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

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

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

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 ?

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

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

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 !

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.

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. 1.7778) Ob: p’ > p <=> non-TCP-friendliness

Convergence for One EBRC over a Link slope K2/2

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

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:

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

Example 2: Numerical Simulations

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:

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

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’

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) ?

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

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

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 ?

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

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

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