無線區域網路中自我相似交通流量之成因與效能評估

The origin and performance impact of self-similar traffic for wireless local area networks

報 告 者：林 文 祺

指導教授：柯 開 維 博士

Outline Background of Self-Similarity Properties of WLAN Traffic Estimation of Self-Similar Traffic The Origin of Self-Similarity in WLAN Impact of Self-Similar to CSMA/CA

performance Impact of Self-Similar to CSMA/CA

performance with RTS/CTS

Background of Self-Similarity(1/8) Self-Similarity and Fractal

Background of Self-Similarity(2/8)

Statistics of Self-SimilarityDefinition of Self-Similar Stochastic Process:

, 0

H

E x atE x t a

a

2H

Var x atVar x t

a

2

( , ), x

H

R at ast s

axR

H: Hurst parameter or self-similarity parameter

Background of Self-Similarity(3/8)

Self-Similarity of StatisticsDefinition of Self-Similar Stochastic Sequence:( )

( 1)

1, 1,2,3,...

kmmk i

i km m

x x km

3 3 2 3 1 3

3k k k

k

x x xx

( ), 1

2m Var x

Var x Hm

Ex.

m xxR k R k

Background of Self-Similarity(4/8)

Properties of Self-Similarity Long range dependence

Slowly decaying variance

Heavy-tailed distribution

, 0 1C k k as k ,

11 ( ) Pr[ ] ~ , 0F x X x x

x , 當

( )m Var xVar x

m

Background of Self-Similarity(5/8)

Self-Similar Traffic

Background of Self-Similarity(6/8)

X(t) is a Pareto distribution random process with shape parameterαand location parameter k.

1

( )f xk

kx

1 , ; 0k

F x x kx

, 11

E X k

22

2 , 22 1

k

3

2H

Pareto Distribution:

Background of Self-Similarity(7/8) Variance-time Plot

( ), 1,2,3,...m Var x

Var x mm ～

log

log

md Var x

d m

( )log[ ( )] ~ log[ ( )] log( )mVar x Var x m

1 ( / 2)H

R/S Plot

jX =inflow during year j, 1 j N

M N = constant yearly outflow

jL =Reservoir level at end of year j, 1 j N

1

1 N

jj

M N XN

1

j

j kk

L X jM N

11max minj j

j Nj NR N L L

21

1 N

jj

S X M NN

log logR N

a H NS N

Background of Self-Similarity(8/8)

Properties of WLAN Traffic(1/2)

WLAN traffic

Time Unit=1 Sec

Time Unit=0.1 Sec

Time Unit=0.01 Sec

Basic: 1 μS

Aggregation: 1, 0.1, 0.01 Sec

Environment: 7NB

Poisson traffic

Properties of Real Network(2/2)

Time Unit=0.01 Sec

Time Unit=0.1 Sec

Time Unit=1 Sec

Estimation of Self-Similar Traffic(1/2)

• Packets Sequence on WLAN

Estimation of Self-Similar Traffic(2/2)

• Variance Plot & R/S Plot

Single Source without CSMA/CA

The Origin of Self-Similar Traffic (1/3)

The Origin of Self-Similar Traffic(2/3)

• Variance Plot & R/S Plot

The Origin of Self-Similar Traffic(3/3)

• Variance Plot & R/S Plot for WLAN based on single

Poisson Traffic. (Simulated)

Impact of Self-Similar to CSMA/CA performance(1/7)

Maximum throughput The influence of nodes on Self-Similar

Traffic and Poisson Traffic The influence of packet length on Self-

Similar Traffic and Poisson Traffic

Impact of Self-Similar to CSMA/CA performance(2/7)

0

1

2

3

4

5

6

7

8

0 10 20 30 40Node

Thro

ughp

ut（

Mbi

ts）

SS 1000SS 2000SS 250P 1000P 2000P 250

40

50

60

70

80

90

100

0 10 20 30 40Node

Util

izat

ion（

%）

SS 1000SS 2000SS 250P 1000P 2000P 250

Maximum throughput

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0 10 20 30 40

Node

Ave

rage

pac

ket d

elay

（se

c）

SS 1000SS 2000SS 250P 1000P 2000P 250

Impact of Self-Similar to CSMA/CA performance(3/7)

Maximum throughput

0

50

100

150

200

250

300

350

400

450

0 5 10 15 20 25 30 35 40

Nodes

Num

ber

of c

ollis

ions

SS 1000SS 2000SS 250P 1000P 2000P 250

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 20 40 60 80Load（%）

Thro

ughp

utM

bits

（）

SS, N=5SS, N=10SS, N=20P, N=5P, N=10P, N=20 0

10

20

30

40

50

60

70

80

0 20 40 60 80Load（%）

Util

izat

ion（

%）

SS, N=5SS, N=10SS, N=20P, N=5P, N=10P,N=20

Impact of Self-Similar to CSMA/CA performance(4/7)

The influence of nodes on Self-Similar Traffic and Poisson Traffic

0

50

100

150

200

250

0 20 40 60 80Load（%）

Num

ber o

f col

lisio

ns

SS, N=5SS, N=10SS, N=20P, N=5P, N=10P, N=20

0

0.0005

0.001

0.0015

0.002

0.0025

0 20 40 60 80Load（%）

Aver

age

pack

et d

elay

（se

c）

SS, N=5SS, N=10SS, N=20P, N=5P, N=10P, N=20

Impact of Self-Similar to CSMA/CA performance(5/7)

The influence of nodes on Self-Similar Traffic and Poisson Traffic

40

50

60

70

80

90

100

20 40 60 80 100Load（%）

Util

lizat

ion（

%）

SS 1000SS 2000SS 250P 1000P 2000P 250

Impact of Self-Similar to CSMA/CA performance(6/7)

The influence of packet length on Self-Similar Traffic and Poisson Traffic

2

2.5

3

3.5

4

4.5

5

5.5

6

6.5

7

20 40 60 80 100

Load(%)

Thro

ughp

ut(M

bits

)

SS 1000SS 2000SS 250P 1000P 2000P 250

0

50

100

150

200

250

20 40 60 80 100Load（%）

Num

ber o

f col

lisio

ns

SS 1000SS 2000SS 250P 1000P 2000P 250

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

20 40 60 80 100Load（%）

Aver

age

pack

et d

elay

（se

c）SS 1000SS 2000SS 250P 1000P 2000P 250

Impact of Self-Similar to CSMA/CA performance(7/7)

• The influence of packet length on Self-Similar Traffic and Poission Traffic

Maximum throughput The influence of nodes on Self-Similar

Traffic and Poisson Traffic The influence of packet length on Self-

Similar Traffic and Poisson Traffic

Impact of Self-Similar to CSMA/CA performance with RTS/CTS (1/4)

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

0 5 10 15 20 25 30 35 40Node

Thro

ughp

ut（

Mbi

ts）

SS 1000SS 2000SS 250P 1000P 2000P 250

50

55

60

65

70

75

80

85

0 5 10 15 20 25 30 35 40Node

Util

izat

ion（

%）

SS 1000SS 2000SS 250P 1000P 2000P 250

Impact of Self-Similar to CSMA/CA performance with RTS/CTS (2/4)

Maximum throughput

1

1.5

2

2.5

3

3.5

0 20 40 60 80Load（%）

Thro

ughput

Mbits

（）

SS, N=5SS, N=10SS, N=20P, N=5P, N=10P, N=20

0

10

20

30

40

50

60

70

80

0 20 40 60 80Load（%）

Util

izat

ion（

%）

SS, N=5SS, N=10SS, N=20P, N=5P, N=10P, N=20

Impact of Self-Similar to CSMA/CA performance with RTS/CTS (3/4)

The influence of nodes on Self-Similar Traffic and Poisson Traffic

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

20 40 60 80 100Load（%）

Thro

ughp

ut（

Mbi

ts）

SS 1000SS 2000SS 250P 1000P 2000P 250

35

40

45

50

55

60

65

70

75

80

85

20 40 60 80 100Load（%）

Util

izat

ion（

%）

SS 1000SS 2000SS 250P 1000P 2000P 250

Impact of Self-Similar to CSMA/CA performance with RTS/CTS (4/4)

The influence of packet length on Self-Similar Traffic and Poisson Traffic

Conclusion WLAN Traffic is Self-Similar regular & Single) WLAN Throughput at node=5 Max WLAN Throughput at node<5 Poisson>SS WLAN Throughput at node>5 Poisson<SS Impact of Packet Length RTS/CTS not influence the characteristic of Poisson and

Self-Similarity

Thanks for your attendance

Impact of Self-Similar to CSMA/CA performance The Number of Nodes increment form 1 to 5

0

1

2

3

4

5

6

7

8

1 2 3 4 5Node

Thro

ughput(

Mbits)

SS 1000SS 2000SS 250P 1000P 2000P 250

50

55

60

65

70

75

80

85

90

1 2 3 4 5Node

Utiliz

ation(%

)

SS 1000SS 2000SS 250P 1000P 2000P 250

Impact of Self-Similar to CSMA/CA performance The Number of Nodes increment form 1 to 5

0

20

40

60

80

100

120

140

1 2 3 4 5

Node

Num

ber

of

colli

sion(%

)

SS 1000SS 2000SS 250P 1000P 2000P 250

0

0.05

0.1

0.15

0.2

0.25

1 2 3 4 5

Node

Ave

rage

pac

ket d

elay

（se

c）SS 1000SS 2000SS 250P 1000P 2000P 250