1. Module C- Part 1 WLAN Performance Aspects
Mobile Networks
Module C- Part 1 WLAN Performance Aspects
Mohammad Hossein Manshaei
Jean-Pierre Hubaux

2. Performance Evaluation of IEEE 802.11(DCF)
Real Experimentations
HoE on IEEE b
Analytical Models
Bianchi’s Model
Simulations
HoE on ns-2

3. Bianchi’s Model: Topology and Parameters
N links with the same physical condition (single-collision domain): 3 2 4 1 2 3 N 1 AP
N-2 N
N-1
We want to calculate the throughput of this network.
PHY Layer
MAC Layer P p
= Probability of Transmission
= Probability of Collision
= More than one transmission at the same time
= 1 – (1- p)N-1

4. 802.11 - CSMA/CA unicast (Review)
Sending unicast packets
station has to wait for DIFS before sending data
receiver acknowledges at once (after waiting for SIFS) if the packet was received correctly (CRC)
automatic retransmission of data packets in case of transmission errors
DIFS
data
sender
SIFS
ACK
receiver
DIFS
data
other
stations t
waiting time
Contention window
The ACK is sent right at the end of SIFS (no contention)

5. 802.11 – DCF with RTS/CTS (Review)
Sending unicast packets
station can send RTS with reservation parameter after waiting for DIFS (reservation determines amount of time the data packet needs the medium)
acknowledgement via CTS after SIFS by receiver (if ready to receive)
sender can now send data at once, acknowledgement via ACK
other stations store medium reservations distributed via RTS and CTS
DIFS
RTS
data
sender
SIFS
SIFS
SIFS
CTS
ACK
receiver
DIFS
NAV (RTS)
data
other
stations
NAV (CTS) t
defer access
Contention window
RTS/CTS can be present for some packets and not for other
NAV: Net Allocation Vector

6. 802.11 – Slot Time in Bianchi’s Model
data
DIFS
Idle
Busy
wait
Idle
wait
Idle
wait
Idle
data
Busy
wait
DIFS
Idle
wait
Collision
Idle
data
Busy
DIFS
wait
channel
sender1
sender2
collision
sender3
sender4
One slot time

7. Bianchi’s Model: Two Dimensional Markov chain
(s(t), b(t))
(Backoff Stage, Backoff Timer) ( , ) 1 2 CW - ( i - 1 , ) m p / CW Cw + ( i , ) 1 2 CW - ( m , ) 1 2 CW -

8. 802.11 – Slot Time in Bianchi’s Model
data
DIFS
Idle
Busy
(7, 3)
(7, 4)
(2, 5)
(2, 6)
(0, 5)
(0, 6)
Idle
(0, 9)
(7, 2)
(2, 4)
(0, 4)
Idle
(0, 8)
(7, 1)
(2, 3)
(0, 3)
Idle
data
Busy
DIFS
(0, 8)
(0, 7)
(2, 2)
(2, 3)
(0, 2)
(0, 3)
Idle
(0, 6)
(0, 1)
(2, 1)
(0, 7)
Collision
Idle
data
Busy
DIFS
(0, 6)
(0, 5)
(0, 7)
channel
sender1
(1, 3)
(3, 6)
(0, 5)
(0, 4)
sender2
collision
sender3
sender4
One slot time

9. Bianchi’s Model: Two Dimensional Markov chain
Stationary distribution:
Probability of transmission:

10. Bianchi’s Model: Two Dimensional Markov chain
Successful
Transmission

11. Bianchi’s Model: Two Dimensional Markov chain
Collision

12. Bianchi’s Model: Stationary Distribution of Chain
bi,0 = p bi-1,0 ( i , ) 1 2 CW - p /
bm,0 = p bm-1,0 + p bm,0

13. Bianchi’s Model: Solution for p and p
After some derivations  system of two nonlinear equations with two variables p and p:
 Can be solved numerically to obtain p and p

14. Bianchi’s model: Throughput Calculation
Throughput of node i:
Ptr: Probability of at least one transmission in slot time
Ps: Probability of successful transmission during a random time slot
L: Average packet payload size
Ts: Average time to transmit a packet of size L
Tc: Average time of collision
Tid: Duration of the idle period
tACK: ACK transmission time
tH: Header transmission time
tL: Payload transmission time

15. Numerical Results
Basic Mode
Basic Mode
RTS/CTS
RTS/CTS

16. Conclusion
Semi-analytical model to express the performance of IEEE networks
More sophisticated models have been developed since then
Don’t forget checking the related write up: «Performance Analysis of the IEEE DCF: Bianchi Model»