Mobile Networks
Module C- Part 1
WLAN
Performance Aspects
Mohammad Hossein Manshaei
Jean-Pierre Hubaux
http://mobnet.epfl.ch
1
Performance Evaluation of IEEE 802.11(DCF)
• Real Experimentations
– HoE on IEEE 802.11b
• Analytical Models
– Bianchi’s Model
• Simulations
– HoE on ns-2
2
Bianchi’s Model: Topology and Parameters
•
N links with the same physical condition (single-collision domain):
3
2
4
1
2
N
3
AP
N-2
N-1
1
N
We want to calculate the throughput of this network.
MAC Layer
PHY Layer
p
= Probability of Transmission
P = Probability of Collision
= More than one transmission at the same time
= 1 – (1- p)N-1
3
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
sender
data
SIFS
receiver
ACK
DIFS
other
stations
waiting time
The ACK is sent right at the end of SIFS
(no contention)
data
t
Contention
window
4
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
sender
RTS
data
SIFS
receiver
other
stations
CTS SIFS
SIFS
NAV (RTS)
NAV (CTS)
defer access
NAV: Net Allocation Vector
ACK
DIFS
data
t
Contention
window
RTS/CTS can be present for
some packets and not for other
5
802.11 – Slot Time in Bianchi’s Model
data
Idle
Idle Idle Idle
data
Idle
Idle Idle Collision
Idle
Idle
sender1
data
DIFS wait wait wait
Busy
wait
wait wait
wait
wait
sender2
Busy
wait wait wait wait
Busy
wait
wait wait data
DIFS wait
sender3
Busy
wait
wait wait wait
Busy
wait
wait wait data
DIFS wait
sender4
Busy
wait
wait wait wait
data
DIFS wait wait
channel
One slot time
Busy
Busy
wait
wait
collision
6
Bianchi’s Model: Two Dimensional Markov chain
(s(t), b(t))
1-p
(Backoff Stage, Backoff Timer)
1 /CW 0
(0 ,0 )
1
(0 ,1 )
1
1
(0,2)
(0,CW 0 -2 )
1
(0,CW 0 -1)
p/CW 1
(i-1,0)
p/CW i
(i,0)
1
(i,1)
1
1
(i,2)
(i,CW i -2)
1
(i,CW i -1)
p/Cw i+ 1
(m -1 ,0 )
p/CW m
(m,0)
1
(m,1)
1
1
(m,2 )
(m,CW m-2)
1
(m,CW m -1)
p
1 /CW m
7
802.11 – Slot Time in Bianchi’s Model
data
Idle
(0, 9) (0, 8)
Busy
(0, 8) (0, 7) (0, 6)
Busy
(0, 6) (0, 5) (0, 4) (0, 3)
Busy
(0, 3) (0, 2) (0, 1) data
DIFS
(1, 3)
sender3
Busy
(2, 6) (2, 5) (2, 4) (2, 3)
Busy
(2, 3) (2, 2) (2, 1) data
DIFS
(3, 6)
sender4
Busy
(7, 4) (7, 3) (7, 2) (7, 1)
data
DIFS
(0, 7) (0, 6) (0, 5)
Idle
sender1
data
DIFS
sender2
One slot time
Idle Idle Collision
Idle
Idle Idle Idle
data
channel
(0, 7)
Busy
Busy
Idle
(0, 6) (0, 5) (0, 4)
collision
8
Bianchi’s Model: Two Dimensional Markov chain
1-p
1/CW0
(0,0)
1
(0,1)
1
1
(0,2)
(0,CW0-2)
1
(0,CW0-1)
p/CW1
Stationary distribution:
bi,k  limt  Ps(t )  i, b(t )  k, i  (0, m), k  (0, CWi 1)
(i-1,0)
p/CWi
(i,0)
1
(i,1)
1
1
(i,2)
(i,CWi-2)
1
(i,CWi-1)
p/Cwi+1
(m-1,0)
Probability of transmission:
p/CWm
(m,0)
1
(m,1)
1
1
(m,2)
(m,CWm-2)
1
(m,CWm-1)
p
1/CWm
9
Bianchi’s Model: Two Dimensional Markov chain
Successful
Transmission
1-p
1/CW0
(0,0)
1
(0,1)
1
1
(0,2)
(0,CW0-2)
1
(0,CW0-1)
p/CW1
(i-1,0)
p/CWi
(i,0)
1
(i,1)
1
1
(i,2)
(i,CWi-2)
1
(i,CWi-1)
p/Cwi+1
(m-1,0)
p/CWm
(m,0)
1
(m,1)
1
1
(m,2)
(m,CWm-2)
1
(m,CWm-1)
p
1/CWm
10
Bianchi’s Model: Two Dimensional Markov chain
1-p
1/CW0
(0,0)
1
(0,1)
1
1
(0,2)
(0,CW0-2)
1
(0,CW0-1)
p/CW1
(i-1,0)
p/CWi
Collision
(i,0)
1
(i,1)
1
1
(i,2)
(i,CWi-2)
1
(i,CWi-1)
p/Cwi+1
(m-1,0)
p/CWm
(m,0)
1
(m,1)
1
1
(m,2)
(m,CWm-2)
1
(m,CWm-1)
p
1/CWm
11
Bianchi’s Model: Stationary Distribution of Chain
(i-1,0)
p/CWi
(i,0)
1
(i,1)
1
1
(i,2)
(i,CWi-2)
(i,CWi-1)
bi,0 = p bi-1,0
(m-1,0)
p/CWm
(m,0)
1
(m,1)
1
1
(m,2)
(m,CWm-2)
(m,CWm-1)
p
1/CWm
bm,0 = p bm-1,0 + p bm,0
12
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
13
Bianchi’s model: Throughput Calculation
• Throughput of node i:
i 
Ps Ptr L
E[ Payload Transmitted by user i in a slot time]

E[ Duration of slot time]
Ps PtrTs  Ptr (1  Ps )Tc  (1  Ptr )Tid
–
–
–
–
–
–
–
–
–
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
Ptr  1  (1  p ) N
N p (1  p ) N 1
Ps 
1  (1  p ) N
Ts  t H  t L  SIFS    t ACK  DIFS  
Tc  t H  t L  DIFS  
14
Numerical Results
Basic Mode
RTS/CTS
15
Conclusion
• Semi-analytical model to express the
performance of IEEE 802.11 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»
16