1. Author: Giuseppe Bianchi
EEL6935: Wireless Ad Hoc Networks
Performance Analysis of IEEE Distributed Coordination Function (DCF)
-- JSAC’2000
Author: Giuseppe Bianchi
Presented by: Rongsheng Huang

2. Outline Overview of IEEE 802.11 DCF Mathematical model
EEL6935: Wireless Ad Hoc Networks
Outline
Overview of IEEE DCF
Mathematical model
Notations and the main idea
One step transition probabilities
Bi-dimensional Markov Chain
Stationary distribution
Maximum throughput
Performance evaluation of DCF
Concluding remarks

3. EEL6935: Wireless Ad Hoc Networks
Overview of IEEE
MAC and PHY layers specifications for wireless LANs
MAC Protocols
Fundamental:
Distributed Coordination Function (DCF) -- CSMA/CA based
Binary Exponential Backoff rules
Optional: Point Coordination Function (PCF)

4. Overview of IEEE 802.11 DCF Two access techniques
EEL6935: Wireless Ad Hoc Networks
Overview of IEEE DCF
Two access techniques
Basic mechanism: 2 way handshaking
RTS/CTS mechanism: 4 way handshaking
RTS
DATA
CTS
DESt
Source
Source
Dest
DATA
ACK
ACK

5. Example of RTS/CTS Access Scheme
EEL6935: Wireless Ad Hoc Networks
Example of RTS/CTS Access Scheme
CSMA/CA based
CSMA: listen at least DIFS before talk
CA: defer transmission for random back-off time after DIFS
SIFS
BO=3 (set)
BO=0
BO=5 (set) A
BO=15 (set)
DIFS
RTS
DATA
DIFS
RTS
DIFS
collision
CTS
ACK B
BO=8 (set)
BO=5(resume)
BO=10 (set)
BO=5 (suspend)
BUSY
DIFS
NAV (RTS)
DIFS
RTS
DIFS
Others
NAV(CTS)

6. Backoff procedure—BEB algorithm
EEL6935: Wireless Ad Hoc Networks
Overview of IEEE DCF
Backoff procedure—BEB algorithm CW
Backoff counter:
Initial: uni~[0,CW-1]
Non zero: decremented for
each idle slot
Zero: transmit
CWmax c c s s c c c
CWmin c c C c s t

7. Analytical Model to Evaluate DCF
EEL6935: Wireless Ad Hoc Networks
Analytical Model to Evaluate DCF
Goal: saturation throughput & Maximum achievable saturation throughput:
Saturation throughput: given all the system parameters, assume each station always has packets to send, the stable throughput of the whole system
Maximum throughput: if the system parameters can be modified, the theoretical maximum saturation throughput achievable.
Basic assumptions
Constant & independent collision probability for each transmitted packet p (suppose that the backoff mechanism can adjust the p to a constant value)
Ideal channel condition (no hidden terminals and capture)
Fixed number of stations n operated under overload (saturation condition)

8. Idea of Applying Markov Chain
EEL6935: Wireless Ad Hoc Networks
Idea of Applying Markov Chain
Transmission probability and conditional collision probability p are needed.
Normalized system throughput S with n stations can be derived.
Markov chain’s property: state transition diagram -> probability of each state
2-dimensional Markovian chain

9. Bi-dimensional Markov Chain model
EEL6935: Wireless Ad Hoc Networks
Bi-dimensional Markov Chain model
Behavior of a single station
Notations
b(t): backoff time counter at time t, stochastic process.
s(t): backoff stage at time t, stochastic process.
Time scale:
Discrete and integer, t, beginning of a slot time, when backoff time counter decrements or regenerated
[t, t+1], interval between 2 consecutive slot time, can be variable length
Makovian State: B(t) ={s(t), b(t)}
CW_i = 2^i*CW_min
m: maximum backoff stage, CW_max = 2^m*CW_min
p: prob.of each transmitted packet being collided
n: number of stations

10. One step transition probabilities (1)
EEL6935: Wireless Ad Hoc Networks
One step transition probabilities (1)
1) P{i,k|i,k+1}=1, k : [0,Wi-2], i : [0,m]
At beginning of t
Backoff counter not reach zero, no transmission
Channel sensed idle for 1 mini-slot till t+1
At beginning of t+1
Backoff counter decremented by 1 1
i , k
i , k+1

11. One step transition probabilities (2)
EEL6935: Wireless Ad Hoc Networks
One step transition probabilities (2)
P{0,k|i,0}=(1-p)/W_0, k : [0,W_0-1], i : [0,m]
At beginning of t
Backoff counter reaches zero, successful transmitted [t,t+1]
At beginning of t+1
Contention window reset to CW_min (backoff stage = 0)
Backoff counter chosen randomly in [0,W_0-1]
P{i+1,k|i,0}= p/W_(i+1), k : [0,W_(i+1)-1], i : [1,m-1]
Backoff counter reaches zero, transmit in [t,t+1], collision
Contention window < CW_max
contention window doubled
Backoff counter chosen randomly in [0,W_(i+1)-1]

12. Illustration of the Backoff After Collison
EEL6935: Wireless Ad Hoc Networks
Illustration of the Backoff After Collison

13. EEL6935: Wireless Ad Hoc Networks
State transits upon backoff counter reach zero (Contention Window <CWmax) Tx
Success
0 , 0
0 , 1 …
0 , W0-2
0, W0-1 .
(1-p)/W0
i , 0
p/Wi+1
i+1, 0
i+1 , 1
i+1,Wi+1-2
i+1,Wi+1-1
. . .
collision

14. One step transition probabilities (3)
EEL6935: Wireless Ad Hoc Networks
One step transition probabilities (3)
P{m,k|i,0}= p/W_m, k : [0,W_m-1], i = m
At beginning of t
Backoff counter reaches zero, transmit in [t,t+1], collision
Contention Window = CW_max
At beginning of t+1
Contention Window remains at CW_max
Backoff time counter chosen randomly in [0,W_m-1]

15. EEL6935: Wireless Ad Hoc Networks
State transits upon backoff counter reach zero (Contention Window = CWmax)
0 , 0
0 , 1 …
0 , W0-2
0, W0-1 .
(1-p)/W0
m , 0
m , 1
m , Wm-2
m , Wm-1 …
p/Wm

16. Bi-dimensional Markov Chain model
EEL6935: Wireless Ad Hoc Networks
Bi-dimensional Markov Chain model

17. Bi-dimensional Markov Chain model
EEL6935: Wireless Ad Hoc Networks
Bi-dimensional Markov Chain model

18. Result from Markovian Chain Model (1)
EEL6935: Wireless Ad Hoc Networks
Result from Markovian Chain Model (1)

19. Result from Markovian Chain Model (2)
EEL6935: Wireless Ad Hoc Networks
Result from Markovian Chain Model (2)

20. Result from Markovian Chain Model (3)
EEL6935: Wireless Ad Hoc Networks
Result from Markovian Chain Model (3)
and

21. Throughput Analysis Based on Model
EEL6935: Wireless Ad Hoc Networks
Throughput Analysis Based on Model
S := Fraction of Time channel is used to successfully transmit payload bits
As an outside observer, see a random slot and observe what is happening
Probability, Exactly 1 TX Occurring on the channel is successful given someone transmits
Hybrid Scheme also possible.
Packet Length may vary and throughput may relate itself to packet size distribution mean
Ts, Tc, s,P are constant for model verification constant, and determined by standard
Maximizing throughput over probabilities which are in terms of t, we get S is max when
Remember Slotted Aloha Stabilization ?
tao depends on m and W and can be changed adaptively
But m and W fixed because of Physical Layer Standard
Result – S can be significantly lower than maximum

22. EEL6935: Wireless Ad Hoc Networks
IMPORTANT RESULTS
For Sufficiently Large n, Smax is practically independent of no. of stations in wireless network
Maximum throughput achievable by BAS is very close to RTS/CTS mechanism
RTS/CTS scheme throughput is less insensitive to transmission probability t
RTS/CTS scheme is network size independent for W <= 64 values. Basic Mechanism throughput increases but significantly decreases with network size
Key to these results – RTS/CTS mechanism reduces the time spent during a collision, and it becomes more effective than Basic Access when W and n increases the collision probability
RTS/CTS even more effective when packet length are longer

23. EEL6935: Wireless Ad Hoc Networks
Model Validation

24. Remarks Classic model for WLAN with good approximation
EEL6935: Wireless Ad Hoc Networks
Remarks
Classic model for WLAN with good approximation
Delay performance can be derived
Only one-hop is considered.
Only saturation is considered.
A small mistake

25. EEL6935: Wireless Ad Hoc Networks
A Small Mistake Found
H. Wu, Y. Peng, K. Long, S. Cheng, and J. Ma, Performance of reliable transport protocol over IEEE wireless LAN: analysis and enhancement,. in Proc. IEEE INFOCOM'02, New York, June 2002
Limit of retransmission m and maximum stage of backoff counter m’: [ m {5 or 7}, m’ {5} ]

26. EEL6935: Wireless Ad Hoc Networks
Modified Model

27. Validation of the Modified Model
EEL6935: Wireless Ad Hoc Networks
Validation of the Modified Model

28. EEL6935: Wireless Ad Hoc Networks
Thank you