PhD thesis

1
Equation-Based Rate Control Is it TCP-friendly
?Milan VojnovicJoint 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
1990s)
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 -gt 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
Non-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
7
Breakdown the TCP-Friendliness Condition

• (I) Does the source verify x lt 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 (Contd)
(I) Conservativeness x lt f(p, r) (II)
Loss-Event Rates p gt p (III) Round-Trip
Times r gt r (IV) Obedience of TCP to the
Formula x gt f(p, r)
If (I), (II), (III), and (IV) hold, that implies
TCP-friendliness.
9
2. Counterexample to TCP-FriendlinessAIMD
experiences larger loss rate than EBRC
Example 1 Either One AIMD or One EBRC over a Link
Ob p gt p ltgt non-TCP-friendliness
10
Convergence for One EBRC over a Link
slope K2/2
11
Convergence for One EBRC over a Link (Contd)
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
• gt 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 (Contd)
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 Zn0

g RL1 -gt 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
TFRC/TCP throughput
x/x
18
3. Conservativeness
Convergence

• The estimator is updated at special points in time

Q. Is x lt 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 ?
InternetLAN to LANEPFL sender
InternetLAN 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.
Why ?
22
What Causes Excessive Conservativeness ?
Palm inversion
Throughput
May make the control conservative ? !
23
What Causes Excessive Conservativeness ? (Contd)

• 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