Internet Traffic Constancy and Predictability | CS 7270, Papers of Computer Science

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Internet traffic constancy and

predictability

Zhongtang Cai

Talk Outline

„^

Paper discussed: On the Constancy of Internet PathProperties.

Yin Zhang, Nick Duffield, Vern Paxson, Scott

Shenker. „^

Motivation

„^

Three notions of constancy^ „

Mathematical „^

Operational „^

Predictive

„^

Constancy of three Internet path properties^ „

Packet loss „^

Packet delays „^

Throughput

„^

Conclusions

Mathematical Constancy

„

Mathematical Constancy^ „

A dataset is

mathematically steady

if it can be

described with a mathematical model.

„^

Simplest form: IID – independent and identically distributed „^

Key:

finding the appropriate model

„

Examples^ „

Mathematical constancy

„^

Session arrivals are well described by a fix-rate Poissonprocess over time scales of 10 minutes to an hour [PF95]

„^

Mathematical non-constancy

„^

Session arrivals over larger time scales

Operational Constancy

„

Operational constancy^ „

A dataset is

operationally steady

if the quantities

of interest remain within bounds consideredoperationally equivalent

„^

Key:

whether an application cares about the changes

„

Examples^ „

Operationally but not mathematically steady

„^

Loss rate remained constant at 10% for 30 minutes andthen abruptly changed to 10.1% for the next 30 minutes.

Analysis Method

„

Mathematical constancy^ „

Identify change-points and partition a timeseries intochange-free regions (CFR)

„^

Test for IID within each CFR

„

Operational constancy^ „

Define operational categories based onrequirements of real applications

„

Predictive constancy^ „

Evaluate the performance of commonly usedestimators

„^

Exponentially Weighted Moving Average (EWMA) „^

Moving Average (MA) „^

Moving Average with S-shaped Weights (SMA)

Predictive Constancy of Loss Rate

„

Estimators^ „

MA, SMA, EWMA

MA

H

Moving

Average

L

S^

H t L

=

⁄

i =

1 M^

Y^

H t

−

i

L

M^

,^

M^

r^

1

SMA

H

S^

−^

shaped

Moving

Average

L

S^

H t L

=

⁄

i =

1 M^

w^ i

Y H

t^

−^

i L

⁄

i =

1 M^

w^ i

,^

M^

r^

1

EWMA

H

Exponentially Weighted Moving Average

L

S^

H t L

= α

Y^

H t L

+

H

1

− α

L S

H

t^

−^

1 L

αε

@ 0, 1

D.

Testing for Change-Points -

CP/RankOrder

„^

Analyze ranks – resistant to the presence ofoutlier

„^

Find a candidate change-point

For

H

X

L i

i

n

r i^

: rank of X

i

S

i

=

‚^ j

i =^1

r

j

S

i

=

i

H

n

+

^1

L ê

^2

S

** ** i =

»

S

i

−

S

i

»

Candidate change

−

point at i

τ^

s.t.

S

i τ

** **^

>

S

i

^ ,

where 1

b

i

b

n,

i

≠

i

τ

Testing for Change-Points -

CP/RankOrder(Cont’d)

„^

Bootstrap analysis

A. Let S

diff

= S

max

− S

min

,^

where

S^ max

=

max i =

1,...,n

H S^ i

L

S^ min

=

min i =

1,...,n

H S^ i

L

B. Generate bootstrap sample : x

k , 1

x

k , 2

...,

x

k ,n

1

b

k

b

M.

H Sampling wo

ê

replacement

L

C. Calculate

kS diff

,^

1

b^

k^

b^

M

Y^ k

= 9

(^1)

if S

k^ diff

<^

S^ diff

0

if S

k^ diff

r^

S^ diff

,

X^

=^

‚ k = M Y^1

,k

Change

−

point at i

τ^

with confidence Level

=

^100

X M

%

Datasets Description

„

Two main sets of data^ „

Winter 1999-2000 (

W

„^

Winter 2000-2001 (

W

113M

W

2

NIMIsites

253M

W

1

W

2

140M

W

1

transfers

thruput

traces

packets

packettraces

Dataset

Individual Loss vs. Loss Episodes

„^

Traditional approach – look at individual losses[Bo93,Mu94,Pa99,YMKT99].^ „

Correlation reported on time scales below 200-1000 ms

„^

Our approach – consider

loss episodes

„^

Loss episode: a series of consecutive packets that are lost „^

Loss episode process – the time series indicating when aloss episode occurs

„^

Can be constructed by collapsing loss episodes and thenon-lost packet that follows them into a single point.

loss process

episode process

Source of Correlation in the

Loss Process(Cont’d)

• Individual Loss vs. Loss Episodes •Loss process is not IID. Loss episode process can beviewed as IID

Traces consistent with IID

Episode

Loss

Poisson Nature of

Loss Episodes within CFRs

„

Independence of loss episodes withinchange-free regions (CFRs) „

Exponential distribution of interarrivals withinchange-free regions^ „

85% CFRs have exponential interarrivals

IID CFRs

IID traces

Loss episodes are well modeled as homogeneous

Poisson process within change-free regions.

Mathematical Constancy of

Loss Episode Process

Cumulative Probability „^

X: size of the largest CFR found for each trace^ „

CFR: Change Free Regions. (Change-point test)

„^

“Lossy” traces are traces with overall loss rate over 1%^ „

Only 50% with largest CFR>20mins „^

Higher loss rate makes the loss episode process less steady

„^

All traces: more than half of the traces are steady over fullhour

Operational Constancy of Loss Rate^ „

Loss rate categories^ „

„

Probabilities of observing a steady intervalof 50 or more minutes „

.

Episode

1 min

Loss

Episode

10 sec

Loss

Prob.

Type

Interval to calculate loss

rate: