2. 1 Long-Run Behavior of Equation-Based Rate Control: Theory and its Empirical Validation Milan Vojnović Seminar on Theory of Communication Networks, ETHZ, Zürich, May 6, 2003 Joint work with Jean-Yves Le Boudec Lab and Internet measurements with C. Laetsch, T. Müller

3. 2 My thesis oequation-based rate control -- is it TCP friendly ? oincrease-decrease controls -- e.g. TCP -- fairness in bandwidth sharing oexpedited forwarding -- queueing bounds for diffserv EF oinput-queued switch -- scheduler latency This talk:

4. 3 Problem we study oTCP -- Internet predominant transport protocol; implements a window-based transmission control oEquation-based rate control -- rate-based transmission control (e.g. for media streaming) -- TFRC (TCP-Friendly Rate Control) Floyd et al (2000), an IETF internet-draft oControls need to be TCP-friendly -- an axiom established by part of Internet research community (mid-nineties) TCP Internet non-TCP

5. 4 Problem we study (cont’d) TCP characterized by: TCP throughput = f(loss-event rate) Basic control law of equation-based rate control: o loss-event rate estimated on-line (call the estimator ) o at some instants send rate = Where is the problem ? o f is non-linear, loss is random o sampling bias -- rate set at special points in time

6. 5 Problem we study (cont’d) In long-run, is the control TCP-friendly ? (TCP-f) Throughput  TCP throughput throughput = time-average send rate (e.g. pkts/sec) Note: ideally, (TCP-f) with (almost) equality

7. 6 Outline of the talk Parts I and II take from: oM. Vojnovic, J.-Y. Le Boudec, ACM SIGCOMM 2002 oM. Vojnovic, J.-Y. Le Boudec, ITC-17, 2001, Best Student Paper Award Is the control conservative ? p = loss-event rate of this protocol Part I Part II Other factors Part III Empirical study of the factors -- lab and Internet measurements

8. 7 Part I Is the control conservative ? Loss events: Loss intervals: Additional control laws exist, not in slides (see papers) Basic control law:

9. 8 Assumptions oloss events -- a stationary ergodic point process on R, with finite non-null intensity osystem stable -- for any initial value, there exists convergence of the send rate to unique stationary ergodic process

10. 9 When (C) holds ? Throughput: => joint probability law of matters (mean-value formula - ‘cycle formula’, ‘Palm inversion’) -- formula quantifies stochastic bias (importance of viewpoint) -- it is different from a naive guess

11. 10 Viewpoint matters ! (Feller’s, Bus stop paradox-like) a random observer (convention: 0 an arbitrary fixed point) an observer sampling at the points falls more likely into a large S n if X n is positively correlated to S n, then it sees more than E[X 0 ]

12. 11 When (C) holds? (cont’d) (F1) x->1/f(1/x) convex (C1) => (C), that is, conservative Follows from:

13. 12 When (F1) is true? c1, c2, c3 = positive-valued constants r = round-trip time q = TCP retransmit timeout (typically, q=4r) PFTK-standard: PFTK-simplified: SQRT PFTK- SQRT:

14. 13 (F1) true for SQRT and PFTK-simplified PFTK- SQRT For PFTK-standard (F1) holds almost, -- deviation from convexity negligible

15. 14 i.i.d. => (C1) true autocorrelation of matters From def.of When (C1) holds ?

16. 15 Claim 1 Assume and negatively or lightly correlated Consider x->1/f(1/x) in an interval where takes its values 1) the more convex x->1/f(1/x) is, the more conservative is 2) the more variable is, the more conservative is

17. 16 SQRT Claim 1, numerical example PFTK-simplified the larger p is, the more convex x->1/f(1/x) is => more conservative PFTK more convex than SQRT => effect stronger i.i.d., has generalized exponential density PFTK- SQRT

18. 17 Claim 1, numerical example (cont’d) SQRT PFTK-simplified the more variable is, the more conservative is

19. 18 ns-2 example for Claim 1 Setting: a RED queue shared by equal number of TFRC and TCP flows, PFTK-simplified the larger p is, the more convex x->1/f(1/x) is => more conservative

20. 19 Recap osufficient conditions for the control to be conservative [(C) holds] ox->f(1/x) -- SQRT => conservative -- PFTK => overly conservative oloss process -- condition on second-order statistics oby-product: explained TFRC throughput-drop -- due to stochastic + convexity bias Next, another set of conditions -- identifies a control for which (C) not true

21. 20 Second set of conditions for (C) to hold, or not => (C) holds, conservative => (C) not holds, non-conservative (F2) x->f(1/x) concave (C2) (F2’) x->f(1/x) convex (C2’) (V) not a fixed constant

22. 21 When is the control non-conservative ? oSQRT: x->f(1/x) concave oPFTK formulae x->f(1/x) convex for small x, else, concave Example: (PFTK) Audio source packet send rate fixed, packets lengths varied Network packets dropped independently of their length (e.g. RED in packet-mode) SQRT PFTK-

23. 22 When is the control non-conservative ? -- ns-2 example L=8 (not shown), the same qualitative observations, but less pronounced (the last part of the claim) for PFTK, not conservative recall, x->f(1/x) is convex for PFTK for small x (large p) Setting: a rate control with fixed packet send rate, variable packet lengths, packets dropped with a fixed probability, L=4

24. 23 (TCP-f) Is control TCP-friendly ? not TCP-friendly ! even though it is conservative

25. 24 Part II Other factors (P) Is loss-event rate no better than TCP’s ? (F) Does TCP conform to its formula ?

26. 25 (P) Is loss-event rate better than TCP’s ? Sources may see different loss-event rates, another artifact of importance of viewpoint Claim 3: in many-sources regime seen by TCP seen by equation- based rate control seen by a non- adaptive sender (Poisson) many-sources regime = state of the network evolves independently of a single source

27. 26 (P) Is loss-event rate better than TCP’s ? (cont’d) made formal by Palm calculus (see paper) Intuition onon-adaptive sender (Poisson) would see time-average loss-event rate oan adaptive source samples ‘bad’ states less frequently othe more adaptive the source is, the smaller loss-event rate it would see oTCP would be more adaptive than an equation-based rate control

28. 27 ns-2 example for Claim 3 estimated loss-event rates

29. 28 (F) Does TCP conform to its formula ? TCP Sack1 => not always

30. 29 (TCP-f) Is control TCP-friendly ? The observed non TCP-friendliness is because TCP does not conform to its formula -- it is not an intrinsic problem of the control Ignoring this might lead a designer to try to “improve” her protocol -- wrongly so Guideline: check the factors separately !

31. 30 Part III Empirical study of the factors Check the factors separately oInternet measurements olab experiments Conclusion

32. 31 Internet measurements TCPTFRC Background Circles = PCs, Linux (FreeBSD, not in slides) TCP = Sack/Fack, D-Sack, timestamps, Linux-specific TFRC = experimental code (ICIR, 2000), we adapted to conform to TFRC spec Background = equal # of TCPs and TFRCs R = UMASS, INRIA, Melbourne, Caltech, KTH, Hong Kong Setting: 100 Mb/s 10 or 100 Mb/s Internet R Slides: R = UMASS Access at R = 100 Mb/s

33. 32 Internet measurements: EPFL -> UMASS (C) Is the control conservative ? => yes (F) Does TCP conform to its formula ? => not always (P) Is loss-rate no better than TCP’s ? => not always

34. 33 => no (TCP-f) Is the control TCP-friendly ? Internet measurements: EPFL -> UMASS both, (P) and (F) not true

35. 34 Lab experiments TCPTFRC 10 Mb/s Background qdisc = RED, Droptail delay= 50 ms Circles = PCs, Linux kernel 2.4.18 Setting: TCP, TFRC, Background = same as with lab experiments Delay = emulated by NIST Net 100 Mb/s

36. 35 Lab experiments with RED (cont’d) (C) Is the control conservative ? => yes (F) Does TCP conform to its formula ? => no, mostly overshoots (P) Is loss-rate no better than TCP’s ? => not always

37. 36 => yes Lab experiments with RED (cont’d) (TCP-f) Is the control TCP-friendly ?

38. 37 Lab experiments with DropTail (100 pkts) (C) Is the control conservative ? => yes (F) Does TCP conform to its formula ? => no (P) Is loss-rate no better than TCP’s ? => yes

39. 38 => not always if yes, mostly excessively Lab experiments with DropTail (100 pkts) (TCP-f) Is the control TCP-friendly ? (P) true, but large discrepancy

40. 39 oSeparate factors ! o(C) conditions for either conservative or non-conservative control -- TFRC throughput-drop explained -- a control with PFTK and fixed packet send rate intrinsically non-conservative for large loss-event rate o(P) in many-sources regime, expect loss- event rate be larger than TCP sees -- other regimes exist where (P) is not true o(F) TCP may deviate from PFTK formula Conclusion

41. 40 ovariability of round-trip time, its correlation with loss process -- do they matter ? oconservativeness -- seek for realistic cases when the control is non- conservative oloss-event rate -- when and why it is smaller (or larger) than TCP’s ? Further work