/f(p’,r’)

b

Breakdown:

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AIMD sees larger loss rate than EBRC (Cont’d)

time t is a loss-event iff at t-the sum of the send rates of the two sources = r

a loss-event is assigned to either AIMD or EBRC Zn = 1 iff the nth loss-event is assigned to EBRC, else Zn=0

g : R+L+1 -> R+ is a non-linear function; the system is non-linear

Example 2: One AIMD and One EBRC Competing for a Link

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Example 2: Numerical Simulations

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Example 2: Validation by ns-2 Simulation

b pakets

TCP

TFRC

x/x’

b

x/f(p,r) p’/p r’/r x’/f(p’,r’)

Breakdown:

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Internet Measurements

INRIA, KTH, UMASS,UMELB

EPFL Long-lived transmissions with TFRC and TCP

Estimated: loss-event rates, average round-trip times, throughputs

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EPFL to UMASS

x/x’

TFRC/TCP throughput

x/f(p,r) p’/p r’/r x’/f(p’,r’)

Breakdown into Sub-Conditions:

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3. Conservativeness

Convergence:

The send rate control:

The estimator is updated at special points in time

Q. Is x <= f(p) ?

assume: the send rate is a stationary ergodic process

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Conditions for Conservativeness

In practice: the conditions are true, or almost the result explains overly conservativeness

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Is Negative or Slightly Positive ?

InternetLAN to LANEPFL sender

InternetLAN to cable-modem

at EPFL

Lab

200 p],ˆcov[ 2

00 p],ˆcov[ 200 p],ˆcov[

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Throughput-Drop PuzzleEmpirical indications: TFRC looses throughput for large loss-event rates

E.g. Bansal et al (ACM SIGCOMM 2001): “ … in return to for smoother transmission rates, slowly-responsive algorithms lose throughput to faster ones (like TCP) under dynamic network conditions.”

Why ?

L=2

48

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PFTK-simplified

Cause:

convexity

of 1/f(1/x)

PFTK

SQRT

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What Causes Excessive Conservativeness ?

Palm inversion:

Throughput: May make the control conservative ? !

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What Causes Excessive Conservativeness ? (Cont’d)

the “overshoot” bounded by a function of p and

1/f(1/x) is assumed to be convex, thus, it is above its tangents take the tangent at 1/p

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Conclusion

1. Breakdown the TCP-friendliness into sub-conditions, study the sub-conditions separately

2. TCP-friendliness is difficult to verify

3. Conservativeness is easier