1. Equation-Based Rate Control: Is it TCP-friendly
Equation-Based Rate Control: Is it TCP-friendly ? Milan Vojnovic Joint work with Jean-Yves Le Boudec
ARC TCP Workshop, ENS, Paris, November 5-7, 2003

2. 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

3. Equation-Based Rate Control: Basic Control
Estimator of 1/p:
Send rate:
Example Protocol: TFRC (RFC 3448, IETF proposed standard, Jan 2003)

4. Is Equation-Based Rate Control a TCP Friend ?
We deduce: the Engineering Intuition
p -> f(p) is TCP loss-throughput formula
So, 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
Problem: When the Intuition is True and when Not ?

5. 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

6. 1. Common Evaluation Practice
Common Practice:
measured throughputs x x’
Non-TCP
TCP
Test: TCP-friendly iff x <= x’
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

7. 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 !

8. Breakdown the TCP-Friendliness Condition (Cont’d)
Equation-Based Rate Control
(x, p, r)
(x’, p’, r’)
throughput
loss-event rate
average RTT
(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.

9. 2. Counterexample to TCP-Friendliness: AIMD experiences larger loss rate than EBRC
Example 1: Either One AIMD or One EBRC over a Link
AIMD
(a,b) r
(1)
EBRC r
Ass. EBRC uses f(p) in (1)
TCP-like (b=1/2)
p’/p=16/9
(approx )
Ob: p’ > p <=> non-TCP-friendliness

10. Convergence for One EBRC over a Link
slope K2/2

11. 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

12. Validation by ns-2 Simulation
x/x’
TFRC
b pakets b
TCP
b pakets
x/f(p,r)
p’/p
r’/r
x’/f(p’,r’)
Breakdown:

13. AIMD sees larger loss rate than EBRC (Cont’d)
Example 2: One AIMD and One EBRC Competing for a Link
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

14. Example 2: Numerical Simulations

15. Example 2: Validation by ns-2 Simulation
x/x’
TCP
TFRC
b pakets b
x/f(p,r)
p’/p
r’/r
x’/f(p’,r’)
Breakdown:

16. Internet Measurements
EPFL
Long-lived transmissions with TFRC and TCP
Estimated: loss-event rates, average round-trip times, throughputs
INRIA, KTH,
UMASS,UMELB

17. EPFL to UMASS x/f(p,r) p’/p r’/r x’/f(p’,r’) x/x’
Breakdown into Sub-Conditions:
TFRC/TCP throughput
x/x’

18. 3. Conservativeness
assume: the send rate is a stationary ergodic process
Convergence:
The send rate control:
The estimator is updated at special points in time
Q. Is x <= f(p) ?

19. Conditions for Conservativeness
In practice:
the conditions are true, or almost
the result explains overly conservativeness

20. Is Negative or Slightly Positive ?
Internet LAN to LAN EPFL sender
Internet LAN to cable-modem at EPFL
Lab

21. Throughput-Drop Puzzle
Empirical 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.”
Cause:
convexity
of 1/f(1/x)
PFTK
SQRT
L=2 4 8 16
PFTK-simplified
Why ?

22. What Causes Excessive Conservativeness ?
Palm inversion:
Throughput:
May make the control conservative ? !

23. What Causes Excessive Conservativeness ? (Cont’d)
1/f(1/x) is assumed to be convex, thus, it is above its tangents
take the tangent at 1/p
the “overshoot” bounded by a function of p and

24. 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