1. Presented by Hoang Nguyen
Performance Analysis of the IEEE Distributed Coordination Function
Giuseppe Bianchi
Presented by Hoang Nguyen
CS598JH - Spring 06

2. Saturation Throughput
Problem Formulation
Saturation Throughput
Asymptotic throughput
Assumptions
Ideal Channel Condition (No Hidden Terminal, No Channel Capture)
Finite Number of Stations
Constant & Independent Collision Probability
Overload Condition

3. Outline
Analytical Model
Saturation Throughput Analysis
Maximum Saturation Throughput
Performance Evaluation
Conclusion

4. Analytical Model

5. Analytical Model
b(t): stochastic process representing the backoff counter
s(t): stochastic process representing the backoff stage (0..m)
W = CWmin and CWmax = 2mW
Wi = 2i W at stage i 2 (0,m)
{s(t), b(t)}: bidimensional process with discrete-time Markov Chain
Conditional Collision Probability p
Transmission Probability 

6. Markov Model for Single Station
(1-p)/W0
Successful Transmission 1 1 …. 1 1 1
0,0
0,1
0,2
0,W0-2
0,W0-1 ….
p/W_1
The backoff time is decremented at the beginning of each slot time
i-1,0
p/Wi
p/Wi 1 1 1 1 1
i,0
i,1
i,2 ….
i,Wi-2
i,Wi-1
Unsuccessful Transmission ….
p/Wm
p/Wm 1 1 1 1 1
m,0
m,1
m,2
m,Wm-2
m,Wm-1
p/Wm
p/Wm
i,j
Stage I, Backoff Window j

7. Stationary Distribution Derivation
Derivation for bi-1,0.p = bi,0
p/Wi
p/Wi 1 1 …. 1
i,0
i,1
i,Wi-1
W_0. (1-p)/W_0
Flow-in
Flow-out
Wi+1. p/Wi+1
bi-1,0.p/Wi + bi+1,0.1
= bi,0 +
bi-1,0.p/Wi + bi+2,0.1
= bi,1 ….
bi-1,0.p/Wi
= bi,Wi-1
bi-1 p = bi,0

8. Stationary Distribution Derivation
Use similar derivation, we get…
Use the fact that
We get
Plus Therefore,
Then,

9. Transmission Probability
Now, we have…
And, p = 1 – (1-)n-1
Thus, p and  can be solve by numerical techniques

10. Saturation Throughput Analysis

11. Saturation Throughput
Consider a slot time…
Probability at least one transmission
Ptr = 1 – (1-)n
Probability of successful transmission
Ps = n(1-)n-1 / Ptr

12. Saturation Throughput (cont.)
S = E[payload information transmitted in a slot time] / E[length of a slot time]
where
Ts = average time channel sensed busy due to a successful transmission
Tc = average time channel sensed busy due to a collision
 = duration of empty slot time
E[P] = average packet payload size
Probability of a collision
Probability of a successful transmission
Probability of idle slot

13. Saturation Throughput (cont.)
Ts and Tc depend on channel access mechanism
For basic access mechanism
Similarly, for RTS/CTS mechanism

14. Model Validation
Very accurate

15. Maximum Saturation Throughput

16. Maximum Saturation Throughput
Re-arrange S
To maximize S, maximize this term…
Take the derivation and impose to 0…

17. Approximate Solution More sensitive
n is unknown;  depends on m and W, which are fixed in hardware!

18. Performance Evaluation

19. Saturation Throughput vs. Initial Window Size
Almost independent when W · 64
Saturation throughput highly depends on W and n

20. Maximum Backoff Stage
Greater than 4 is fine

21. Conclusions

22. Conclusions Pros Cons: Analytical Model
Accurate
Simple
Performance Evaluation on saturation Throughput
Cons:
Only Saturation Throughput
Only Overload Condition
Only Ideal Channel Condition

23. Thank You!

24. Backup Slides

25. Markov Model for Single Station
(1-p)/W0 1 1 1 …. 1 1
0,0
0,1
0,2
0,W0-2
0,W0-1 ….
p/W_1
i-1,0
p/Wi
p/Wi 1 1 1 1 1
i,0
i,1
i,2 ….
i,Wi-2
i,Wi-1 ….
p/Wm
p/Wm 1 1 1 1 1
m,0
m,1
m,2
m,Wm-2
m,Wm-1
p/Wm
p/Wm
i,j
Stage I, Backoff Window j