The Final Present

The Final Present

Lee Jeng-Shiou

Computer Network of E.E

Outline Throughput Analysis Review for Single-hop Netw

orks Throughout Analysis for Multi-hop Networks Mathematical Analysis of the String Topology Analytical and Simulation Results An Alternative Mathematical Analysis of the Strin

g Topology Conclusion

Throughput Analysis Review for Single-hop Networks (s(t), b(t))

s(t): the backoff stage b(t): the backoff time counter p: the conditional collision probability τ: the probability that a station transmits in a generic slot time

Throughput Review for Single-hop Networks (cont~) The transmission probability τ in a randoml

y chosen ”generic” slot is

The collision probability is expressed by

Throughput S is obtained by

0

2(1 2 )

(1 2 )( 1) (1 (2 ) )

m

mi

p

p W pW p

11 (1 )np

cstrsstrtr

str

TPPTPPP

PEPPS

)1()1(

][

Throughout Analysis for Multi-hop Networks We concentrate on the impact of the hidden node

problem. We analyze the throughput based on a single

station’s point of view. The analysis method is similar to the single-hop

case. Obtaining the stationary probability τ using a Markov

model. Expressing the throughput as function of τ by studying

the events that can occur within a generic slot time.

Throughout Analysis for Multi-hop Networks Assumption:

All packets are destined for neighbor nodes.

There is no capture effect. Each station always has packets to trans

mit.

A Simplified Condition The carrier sense range is equal to the

transmission range.

BA

R=r

A1

A Simplified Condition (cont~)

A Simplified Condition (cont~) The simulations have been done by the network si

mulator - ns2. Simulation area 1500x1500 m2. We consider five topology scenarios and each sce

nario includes four traffic patterns. Each node generates packets based on CBR model

with packet sizes 256, 512, 1024 and 2048 bytes. They correspond to packet arrival interval of 0.001

3, 0.0026, 0.0052 and 0.01 sec.

A Simplified Condition (cont~)

A Simplified Condition (cont~)

A Simplified Condition (cont~)

A Realistic Carrier Sense Range The carrier sense range is 550 meters and th

e transmission range is 250 meters.

BA

R

r

A1

A Realistic Carrier Sense Range (cont~)

A Realistic Carrier Sense Range (cont~)

A Realistic Carrier Sense Range (cont~)

Throughout Analysis for Single-hop Networks (cont~)

Throughout Analysis for Single-hop Networks (cont~)

Conclusions The throughput performance of the IEEE

802.11 DCF scheme in multi-hop ad hoc networks is analyzed.

It also shows the proposed model is accurate when degenerated into single-hop networks.

The throughput of a single station is decreased as the number of stations increases.

The total throughout almost stays at a constant value.

Conclusions (cont~) The total network throughput is decreased

as much as by 55% when the carrier sense range is equal to 550 meters.

The larger packet size results in the higher network throughput.

For spatial reuse factor, the results shows that there no clear relationship with the number of stations and packet size.

Mathematical Analysis of the String Topology

6 4 2 0 1 3 5

Mathematical Analysis of the String Topology (cont.)

Six possible situations observed by station 0 at the beginning of a slot.

Node 0 “idle” (1-τ) (cont.)

One of n1 and n2 Tx (P2) (assume n1 Tx)

(2)

0 1

0 1 3

Success(n2 idle)

Collided byhidden node

(n2 tx during Tv)

1/2

1/2

Psucc

Pcoll

T2_1_succ

1/2

1/2

0 12

0 12

T2_1_1_coll

T2_1_2_coll

0 12

0 12

1/2

1/2

T2_2_1_coll

T2_2_2_coll

n2 idle

n2 tx during Tv

T2_2_succPsucc

Pcoll

0 1 324

0 1 324

success: n2 idle during

collision: n2 Tx during Tv

0 1 324

Mathematical Analysis of the String Topology (cont.)

1 1 1

2 2 2_1_ 2_1_ 2_1_ 2 _1_1_ 2 _1_ 2_

2 _ 2_ 2 _ 2_ 2_ 2_ 2 _ 2_1_ 2 _ 2_ 2_

3 3 3

4 4 4_ 4 _

(1 )

1 1 1(1 ) { [ ( )]

2 2 21 1 1

[ ( )]}2 2 2(1 )

[

succ succ coll coll coll

succ succ coll coll coll

succ s

L P T

L P P T P T T

P T P T T

L P T

L P P T

4 _ 4_

5 5 5_1 5_ 2_ 5_ 2_ 5_ 2 _ 5_ 2 _ 5_ 3

5_ 4_ 5_ 4 _ 5_ 4 _ 5_ 4 _

6 6 6

]

1 1 1{ [ ]

4 4 41

[ ]}4

ucc coll coll

succ succ coll coll

succ succ coll coll

P T

L P T P T P T T

P T P T

L P T

4 4_ 5 5_ 2_ 5_ 4_

1 2 3 4 5 6

1[ [ ] ( [ ] [ ])]

4succ succ succP P E P P P E P P E PS

L L L L L L

26

Analytical and Simulation Results (cont.)

The simulation throughput (13 stations) and the analytical throughput.

An Alternative Mathematical Analysis of the String Topology

One directional traffic between two stations

No collisions

->

0 1

min

1The avg. backoff time

2 3 ec10 s

CW aSlotTime

An Alternative Mathematical Analysis of the String Topology (cont.)

The normalized throughput of the basic access scheme when there is one traffic.

PktSize

(byte)

DIFS + Avg. Backoff + Time + Data + SIFS + ACK

Total(μsec)

Normalized

Throughput

　 Max.Throughpu

t(backoff=0)

256 50+310+342*8/2+10+152 1890 0.601058 0.718987

512 50+310+598*8/2+10+152 2914 0.741249 0.829493

1024 50+310+1110*8/2+10+152 4962 0.848045 0.904557

2048 50+310+2134*8/2+10+152 9058 0.916759 0.949246

An Alternative Mathematical Analysis of the String Topology (cont.)

The normalized throughput of the RTS/CTS access scheme when there is one traffic.

PktSize(byt

e)

DIFS + Avg. Backoff + Time + RTS + CTS

+ Data + SIFS + ACK

Total(μse

c)　

Normalized

Throughput

　 Max.Throughpu

t(backoff=

0)

25650+310+176+10+152+10+342*8

/2+10+1522238 0.507596 0.589212

51250+310+176+10+152+10+598*8

/2+10+1523262 0.662170 0.731707

1024

50+310+176+10+152+10+1110*8/2+10+152

5310 0.792467 0.841600

2048

50+310+176+10+152+10+2134*8/2+10+152

9406 0.882841 0.912929

An Alternative Mathematical Analysis of the String Topology (cont.)

Bi-directional traffic between two stations

Collisions may occur. Evaluating the average backoff time

All newly generated backoff values, such as X ,Y ,and M ,are identically distributed from uniform distribution.

where A represents the CWmin

0 1

1( ) , ( ) , 0X X

xf x F x x A

A A

An Alternative Mathematical Analysis of the String Topology (cont.)

Let Z=|X-Y|. We have

A newly generated backoff value is M with the probability distribution as X, and Y. Let W=|M-Z|. We have

-> Z and W are identical distribution. The expected backoff interval is

2( ) (1 ), 0Z

zf z z A

A A

2( ) (1 ), 0W

wf w w A

A A

min( , ), 4

sec4

155

U

AU X Z m

AaSlotTime

An Alternative Mathematical Analysis of the String Topology (cont.)

Evaluating the collision probability2 1

[collision] [ 1] (1 )2

2[succes

2

3129

3s

1] 1

31

P P wA A

P

An Alternative Mathematical Analysis of the String Topology (cont.)

The normalized throughput of the basic access scheme considering the collisions when there is two traffic.

PktSize(byt

e)

DIFS + Avg. Backoff + Time + Data + SIFS + ACK

Total(μsec)

Normalized

Throughput

Max.Throughp

ut(backoff=

0)

Simulation

Throughput

25629/31*(50+155+342*8/2+10+1

52+50) +2/31*(50+155+342*8/2+162)

1781.77

0.596433 0.653262 0.649542

51229/31*(50+155+598*8/2+10+1

52+50) +2/31*(50+155+598*8/2+162)

2805.77

0.720174 0.762285 0.770645

1024

29/31*(50+155+1110*8/2+10+152+50)

+2/31*(50+155+1110*8/2+162)

4853.77

0.811022 0.837775 0.853088

2048

29/31*(50+155+2134*8/2+10+152+50)

+2/31*(50+155+2134*8/2+162)

8949.77

0.867984 0.883281 0.899572

An Alternative Mathematical Analysis of the String Topology (cont.)

The normalized throughput of the RTS/CTS access scheme considering the collisions when there is two traffic.

PktSize(byt

e)

DIFS + Avg. Backoff + Time + RTS + CTS + Data + SIFS + ACK

Total(μsec)

Normalized

Through-put

Max.Throughp

ut(backoff

=0)

Simulation

Through-put

256

29/31*(50+155+176+10+152+10+342*8/2

+10+152+50) +2/31*(50+155+176+162)

2030.42

0.523394

0.566652 0.55067

6

512

29/31*(50+155+176+10+152+10+598*8/2

+10+152+50)+2/31*(50+155+176+162)

2988.35

0.676173

0.713163 0.69984

0

1024

29/31*(50+155+176+10+152+10+1110*8/2

+10+152+50)+2/31*(50+155+176+162)

4904.23

0.802678

0.828875 0.81963

4

2048

29/31*(50+155+176+10+152+10+2134*8/2

+10+152+50)+2/31*(50+155+176+162)

8735.97

0.889227

0.905289 0.89957

2

Appendix (simulation results)

Appendix (simulation results)

Appendix (simulation results)

Appendix (simulation results)

Conclusions We first analyze the transmission behavior of stations in

a string topology in the multi-hop environment. In the presence of the hidden and exposed terminal

problems, the mathematical analysis is more complicated compared to the single-hop wireless network.

From the analytical and simulation results, we find that a larger packet size can increase the normalized throughput.

Conclusions (cont.) For future research, we will proceed with the

alternative mathematical analysis. We may discuss the behavior under the

assumption that the carrier sensing range is much larger than the transmission range, and the capture effect may be included.

Besides, we may extend our one-dimension topology to different types of topology.

Conclusion

What we have done We propose a new method to improve

IEEE 802.11 performance and establish a model for analysis.

Simulation and comparison What we are going to do

A general equation (even solution) for our model

More simulation