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
Poisson probes ?

Application
Sink
data packets

• 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.)

• 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 MM/M/1/K queue
  (expressions for 5 metrics of interest, including
  loss-related conditional probabilities)
• New analysis of the MM/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 MM/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
• TiDi 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
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

• Stationary version
• Optimal filter ? minimal mean-square error

System dynamics ?n1 ? ?n wn Measurement
mn p?n vn wn and vn white
noise variances Q and R
actualization
prediction
24
Optimal estimation - Kalman filter
25
To summarize
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

27
(No Transcript)
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
33
Optimal estimation - Wiener filter

• 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

43
(No Transcript)
44
(No Transcript)
45
(No Transcript)
46
(No Transcript)
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

49
Large audience multicast applications

• Motivation - Objective
• Kalman filter
• Wiener filter
• Least square estimation
• Extension

50
Extension
51
(No Transcript)
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 Source O mobile Object F
Forwarder reference
58
Forwarders mechanism description
S Source O mobile Object F
Forwarder reference
Migrating
Migrating
59
Forwarders mechanism description
S Source O mobile Object F
Forwarder reference
Update
O
60
Forwarders mechanism description
S Source O mobile Object F
Forwarder reference
F
O
Subsequent messages use new reference
61
Centralized mechanism description
S Source O mobile Object reference
62
Centralized mechanism description
S Source O mobile Object reference
63
Centralized mechanism description
S Source O mobile Object reference
64
Centralized mechanism description
S Source O mobile Object reference
65
Centralized mechanism the server

• may need to send Reply after processing request
  from Source

?
?
66
Mobile code applications

• Forwarders mechanism
• infinite state-space Markov chain
• expression for expected response time TF
• expression for expected number of forwarders
• Centralized mechanism
• finite state-space Markov chain
• expression for expected response time TS
• Models validated through simulations and
  experiments (LAN MAN)

67
Forwarder LAN (100 Mb/s)
Mean response time (ms) vs. communication rate
? migration rate
? 10
? 5
? 1
1 2 3 4 5 6 7 8
9 10 11
68
Server LAN (100Mb/s)
Mean response time (ms) vs. communication rate
? 10
? 5
? 1
1 2 3 4 5 6 7 8
9 10 11
69
Forwarder MAN (7Mb/s)
Mean response time (ms) vs. communication rate
? 10
? 5
? 1
1 2 3 4 5 6 7 8
9 10 11
70
Server MAN (7Mb/s)
Mean response time (ms) vs. communication rate
? 10
? 5
? 1
1 2 3 4 5 6 7
8 9 10 11
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!