Modeling and Throughput Analysis for SMAC

1. 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 terminals no capture effects no channel fading

8. 0 pkts in the queue 1 pkts in the queue 2 pkts in the queue Maximum Q pkts in the queue Methodology • 1-D Markov Model for SMAC without retx

9. Methodology • 1-D Markov Model for SMAC without retx

10. TransitionMatrix P known unknown Methodology 0 1 2 • Example of the 1-D Markov Model

11. 1 pkt in the queue Q pkts in the queue Retx stage 0 Retx stage 1 Retx stage R Methodology • 2-D Markov Modelfor SMAC with retx

12. 0,0 0,1 0,2 Methodology 0,0 0,1 0,2 1,1 1,2 • Example of the 2-D Markov Model 2,1 2,2

13. 1,1 1,2 Methodology 0,0 0,1 0,2 • Example of the 2-D Markov Model 1,1 1,2 2,1 2,2

14. 2,1 2,2 Methodology 0,0 0,1 0,2 • Example of the 2-D Markov Model 1,1 1,2 2,1 2,2

15. Throughput Analysis • Definition of throughput 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

17. Throughput Analysis – 1-D Markov Model

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]--

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

20. Throughput Analysis – 2-D Markov Model 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. TransitionMatrix P known unknown Methodology 0 1 2 • Example of the 1-D Markov Model

29. Background – Markov Model • Markov model of IEEE 802.11