Long-Run Behavior of Equation-Based Rate Control: Theory and its Empirical Validation

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

2. My thesis • equation-based rate control-- is it TCP friendly ? • increase-decrease controls-- e.g. TCP-- fairness in bandwidth sharing • expedited forwarding-- queueing bounds for diffserv EF • input-queued switch-- scheduler latency This talk:

3. Problem we study • TCP -- Internet predominant transport protocol; implements a window-based transmission control • Equation-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 • Controls need to be TCP-friendly -- an axiom established by part of Internet research community (mid-nineties) non-TCP non-TCP Internet TCP TCP

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

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

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

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

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

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

10. Viewpoint matters ! (Feller’s, Bus stop paradox-like) an observer sampling at the points a random observer falls more likely into a large Sn if Xn is positively correlated to Sn, then it sees more than E[X0] (convention: 0 an arbitrary fixed point)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 a non-adaptive sender (Poisson) seen by equation-based rate control seen by TCP many-sources regime = state of the network evolves independently of a single source

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

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

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

29. (TCP-f) Is control TCP-friendly ? The observed non TCP-friendlinessis 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 !

30. Part IIIEmpirical study of the factors Check the factors separately • Internet measurements • lab experiments Conclusion

31. Internet measurements Setting: TCP TFRC • 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 Background 100 Mb/s Internet 10 or 100 Mb/s Slides: R = UMASSAccess at R = 100 Mb/s R Circles = PCs, Linux (FreeBSD, not in slides)

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

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

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

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

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

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

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

39. Conclusion • Separate factors ! • (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 • (P) in many-sources regime, expect loss-event rate be larger than TCP sees-- other regimes exist where (P) is not true • (F) TCP may deviate from PFTK formula

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