Modeling and
Throughput Analysis
for SMAC
Ou Yang
4-29-2009
Outline





Motivation and Background
Methodology
- 1-D Markov Model for SMAC without retx
- 2-D Markov Model for SMAC with retx
Throughput Analysis
- 1-D Markov Model for SMAC without retx
- 2-D Markov Model for SMAC with retx
Model Validation
Conclusions
2
Motivation
Good to know the performance of SMAC
- sleep at MAC layer or not?
- which duty cycle should be chosen?
 No analytical model for SMAC
- quantitative estimation of throughput
- throughput under different scenarios

3
Background – SMAC Protocol

Duty-cycled MAC to reduce idle listening
- fixed active period in a cycle
- variable sleep period in a cycle
- duty cycle = active period / cycle length
4
Background – SMAC Protocol
Synchronization
- SYNC pkt carries sleep-awake schedule
- broadcast SYNC pkt
 Medium access
- RTS/CTS/DATA/ACK
- carrier sensing ( virtual + physical )
- fixed contention window size

5
Background – SMAC Protocol

Reasons of packet loss (ideal channel)
- SMAC without retx: RTS failed
- SMAC with retx: retx over limit
- queue overflow
6
Methodology

Assumptions
- packet arrive independently
- finite FIFO queue at each node
- channel is ideal
no hidden terminals
no capture effects
no channel fading
7
Methodology

1-D Markov Model for SMAC without retx
0 pkts in the
1 pkts
queue
in the2 queue
pkts in the queue
Maximum Q pkts in the queue
8
Methodology

1-D Markov Model for SMAC without retx
9
Methodology

0
1
Example of the 1-D Markov Model
2
Transition Matrix P
P0,0  A0
P0,1  A1
P0, 2  A 2
P1, 0  p  A0
P1,1  p  A1  (1  p )  A0
P1, 2  p  A 2  (1  p)  A1
P2, 0  0
P2,1  p  A0
P2, 2  p  A1  (1  p)  A0
known
Ai is the probabilit y of i pkt arrivals in a cycle
Ai is the probabilit y of no less than i pkt arrivals in a cycle
p is the probabilit y of winning the contention
unknown
10
Methodology

1 pkt in the queue
Q pkts in the queue
2-D Markov Model
for SMAC with
retx
Retx stage 0
Retx stage 1
Retx stage R
11
Methodology

0,0
Example of the 2-D Markov Model
0,0
0,1
P( 00, 00)  A0
P( 00, 01)  A1
P( 00, 02)  A 2
P( 01,00)  ps  A0 P( 01,01)  ps  A1  (1  p)  A0
P( 01,11)  p f  A0
0,2
P( 02,01)  ps  A0 P( 02, 02)  ps  A1  (1  p)  A0
0,1
0,2
1,1
1,2
2,1
2,2
P( 01, 02)  ps  A 2  (1  p)  A1
P( 01,12)  p f  A1
P( 02,12)  p f  A0
Ai is the probabilit y of i pkt arrivals in a cycle
Ai is the probabilit y of no less than i pkt arrivals in a cycle
ps is the probabilit y of sucessfull y txing a DATA packet
p f is the probabilit y of tx failure of a DATA packet
p is the probabilit y of winning the contention , p  p s  p f
12
Methodology

0,0
Example of the
2-D Markov Model
1,1
P(11,00)  ps  A0
0,1
0,2
1,1
1,2
2,1
2,2
P(11, 01)  ps  A1
P(11, 02)  ps  A 2
P(11,11)  (1  p)  A0
P(11,12)  (1  p)  A1
P(11, 21)  p f  A0
P(11, 22)  p f  A1
P(12,01)  ps  A0
P(12,02)  ps  A1
1,2
P(12,12)  (1  p )  A0
P(11, 22)  p f  A0
13
Methodology

0,0
Example of the
2-D Markov Model
2,1
P( 21, 00)  p  A0
P( 21, 01)  p  A1
P( 21, 02)  p  A 2
P( 21, 21)  (1  p)  A0
P( 21, 22)  (1  p )  A1
P( 22, 01)  p  A0
P( 22, 02)  p  A1
0,1
0,2
1,1
1,2
2,1
2,2
2,2
P( 22, 22)  (1  p)  A0
14
Throughput Analysis

Definition of throughput
THRsys  N  (1   emptyQ )  ps  S / T
Solve
2
variables!
N is the number of nodes in the neighborho od
 emptyQ is the stationary probabilit y of the empty queue state
ps is the probabilit y of successful ly txing a DATA packet
S is the the MAC layer DATA packet size
T is the length of a cycle
15
Throughput Analysis – 1-D Markov Model

According to the Markov Model
- stationary distribution: P  
- p is the only unknown variable in P
- curve  emptyQ   0  f ( p )

Assume each node behaves independently
- prob. of 1   0 to contend the media in a cycle
- randomly select a backoff window in [0,W-1]
- curve p  g ( 0 )
16
Throughput Analysis – 1-D Markov Model
 0
p
17
Throughput Analysis – 1-D Markov Model



Intersections of  0  f ( p) and p  g ( 0 )


- ( p , 0 )
-  0 is obtained

To solve ps similar to p  g ( 0 )
Assume each node behaves independently
- prob. of 1   0 to contend the media in a cycle
- randomly select a backoff window in [0,W-1]
- p s  h( 0 )
- p s   h(  )
0
18
Throughput Analysis – 2-D Markov Model


According to the Markov Model
- stationary distribution: P  
- ps and p f are unknown variables in P
- surface  emptyQ   ( 0,0)  F ( ps , p f )
Assume each node behaves independently
- prob. of 1   ( 0, 0) to contend the media in a cycle
- randomly select a backoff window in [0,W-1]
- curve
( ps , p f )  (h( ( 0,0) ), g ( ( 0,0) )  h( ( 0,0) ))  H ( ( 0,0) )
19
Throughput Analysis – 2-D Markov Model



( ps , p f ,  ( 0 , 0 ) )
is obtained!
20
Model Validation
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Varying the number of nodes
21
Model Validation
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Varying the queue capacity
22
Model Validation

Varying the contention window size
23
Model Validation
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Varying the data arrival rate
24
Discussions


Effects of retransmissions
- not obvious difference in throughput
- extra traffic at the head of the queue
Reasons
- saturation: no improvement
- far from saturation: trivial improvement
- close to saturation: some improvement
25
Conclusion




1-D Markov Model to describe the behavior of
SMAC without retx
2-D Markov Model to describe the behavior of
SMAC with retx
Models well estimate the throughput of SMAC
Application
- estimate throughput
- optimize the parameters of SMAC
- trade off throughput and lifetime
26
Thank you
Q&A
27
Methodology

0
1
Example of the 1-D Markov Model
2
Transition Matrix P
P0,0  A0
P0,1  A1
P0, 2  A 2
P1, 0  p  A0
P1,1  p  A1  (1  p )  A0
P1, 2  p  A 2  (1  p)  A1
P2, 0  0
P2,1  p  A0
P2, 2  p  A1  (1  p)  A0
known
Ai is the probabilit y of i pkt arrivals in a cycle
Ai is the probabilit y of no less than i pkt arrivals in a cycle
p is the probabilit y of winning the contention
unknown
28
Background – Markov Model

Markov model of IEEE 802.11
29