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Parameter Estimation and Performance Analysis of Several Network Applications. Sara Alouf Ph.D. defense - November 8, 2002. Advisor: Philippe Nain. Thesis topics. Adaptive unicast applications Background: network does not offer guarantee Objective: estimate network internal state.

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Parameter Estimation and Performance Analysis of Several Network Applications


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parameter estimation and performance analysis of several network applications

Parameter Estimation and Performance Analysis of Several Network Applications

Sara Alouf

Ph.D. defense - November 8, 2002

Advisor: Philippe Nain

thesis topics
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
thesis topics3
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
adaptive unicast applications
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
adaptive unicast applications5
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
thesis topics6
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
large audience multicast applications
Large audience multicast applications
  • Motivation - Objective
  • Kalman filter
  • Wiener filter
  • Least square estimation
  • Extension
large audience multicast applications8
Large audience multicast applications
  • Motivation - Objective
  • Kalman filter
  • Wiener filter
  • Least square estimation
  • Extension
motivation
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, ...
previous work
Previous work
  • Need for unbiased estimator that efficiently uses previous estimates
methodology
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)
naive estimation
Naive estimation

Drawbacks:

  • very noisy (s.l.l.n. lim N   Y/N = p)
  • no profit from correlation (no use of previous estimate)
ewma estimation
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
slide17
Objective

Use optimal filtering techniques to find estimator

notation
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 …
large audience multicast applications19
Large audience multicast applications
  • Motivation - Objective
  • Kalman filter
  • Wiener filter
  • Least square estimation
  • Extension
m m model heavy traffic case
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

optimal estimation kalman filter
Optimal estimation - Kalman filter
  • Ornstein-Ühlenbeck process in discrete time

wn are white noise with variance Q = r(1-g2)

optimal estimation kalman filter22
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)

optimal estimation kalman filter23
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

to summarize
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

simulations
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

validation with real traces
Validation with real traces
  • Objective: further validate model
  • Robustness to “real” distributions?
  • Independence-related assumptions are violated

Distribution of traces investigated

slide30
Objective

Find optimal estimator under more general assumptions

large audience multicast applications31
Large audience multicast applications
  • Motivation - Objective
  • Kalman filter
  • Wiener filter
  • Least square estimation
  • Extension
m g model
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:
optimal estimation wiener filter
Optimal estimation - Wiener filter

yn

Wiener filter

Ho(z)

  • Noisy observation Yn

Optimal linear filter  minimal mean-square error

application to m m model36
Application to M/M/ model

Non-centered processes:

kalman filter vs wiener filter
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
large audience multicast applications38
Large audience multicast applications
  • Motivation - Objective
  • Kalman filter
  • Wiener filter
  • Least square estimation
  • Extension
distribution of inter arrivals and on times
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
mean variance of the error
Mean & Variance of the error

theoretical

empirical

and the winner is
And the winner is …

Estimator !

Advantages:

  • optimal for M/M/ queue
  • efficient over real traces
  • only two parameters required

Drawbacks:

  • a priori knowledge needed
large audience multicast applications49
Large audience multicast applications
  • Motivation - Objective
  • Kalman filter
  • Wiener filter
  • Least square estimation
  • Extension
large audience multicast applications52
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
thesis topics53
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
mobile code applications
Mobile code applications
  • Code mobility paradigm
  • Forwarders mechanism
  • Centralized mechanism
  • Simulations & experiments
  • Contributions
code mobility paradigm
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

code mobility paradigm56
Code mobility paradigm
  • Two widely used solutions:
    • distributed approach (use forwarders)
    • centralized approach (use server)
  • Objective: identify best approach in terms of response time
forwarders mechanism description
Forwarders mechanism: description

Host A

S

O

Host B

Host C

Host D

S : Source

O : mobile Object

F : Forwarder

reference

forwarders mechanism description58
Forwarders mechanism: description

Host A

S

Message

Forwarding

Forwarding

F

O

F

O

Host B

Host C

Host D

S : Source

O : mobile Object

F : Forwarder

reference

Migrating

Migrating

forwarders mechanism description59
Forwarders mechanism: description

Host A

S

F

F

Host B

Host C

Host D

S : Source

O : mobile Object

F : Forwarder

reference

Update

O

forwarders mechanism description60
Forwarders mechanism: description

Host A

S

F

Host B

Host C

Host D

S : Source

O : mobile Object

F : Forwarder

reference

F

O

Subsequent messages use new reference

centralized mechanism description
Centralized mechanism: description

Host A

Server

S

O

Host B

Host C

Host D

S : Source

O : mobile Object

reference

centralized mechanism description62
Centralized mechanism: description

Host A

Server

S

Migrating

Update

O

Host B

Host C

Host D

S : Source

O : mobile Object

reference

centralized mechanism description63
Centralized mechanism: description

Host A

Server

S

Message

Migrating

Update

Fail

O

Host B

Host C

Host D

S : Source

O : mobile Object

reference

centralized mechanism description64
Centralized mechanism: description

Host A

Server

Query

location

S

!

Object may have moved in the meantime

Reply

Message

O

Host B

Host C

Host D

S : Source

O : mobile Object

reference

centralized mechanism the server
Centralized mechanism: the server

send Reply

S

S

S

O

O

  • may need to send Reply after processing request from Source

mobile code applications66
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)
slide67

Forwarder LAN (100 Mb/s)

Mean response time (ms) vs. communication rate

 migration rate

 = 10

 = 5

 = 1

12 3 4 5 6 7 8 9 10 11

slide68

Server LAN (100Mb/s)

Mean response time (ms) vs. communication rate

 = 10

 = 5

 = 1

12 3 4 5 6 7 8 9 10 11

slide69

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

slide70

Server MAN (7Mb/s)

Mean response time (ms) vs. communication rate

 = 10

 = 5

 = 1

1234 5 6789 10 11

slide71
Overall performance is fair

models can safely be

  • used for performance evaluation
mobile code applications72
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
conclusion
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
conclusion74
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