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 å acquire some knowledge on network å change application policy accordingly

4. Adaptive unicast applications Application Poisson probes  data packets Sink 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.) K    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 è 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 Y n number of ACKs received at time nS Objective: use noisy observation Y n to estimate membership N n  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  ? estimator does not depend on ACK interval S

16. EWMA estimation

17. Objective Use optimal filtering techniques to find estimator

18. Notation T i join time of participant i T i +D i 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 T exponential on-times, parameter   Occupation process in the M/M/  queue average membership: if T  , Z T (t)  Ornstein-Ühlenbeck process {B(t), t  0} standard Brownian motion Define normalized membership

21. Optimal estimation - Kalman filter Ornstein-Ühlenbeck process in discrete time w n are white noise with variance Q =  (1  2 )

22. Number of ACKs at step n : Y n Define normalized measurement Weak limit T   : Optimal estimation - Kalman filter v n are white noise with variance R =  p(1  p) Z T (nS) VT(n)VT(n)

23. Optimal estimation - Kalman filter Stationary version Optimal filter  minimal mean-square error System dynamics  n+1    n  w n Measurement m n  p  n  v n w n and v n white noise variances Q and R Error variance P = ( [  2 P + Q]  1 + p 2 / R )  1 Filter gain K = Pp/R State estimator actualizationprediction

24. Optimal estimation - Kalman filter EWMA estimator

25. Kalman filter To summarize Estimation ZT(t)ZT(t) X(t)X(t) NT(t)NT(t) Continuous time System state normalize weakly Z n = Z T (nS)  n  X(nS)  n+1   n + w n N n  N T (nS) Discrete time weakly normalize M n = p Z n + V T (n) m n  p  n + v n Measurement weakly normalize

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  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   D   Autocorrelation function Notation:

33. Optimal estimation - Wiener filter ynyn Wiener filter H o (z) Optimal linear filter  minimal mean-square error Noisy observation Y n

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

35. Application to M/M/  model

36. Non-centered processes:

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

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

39. 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 … Advantages: optimal for M/M/  queue efficient over real traces only two parameters required Drawbacks: a priori knowledge needed Estimator !

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

52. Large audience multicast applications Main contributions: Proposition of several unbiased estimators that efficiently track membership Validation through simulated and real traces Identification of “best” estimator among those proposed Proposition of estimators for a priori parameters

53. 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

54. Mobile code applications Code mobility paradigm Forwarders mechanism Centralized mechanism Simulations & experiments Contributions

55. Code mobility paradigm Definition: components of application might change host (migrate) during execution Utility: load balancing data mining (data available on different hosts) e-commerce (find the cheapest airline fare) Issue: ensure communications with mobile objects

56. Code mobility paradigm Two widely used solutions: distributed approach (use forwarders) centralized approach (use server) Objective: identify best approach in terms of response time

57. Forwarders mechanism: description S Host A O Host BHost CHost D S : Source O : mobile Object F : Forwarder reference

58. Forwarders mechanism: description S Host A Host B O Host CHost D S : Source O : mobile Object F : Forwarder reference Message Forwarding FO F Migrating

59. Forwarders mechanism: description Host B F Host C O Host D S : Source O : mobile Object F : Forwarder reference Update F S Host A

60. Forwarders mechanism: description Host B F Host C O Host D S : Source O : mobile Object F : Forwarder reference F S Host A Subsequent messages use new reference

61. Centralized mechanism: description S Host A O Host BHost CHost D S : Source O : mobile Object reference Server

62. Centralized mechanism: description S Host A Host B O Host CHost D S : Source O : mobile Object reference Migrating Server Update

63. Centralized mechanism: description S Host A Host BHost CHost D S : Source O : mobile Object reference Message Migrating O Server Update Fail

64. Centralized mechanism: description S Host A Host BHost CHost D S : Source O : mobile Object reference O Server Query location Reply Message Object may have moved in the meantime !

65. Centralized mechanism: the server may need to send Reply after processing request from Source S O S send Reply S O  

66. Mobile code applications Forwarders mechanism: 4 infinite state-space Markov chain  expression for expected response time T F 4 expression for expected number of forwarders Centralized mechanism: 4 finite state-space Markov chain  expression for expected response time T S Models validated through simulations and experiments (LAN & MAN)

67. Forwarder LAN (100 Mb/s) = 10 = 1 = 5 1 2 3 4 5 6 7 8 9 10 11 Mean response time (ms) vs. communication rate migration rate

68. Server LAN (100Mb/s) = 5 = 1 = 10 1 2 3 4 5 6 7 8 9 10 11 Mean response time (ms) vs. communication rate

69. Forwarder MAN (7Mb/s) = 10 = 5 = 1 1 2 3 4 5 6 7 8 9 10 11 Mean response time (ms) vs. communication rate

70. Server MAN (7Mb/s) = 10 = 5 = 1 1 2 3 4 5 6 7 8 9 10 11 Mean response time (ms) vs. communication rate

71. Overall performance is fair models can safely be  used for performance evaluation

72. Mobile code applications Main contributions: Proposition of Markovian models for two communication mechanisms Validation through simulations and experiments (LAN & MAN) Theoretical comparison:  prediction of fastest mechanism in general

73. Conclusion General methodology Propose mathematical models for system at hand Derive metrics of interest or estimators under models assumptions Validate models via simulations and/or experiments Simple tools applicable over wide range of applications

74. Conclusion Optimal filtering techniques estimation of RTT in TCP protocol estimation of average queue size in RED routers … Performance analysis tools very useful in design of mobile code applications (high cost of implementation) protocol evaluation …

75. Thank you!