Parameter Estimation and Performance Analysis of Several Network Applications

1. Parameter Estimation and Performance Analysis of Several Network Applications Sara Alouf Ph.D. defense - November 8, 2002 Advisor: Philippe Nain

2. Thesis topics Adaptive unicast applications • Background: network does not offer guarantee • Objective: estimate network internal state Large audience multicast applications • Background: need for membership estimates • Objective: efficiently track membership Mobile code applications • Background: existence of several mechanisms for objects communication • Objective: determine fastest among two of them

3. Thesis topics Adaptive unicast applications • Background: network does not offer guarantee • Objective: estimate network internal state Challenges: • efficient congestion control, good QoS Two distinct approaches: • adding intelligence to network • adding intelligence to applications • acquire some knowledge on network • change application policy accordingly

4. Adaptive unicast applications   K  Poisson probes  Methodology: • source probes network • having feedback from destination, source measures some performance metrics (e.g. loss probability, end-to-end delay, conditional loss probability, etc.) Application Sink data packets • given model for connection, metrics are expressed in terms of network internal state • given performance metrics, source infers network internal state

5. Adaptive unicast applications Main contributions: • Detailed analysis of the M+M/M/1/K queue (expressions for 5 metrics of interest, including loss-related conditional probabilities) • New analysis of the M+M/D/1/K queue (explicit information on stationary distribution; expressions for 3 metrics of interest) • Identification of “best” way of inferring network internal characteristics: use loss rate and network response time • given by M+M/M/1/K queue model

6. Thesis topics Adaptive unicast applications • Background: network does not offer guarantee • Objective: estimate network internal state Large audience multicast applications • Background: need for membership estimates • Objective: efficiently track membership Mobile code applications • Background: existence of several mechanisms for objects communication • Objective: determine fastest among two of them

7. Large audience multicast applications • Motivation - Objective • Kalman filter • Wiener filter • Least square estimation • Extension

8. Large audience multicast applications • Motivation - Objective • Kalman filter • Wiener filter • Least square estimation • Extension

9. Motivation • Interesting multicast applications (distance learning, video-conferences, events, radios, televisions (?), live sports(?), etc.) • Membership is required for: • feedback suppression (RTP, SRM) • tuning amount of FEC packets for reliability • pricing • stopping transmission when no more receivers and especially for radios and future TVs, to: • adapt transmission content, advertise, ...

10. Previous work • Need for unbiased estimator that efficiently uses previous estimates

11. Methodology • Source: • periodically requests from receivers to send ACK with probability p every S seconds • Receivers: • each S seconds, send ACK to source with prob. p • Source: • stores Yn number of ACKs received at time nS • Objective: use noisy observation Yn to estimate membership Nn = N(nS)

12. Naive estimation Drawbacks: • very noisy (s.l.l.n. lim N   Y/N = p) • no profit from correlation (no use of previous estimate)

13. Naive estimation : p= 0.01

14. Naive estimation : p= 0.50

15. EWMA estimation Advantages: • use of previous estimate • no a priori information needed Drawbacks: • what value for a ? • estimator does not depend on ACK interval S

16. EWMA estimation

17. Objective Use optimal filtering techniques to find estimator

18. Notation • Ti join time of participant i • Ti+Di leave time of participant i • N(t) number of participants at time t • Occupation process in the G/G/ queue • … not much is known about it …

19. Large audience multicast applications • Motivation - Objective • Kalman filter • Wiener filter • Least square estimation • Extension

20. M/M/ model - heavy traffic case • Assumptions: • Poisson arrival process, intensity lT • exponential on-times, parameter m • Occupation process in the M/M/ queue average membership: • Define normalized membership if T  , ZT(t)  Ornstein-Ühlenbeck process {B(t), t  0} standard Brownian motion

21. Optimal estimation - Kalman filter • Ornstein-Ühlenbeck process in discrete time wn are white noise with variance Q = r(1-g2)

22. Optimal estimation - Kalman filter • Number of ACKs at step n: Yn • Define normalized measurement ZT(nS) VT(n) • Weak limit T : vn are white noise with variance R = rp(1-p)

23. Optimal estimation - Kalman filter Error variance P = ([2 P + Q]1 + p2 /R)1 Filter gain K = Pp/R State estimator • Stationary version • Optimal filter  minimal mean-square error System dynamics n+1 = n+ wn Measurement mn=pn+ vn wnand vnwhite noise variancesQ and R prediction actualization

24. Optimal estimation - Kalman filter EWMA estimator

25. To summarize System state Measurement Estimation Continuous time Discrete time NT(t) Nn= NT(nS) normalize normalize normalize ZT(t) Zn= ZT(nS) Mn = pZn + VT(n) weakly weakly weakly weakly weakly X(t) n=X(nS) n+1=n+ wn mn=pn + vn Kalman filter

26. Simulations • Objective: validate model • Assumptions made in theory • Poisson arrivals • Exponential on-times • Heavy-traffic regime • Simulations: • 2 regimes investigated: light load/heavy-load • 2 distributions: Exponential/Pareto  8 different scenarios simulated

28. Validation with real traces • Objective: further validate model • Robustness to “real” distributions? • Independence-related assumptions are violated Distribution of traces investigated

29. Membership in real traces vs. time

30. Objective Find optimal estimator under more general assumptions

31. Large audience multicast applications • Motivation - Objective • Kalman filter • Wiener filter • Least square estimation • Extension

32. M/G/ model • Assumptions: • Poisson arrival process, intensity l • on-times have common probability distribution D denotes a generic random variable • Occupation process in the M/G/ queue • Characteristics of N(t) in steady-state: • Poisson random variable, Mean = Variance =r = l E[D] • Autocorrelation function • Notation:

33. Optimal estimation - Wiener filter yn Wiener filter Ho(z) • Noisy observation Yn Optimal linear filter  minimal mean-square error

34. Optimal estimation - Wiener filter Introduce: We have:

35. Application to M/M/ model

36. Application to M/M/ model Non-centered processes:

37. Kalman filter vs. Wiener filter Estimators are the same! But Kalman filter  M/M/ queue, heavy traffic Wiener filter  M/M/ queue • we relaxed one assumption

38. Large audience multicast applications • Motivation - Objective • Kalman filter • Wiener filter • Least square estimation • Extension

39. Optimal first-order linear filter

40. Optimal first-order linear filter

41. Validation with real traces

42. Distribution of inter-arrivals and on-times Almeroth & Ammar • inter-arrivals are exponentially distributed • on-time distribution: • Short sessions (1-2 days)  exponential • Long sessions  Zipf

47. Mean & Variance of the error theoretical empirical

48. And the winner is … Estimator ! Advantages: • optimal for M/M/ queue • efficient over real traces • only two parameters required Drawbacks: • a priori knowledge needed

49. Large audience multicast applications • Motivation - Objective • Kalman filter • Wiener filter • Least square estimation • Extension

50. Extension