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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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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

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3 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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4 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 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

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5 Outline 1. Breakdown the TCP-friendliness into sub-conditions, study the sub-conditions separately oWhy the common evaluation practice to verify TCP- friendliness is not good ? 2. TCP-friendliness is difficult to verify oCounterexamples to TCP-friendliness 3. Conservativeness is easier oSufficient conditions for conservativeness oOr bounded non-conservativeness

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6 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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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 !

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8 Breakdown the TCP-Friendliness Condition (Contd) (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. TCP Equation-Based Rate Control (x, p, r) throughputloss-event rateaverage RTT

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9 2. Counterexample to TCP-Friendliness: AIMD experiences larger loss rate than EBRC EBRC r Ass. EBRC uses f(p) in (1) AIMD (a,b) 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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10 Convergence for One EBRC over a Link slope K 2 /2

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11 Convergence for One EBRC over a Link (Contd) Can be seen as Jacobi iterative solving of: The equilibrium point: If stable: Remarks oboth AIMD and EBRC are rate-based oboth 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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12 Validation by ns-2 Simulation b pakets TFRC b pakets TCP x/x x/f(p,r)p/pr/rx/f(p,r) b Breakdown:

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13 AIMD sees larger loss rate than EBRC (Contd) otime t is a loss-event iff at t- the sum of the send rates of the two sources = r oa loss-event is assigned to either AIMD or EBRC oZ n = 1 iff the nth loss-event is assigned to EBRC, else Z n =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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14 Example 2: Numerical Simulations

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

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16 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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17 EPFL to UMASS x/x TFRC/TCP throughput x/f(p,r)p/pr/rx/f(p,r) Breakdown into Sub-Conditions:

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

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

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

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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 ? L=2 4 8 16 PFTK-simplified Cause: convexity of 1/f(1/x) PFTK SQRT

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

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

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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

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1 Long-Run Behavior of Equation-Based Rate Control: Theory and its Empirical Validation Milan Vojnović Seminar on Theory of Communication Networks, ETHZ,

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