Modeling and Throughput Analysis for SMAC

Ou Yang4-29-2009

2

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

3

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

4

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

5

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

6

Background – SMAC Protocol

Reasons of packet loss (ideal channel)- SMAC without retx: RTS failed- SMAC with retx: retx over limit- queue overflow

7

Methodology Assumptions

- packet arrive independently- finite FIFO queue at each node- channel is ideal

no hidden terminalsno capture effectsno channel fading

8

Methodology 1-D Markov Model for SMAC without retx

0 pkts in the queue1 pkts in the queue2 pkts in the queue Maximum Q pkts in the queue

9

Methodology

1-D Markov Model for SMAC without retx

10

Methodology

Example of the 1-D Markov Model

00,0 AP

0 1 2

11,0 AP 22,0 AP

00,1 ApP 011,1 )1( ApApP 122,1 )1( ApApP

00,2 P 01,2 ApP 012,2 )1( ApApP

cycle ain arrivalspkt ofy probabilit theis iAi

cycle ain arrivalspkt than less no ofy probabilit theis iA i

contention the winningofy probabilit theis p

Transition Matrix P

known

unknown

11

Methodology 2-D Markov Model

for SMAC with retx

Retx stage 0

Retx stage 1

Retx stage R

1 pkt in the queue Q pkts in the queue

12

Methodology Example of the 2-D Markov Model

0)00,00( AP

0,0 0,1 0,2

1,1 1,2

2,1 2,21)01,00( AP 2)02,00( AP

0)00,01( ApP s 01)01,01( )1( ApApP s 12)02,01( )1( ApApP s

0)01,02( ApP s 01)02,02( )1( ApApP s

0)11,01( ApP f 1)12,01( ApP f

0)12,02( ApP f

0,0

0,1

0,2

cycle ain arrivalspkt ofy probabilit theis iAi

cycle ain arrivalspkt than less no ofy probabilit theis iA i

packetDATA a y txingsucessfull ofy probabilit theis sp

packetDATA a of failure tx ofy probabilit theis fp

fs pppp ,contention the winningofy probabilit theis

13

Methodology

Example of the 2-D Markov Model

1)22,11( ApP f

0,0 0,1 0,2

1,1 1,2

2,1 2,2

0)00,11( ApP s 1)01,11( ApP s 2)02,11( ApP s

0)11,11( )1( ApP 1)12,11( )1( ApP

0)21,11( ApP f

1,1

1,2

0)22,11( ApP f

0)01,12( ApP s 1)02,12( ApP s

0)12,12( )1( ApP

14

Methodology Example of the

2-D Markov Model

0,0 0,1 0,2

1,1 1,2

2,1 2,22,1

1)22,21( )1( ApP

0)00,21( ApP 1)01,21( ApP 2)02,21( ApP

0)21,21( )1( ApP

2,2

0)22,22( )1( ApP

0)01,22( ApP 1)02,22( ApP

15

Throughput Analysis

Definition of throughput

cycle a oflength theis

sizepacket DATA layer MAC the theis

packetDATA a ly txingsuccessful ofy probabilit theis

state queueempty theofy probabilit stationary theis

odneighborho in the nodes ofnumber theis

/)1(

T

S

p

N

TSpNTHR

s

emptyQ

semptyQsys

Solve

2 variables!

16

Throughput Analysis – 1-D Markov Model

According to the Markov Model- stationary distribution: - is the only unknown variable in- curve

Assume each node behaves independently- prob. of to contend the media in a cycle- randomly select a backoff window in [0,W-1] - curve

P

)(0 pfemptyQ p P

01

)( 0gp

17

Throughput Analysis – 1-D Markov Model

0

p

18

Throughput Analysis – 1-D Markov Model

Intersections of and-- is obtained

To solve similar to Assume each node behaves independently

- prob. of to contend the media in a cycle- randomly select a backoff window in [0,W-1]--

)(0 pf),( 0

p)( 0gp

0

sp )( 0gp

)( 0hp s

01

)( 0 hp s

19

Throughput Analysis – 2-D Markov Model

According to the Markov Model- stationary distribution: - and are unknown variables in- surface

Assume each node behaves independently- prob. of to contend the media in a cycle- randomly select a backoff window in [0,W-1] - curve

P

),()0,0( fsemptyQ ppFsp P

)0,0(1

)())()(),((),( )0,0()0,0()0,0()0,0( Hhghpp fs

fp

20

Throughput Analysis – 2-D Markov Model

),,( )0,0( fs pp

is obtained!

21

Model Validation Varying the number of nodes

22

Model Validation Varying the queue capacity

23

Model Validation Varying the contention window size

24

Model Validation Varying the data arrival rate

25

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

26

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

27

Thank you

Q & A

28

Methodology

Example of the 1-D Markov Model

00,0 AP

0 1 2

11,0 AP 22,0 AP

00,1 ApP 011,1 )1( ApApP 122,1 )1( ApApP

00,2 P 01,2 ApP 012,2 )1( ApApP

cycle ain arrivalspkt ofy probabilit theis iAi

cycle ain arrivalspkt than less no ofy probabilit theis iA i

contention the winningofy probabilit theis p

Transition Matrix P

known

unknown

29

Background – Markov Model Markov model of IEEE 802.11