qingjiang tian and edward j. coyle center for wireless systems and applications ( cwsa )

1SenMetrics’05, San Diego, 07/21/2005

SOSBRA: SOSBRA: A MAC-Layer A MAC-Layer Retransmission Algorithm Designed Retransmission Algorithm Designed

for thefor the Physical-Layer Characteristics Physical-Layer Characteristics of Clustered Sensor Networksof Clustered Sensor Networks

Qingjiang Tian and Edward J. Coyle

Center for Wireless Systems and Applications (CWSA)

School of Electrical and Computer Engineering

Purdue University

{tianq,coyle}@ecn.purdue.edu


OutlineOutline

Background

SOSBRA Approach for Clustered Sensor Networks

Numerical Results

Optimal Contention Window

Conclusions


IntroductionIntroduction

Design for Energy Efficiency Through All Layers of the Protocol Stack

Cross-Layer Design to Improve Performance• Need to avoid fragility

My Work: Physical-MAC Layer Interface• Small Propagation delay in sensor

net applications• Opportunity to redesign

Retransmission algorithms

Physical

Energy

Efficiency

MAC

Network

Application


BackgroundBackground

General – 802.11 MAC Layer• CSMA/CA Collision Avoidance• Binary Exponential Backoff• Homogeneous peer-to-peer• Designed for hidden nodes (RTS-CTS Handshake)

V. Bharghavan, “MACAW: A Media Access Protocol for Wireless LANS” • All nodes can hear each other

Y. Kwon,etc, “A Novel MAC Protocol with Fast Collision Resolution for Wireless LANs” • multiplicative-increase, linear-decrease

C. Wang,etc, “A new collision resolution mechanism to enhance the performance of IEEE 802.11 DCF,”• contention window size is halved after c consecutive successful

transmission


Motivation for My WorkMotivation for My Work

IEEE 802.11 Distributed Coordination Function (DCF)• Called WiFi• Homogeneous, peer-to-peer Communications• Binary exponential backoff & cross-stage collisions


Motivation for My WorkMotivation for My Work

Clustering in Sensor Networks

• Clusterhead: central control, broadcasting, synchronization of other nodes

• Energy efficiency is a goal• Increase throughput on the

channel» Minimize collisions and idle time

• Very Small Propagation Delayfd

SENSOR

fd

SENSOR

fd

SENSOR

fd

SENSOR

fd

SENSOR

fd

SENSOR

fd

SENSOR

100m


SOSBRA: SOSBRA: Synchronized, One-Stage-Backoff Synchronized, One-Stage-Backoff

Retransmission AlgorithmRetransmission Algorithm

Assumptions• One-hop cluster considered• Traffic model: collect one packet from each node

within the cluster • We ignore the small propagation delay between

sensor nodes and CH• All nodes within one cluster can be synchronized to

within 1 microsecond• Synchronization beam – similar to ZigBee – starts

“rounds” or retransmissions on the channel• Nodes can sense each other’s activity


SOSBRA ApproachSOSBRA Approach

1. Each node that needs to either transmit or retransmit at the beginning of a round will chose a slot at random in a contention window of size W for its retransmission.

2. Nodes that transmit without collision are done.

3. Nodes in collisions in the current round will reschedule transmissions in the next round of W slots.

4. W is the same for every round.


SOSBRA vs 802.11 DCFSOSBRA vs 802.11 DCF

A A

A C

Standard 802.11 DCF

1 2…………………W 1 2 ……………. W

New Round

A B

SOSBRA-based802.11 DCF

Window 1 Window 2

B C

B

A B C


PerformancePerformance AnalysisAnalysis

N: Total non-CH nodes within the clusterW: fixed one stage contention window :Total time required to collect one packet from each node : The duration of a RTS collision : The duration of a data packet transmission

W)(N,TE

DIFSEIFSRTSC TTTT

DIFSACKSIFSDATACTSRTSD TTTTTTT 3



No collisions

NN

NsW

W

W

NWWWP

)()1(....)1(

DE TNWT

(1)

(2)



N1 nodes succeed in the first round and all of remaining N2 nodes succeed in the second round,C1 collisions in the first round

DC

DCD

E

TTcW

TnWTcTnW

TTT

N2

1

211

21

NN

n

W

nW

W

cnNScc

nWW

n

N

cnNP

2

11211

1

1

1111

)(),()!()(

} round second in the collisions no ,C ,{

1

(3)

(4)



(5)

DC

I

ii

DI

I

iDiCi

I

iiE

TNTcWI

TnWTnTcW

TWNT

)(

)()(

),(

1

1

1

1

1

(6)

•General Case

I

i

nI

rn

in

N

n

II

W

nW

W

crScc

nW

n

rn

W

crScc

nW

n

CcCcCnNnNnNP

)(...

),()!(-W

)(

...

),()!(-W

)(N

)} c ,...,,(),,...,,{(

ii

1

1

ii21

1

i

ii

11211

1

1

1-I1-I22112211


Numerical And Simulation Numerical And Simulation ResultsResults

Fig.1 Numerical results for the probability mass function of , the total time to empty the cluster, for the SOSBRA-based 802.11 protocol.

Here, N =50 nodes and W =120.

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

x 104

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

Total Time to Empty the Cluster

Pro

babi

lity

Mas

s fu

nctio

n

ET



Fig. 2 Simulations for the SOSBRA-based 802.11 protocol that show during empty the cluster for different contention window sizes.

is the number of nodes in the cluster.

0 200 400 600 800 1000 12000

500

1000

1500

2000

2500

3000

Contention Window Size

To

tal W

ast

ed

Tim

e D

uri

ng

Em

pty

ing

the

Clu

ste

r

N=20N=30N=50N=100

NWT



Fig.3 Simulations for the SOSBRA-based 802.11 protocol that show the average channel throughput during the emptying the cluster for different

contention window sizes. N is the number of nodes in the cluster.

0 200 400 600 800 1000 12000.86

0.87

0.88

0.89

0.9

0.91

0.92

0.93

0.94

Contention Window Size

Ave

rag

e C

ha

nn

el T

hro

ug

hp

ut

N=20N=30N=50N=100



Fig. 4 Simulations determining the optimal contention window size for different for the SOSBRA-based 802.11 protocol

N

0 100 200 300 400 500 600 700 800 900 10000

500

1000

1500

2000

2500

3000

3500

Total Number of Nodes

Op

tima

l SO

SB

RA

Co

nte

ntio

n W

ind

ow



Fig. 5 Simulations determining the minimum , for different cluster sizes for the SOSBRA-based 802.11 protocol.

N

ET

0 100 200 300 400 500 600 700 800 900 10000

0.5

1

1.5

2

2.5x 10

5

Total Nubmer of Nodes

Min

imu

m T

ota

l Tim

e to

Em

pty

the

Clu

ste

r



Fig. 7. : Simulations comparing the wasted-time before the cluster is emptied for the SOSBRA-based 802.11, Standard 802.11 DCF,

and ZigBee with and without GTS.

20 40 60 80 100 120 140 160 180 2000

2000

4000

6000

8000

10000

12000

14000


To

tal W

ast

ed

Tim

e D

uri

ng

Em

pty

ing

the

Clu

ste

r

ZigBee without GTSZigBee with GTSStandard 802.11 DCFSOSBRA-based 802.11 DCF

WT



Fig. 8. : Simulations comparing total energy consumption to empty the cluster for the SOSBRA-based 802.11, Standard 802.11 DCF, and ZigBee with/without GTS.

The energy consumption ratios used was idle:receive:send=1:2:2.5 11

50 100 150 200

2000

4000

6000

8000

10000

12000

14000

16000


To

tal E

ne

rgy C

on

su

me

d W

hile

Em

pty

ing

th

e C

luste

r

ZigBee without GTSZigBee with GTSStandard 802.11 DCFSOSBRA-based 802.11 DCF



Fig. 9. Comparison between SOSBRA and TDMA-based approaches. Here , and a slot time is 10 microsecond in SOSBRA.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

1

2

3

4

5

6

7

8x 10

4

Node Failure Probability

Wa

ste

d T

ime

Du

rin

g E

mp

tyin

g th

e C

lust

er

TDMASOSBRA

1000N bitsPL 1000


Probabilistic Approach• Cost Function• Cost results from two sources

»The first is from the total idle slot W

»The other one comes from possible collisions

• (7)

Optimal Contention Window SizeOptimal Contention Window Size

WNf ,

WNcollCcollcollWN fPTPPWf ,, ))1(1(


Optimal Contention WindowOptimal Contention Window

Fig.10. Numerical Results showing Cost Function Vs 1/W

10-6

10-5

10-4

10-3

10-2

103

104

105

106

107

108

1/W

Co

st F

un

ctio

n

10-6

10-5

10-4

10-3

10-2

103

104

105

106

107

108

1/W

Co

st F

un

ctio

n

Minimum Value

N=1000

N=400

N=200

N=100



Fig.11. Comparison between simulation and analytical results



Fig. 12. Average Total time obtained with from both simulation and analysis.


Large Number of NodesLarge Number of Nodes

if for very large N, We may approximate the total cost to be

,NW

. 1

1

))1

1(1

)1

1(1(lim

lim

11

1

,

,

ee

WWN

W

P

NN

NWN

collNWN

(11)


Large Number of NodesLarge Number of Nodes

W

ff WN

WN,1

,

. )(1

1

])

11()

11(

1[limlim

11

1,

1,

,

CT

ee

T

T

WW

N

W

Tf

cc

cNN

c

NWNWN

NWN

)(1,, CNfWf WNWN

DDWN

WNEW TC

C

TNf

fTT

)(

)(/

,

,

Define

(12)

(13)

(14)


ConclusionsConclusions

SOSBRA provides better performance in term of both time and energy compare to 802.11 DCF

Help minimize the multi-access interference (collisions) in design of physical access scheme, especially for CDMA approach

Our future work includes• analysis of cross layer designs for wireless sensors

with directional transmission capability• physical layer improvements, including adaptive

modulation schemes• synchronization across a sensor network• CDMA based optimization of PHY/MAC design


Derivations of FormulasDerivations of Formulas

N: Total non-CH nodes within the cluster

W: fixed one stage contention window

:Total time required to collect one packet from each node

: The duration of a RTS collision

: The duration of a data packet transmission

W)(N,ET

DIFSEIFSRTSC TTTT

DIFSACKSIFSDATACTSRTSD TTTTTTT 3



)N.....N,N(N I21

)C.....C,C(C 1I21

).....,( 121

_

IRRRR

I

ijji NR

1

NNI

1ii

. }c ,...,,, ,...,

,| roundth -Iin collisions no ,{

...},|,(},{

)} c ,...,,(),,...,,{(

1-I1-I22111122

11

111122221111

1-I1-I22112211

CcCcCnNnN

nNnNP

cCnNcCnNPcCnNP

CcCcCnNnNnNP

II

II

II



.

),()!()(

},{

11211

1

1

1111

1

N

n

W

crScc

nWW

n

N

cCnNP

.

),( )!()(

),( )!()1(...)1(

} ...,|,{

},...,, ,...,|,{

2

2

112211

11111111

ii

i

ii

rn

iiii

in

i

ii

rn

iiii

ii

i

ii

iiiiii

iiiiiiii

W

crScc

nWW

n

rnW

crScc

nWnWWW

n

rn

nNnNnNcCnNP

cCcCnNnNcCnNP

. )1(...)1(

}..., | collisions no ,{ 112211

In

I

IIII

W

nWWW

nNnNnNnNP

(7)

(8)

(9)



Given N nodes and length W contention window, for each of the W Slots:

1. No nodes choose this slot……………………….

1. Only one node chooses this slot……………......

1. More than one nodes choose this slot…………

Cost Function:• Cost results from two sources: total # of empty slots and possible

collisions • Minimize the Cost Function:

Nempty W

P )1

1(

1)1

1(1 N

succ WWNP

succemptycoll PPP 1

WW

fTPWf WNCcollWN )( ,

,

1

1

,

)1

1(1

)1

1(

))1

1(1

)1

1(1(

NN

NNC

WN

WWN

W

WWN

WWTW

f(10)



if for very large N, We may approximate the total cost to be

,NW

. 1

1

))1

1(1

)1

1(1(lim

lim

11

1

,

,

ee

WWN

W

P

NN

NWN

collNWN

(11)



W

ff WN

WN,1

,

. )(1

1

])

11()

11(

1[limlim

11

1,

1,

,

CT

ee

T

T

WW

N

W

Tf

cc

cNN

c

NWNWN

NWN

)(1,, CNfWf WNWN

DDWN

WNEW TC

C

TNf

fTT

)(

)(/

,

,

Define

(12)

(13)

(14)

qingjiang tian and edward j. coyle center for wireless systems and applications ( cwsa )

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