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
2SenMetrics’05, San Diego, 07/21/2005
OutlineOutline
Background
SOSBRA Approach for Clustered Sensor Networks
Numerical Results
Optimal Contention Window
Conclusions
3SenMetrics’05, San Diego, 07/21/2005
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
4SenMetrics’05, San Diego, 07/21/2005
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
5SenMetrics’05, San Diego, 07/21/2005
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
6SenMetrics’05, San Diego, 07/21/2005
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
7SenMetrics’05, San Diego, 07/21/2005
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
8SenMetrics’05, San Diego, 07/21/2005
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.
9SenMetrics’05, San Diego, 07/21/2005
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
10SenMetrics’05, San Diego, 07/21/2005
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
11SenMetrics’05, San Diego, 07/21/2005
PerformancePerformance AnalysisAnalysis
No collisions
NN
NsW
W
W
NWWWP
)()1(....)1(
DE TNWT
(1)
(2)
12SenMetrics’05, San Diego, 07/21/2005
PerformancePerformance AnalysisAnalysis
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)
13SenMetrics’05, San Diego, 07/21/2005
PerformancePerformance AnalysisAnalysis
(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
14SenMetrics’05, San Diego, 07/21/2005
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
15SenMetrics’05, San Diego, 07/21/2005
Numerical And Simulation Numerical And Simulation ResultsResults
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
16SenMetrics’05, San Diego, 07/21/2005
Numerical And Simulation Numerical And Simulation ResultsResults
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
17SenMetrics’05, San Diego, 07/21/2005
Numerical And Simulation Numerical And Simulation ResultsResults
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
18SenMetrics’05, San Diego, 07/21/2005
Numerical And Simulation Numerical And Simulation ResultsResults
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
19SenMetrics’05, San Diego, 07/21/2005
Numerical And Simulation Numerical And Simulation ResultsResults
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
Total Number of Nodes
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
20SenMetrics’05, San Diego, 07/21/2005
Numerical And Simulation Numerical And Simulation ResultsResults
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
Total Number of Nodes
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
21SenMetrics’05, San Diego, 07/21/2005
Numerical And Simulation Numerical And Simulation ResultsResults
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
22SenMetrics’05, San Diego, 07/21/2005
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(
23SenMetrics’05, San Diego, 07/21/2005
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
24SenMetrics’05, San Diego, 07/21/2005
Optimal Contention WindowOptimal Contention Window
Fig.11. Comparison between simulation and analytical results
25SenMetrics’05, San Diego, 07/21/2005
Optimal Contention WindowOptimal Contention Window
Fig. 12. Average Total time obtained with from both simulation and analysis.
26SenMetrics’05, San Diego, 07/21/2005
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)
27SenMetrics’05, San Diego, 07/21/2005
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)
28SenMetrics’05, San Diego, 07/21/2005
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
29SenMetrics’05, San Diego, 07/21/2005
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
30SenMetrics’05, San Diego, 07/21/2005
Derivations of FormulasDerivations of Formulas
)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
31SenMetrics’05, San Diego, 07/21/2005
Derivations of FormulasDerivations of Formulas
.
),()!()(
},{
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)
32SenMetrics’05, San Diego, 07/21/2005
Derivations of FormulasDerivations of Formulas
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)
33SenMetrics’05, San Diego, 07/21/2005
Derivations of FormulasDerivations of Formulas
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)
34SenMetrics’05, San Diego, 07/21/2005
Derivations of FormulasDerivations of Formulas
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)
Top Related