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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

Large audience multicast applicationsLarge audience multicast applicationsLarge audience multicast 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

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 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

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 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 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

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

Large audience multicast applications

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

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

- Need for unbiased estimator that efficiently uses previous estimates

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

Drawbacks:

- very noisy (s.l.l.n. lim N Y/N = p)
- no profit from correlation (no use of previous estimate)

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

Objective

Use optimal filtering techniques to find estimator

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 applications

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

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

- Ornstein-Ühlenbeck process in discrete time

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

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 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=pn+ vn

wnand vnwhite noise

variancesQ and R

prediction

actualization

Optimal estimation - Kalman filter

EWMA estimator

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=pn + vn

Kalman filter

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

- Objective: further validate model
- Robustness to “real” distributions?
- Independence-related assumptions are violated

Distribution of traces investigated

Objective

Find optimal estimator under more general assumptions

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

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

yn

Wiener filter

Ho(z)

- Noisy observation Yn

Optimal linear filter minimal mean-square error

Application to M/M/ model

Non-centered processes:

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

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

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

And the winner is …

Estimator !

Advantages:

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

Drawbacks:

- a priori knowledge needed

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

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 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

- Code mobility paradigm
- Forwarders mechanism
- Centralized mechanism
- Simulations & experiments
- Contributions

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 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

Host A

S

O

Host B

Host C

Host D

S : Source

O : mobile Object

F : Forwarder

reference

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: description

Host A

S

F

F

Host B

Host C

Host D

S : Source

O : mobile Object

F : Forwarder

reference

Update

O

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

Host A

Server

S

O

Host B

Host C

Host D

S : Source

O : mobile Object

reference

Centralized mechanism: description

Host A

Server

S

Migrating

Update

O

Host B

Host C

Host D

S : Source

O : mobile Object

reference

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: 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

send Reply

S

S

S

O

O

- may need to send Reply after processing request from Source

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)

Mean response time (ms) vs. communication rate

migration rate

= 10

= 5

= 1

12 3 4 5 6 7 8 9 10 11

Mean response time (ms) vs. communication rate

= 10

= 5

= 1

12 3 4 5 6 7 8 9 10 11

Mean response time (ms) vs. communication rate

= 10

= 5

= 1

1 2 3 4 5 6 7 8 9 10 11

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

- 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

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
- …

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