Post on 18-Dec-2015
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Module C- Part 1
WLAN Performance Aspects
Mohammad Hossein ManshaeiJean-Pierre Hubaux
Mobile Networks
http://mobnet.epfl.ch
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Performance Evaluation of IEEE 802.11(DCF)
• Real Experimentations– HoE on IEEE 802.11b
• Analytical Models– Bianchi’s Model
• Simulations– HoE on ns-2
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Bianchi’s Model: Topology and Parameters• N links with the same physical condition (single-collision domain):
PHY Layer
MAC Layer
P
= Probability of Transmission
= Probability of Collision= More than one transmission at the same time= 1 – (1- )N-1
1 2 3 NAP
1
234
NN-1
N-2
We want to calculate the throughput of this network.
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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
t
SIFS
DIFS
data
ACK
waiting time
otherstations
receiver
senderdata
DIFS
Contentionwindow
The ACK is sent right at the end of SIFS(no contention)
The ACK is sent right at the end of SIFS(no contention)
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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
t
SIFS
DIFS
data
ACK
defer access
otherstations
receiver
senderdata
DIFS
Contentionwindow
RTS
CTSSIFS SIFS
NAV (RTS)NAV (CTS)
NAV: Net Allocation VectorNAV: Net Allocation Vector RTS/CTS can be present forsome packets and not for other
RTS/CTS can be present forsome packets and not for other
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802.11 – Slot Time in Bianchi’s Model
channel
sender1
sender2
sender3
One slot time
sender4
Collision Idle
data
Busy
data
DIFS
waitwait
Idle
DIFS
Busy waitwait
wait
wait
Idle
wait
wait
wait
wait
Idle
wait
wait
wait
wait
Idledata Idle
Busy
Busy
wait
wait
wait
wait
data DIFS
Busy waitwait
Idle
wait
wait
wait
wait
collision
data
DIFS
Idle
data
Idle
Busy
Busy
wait wait
wait wait
wait
waitBusy wait wait
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Bianchi’s Model: Two Dimensional Markov chain
(i,0) (i,1) (i,2) (i,CW i-2) (i,CW i-1)1 1 1 1
(m,0) (m,1) (m,2) (m,CW m-2) (m,CW m-1)1 1 1 1
(s(t), b(t))(Backoff Stage, Backoff Timer)
(0 ,0 ) (0 ,1 ) (0,2) (0,CW0 -2 ) (0,CW 0 -1)1 1 1 1
(i-1,0)
(m-1,0 )
1-p
p
1 /CW 0
p/CW 1
p/CW i
p/Cw i+1
p/CWm
1/CWm
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802.11 – Slot Time in Bianchi’s Model
channel
sender1
sender2
sender3
One slot time
sender4
collision
Idledata Idle
Busy
Busy
data DIFS
Busy (0, 8) (0, 7)
(2, 2)(2, 3)
(0, 2)(0, 3)
Idle
(0, 8)
(7, 1)
(2, 3)
(0, 3)
Idle
(0, 9)
(7, 2)
(2, 4)
(0, 4)
data
DIFS
Idle
data
Idle
Busy
Busy
Busy (7, 3)(7, 4)
(2, 5)(2, 6)
(0, 5)(0, 6)
Idle
(0, 6)
(0, 1)
(2, 1)
(0, 7)
Collision Idle
data
Busy
data
DIFS
Idle
DIFS
Busy
(0, 6) (0, 5)
(0, 7) (0, 6)
(1, 3)
(3, 6)
(0, 5)
(0, 4)
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Bianchi’s Model: Two Dimensional Markov chain
Probability of transmission:
(0,0) (0,1) (0,2) (0,CW0-2) (0,CW0-1)
(i,0) (i,1) (i,2) (i,CWi-2) (i,CWi-1)
(i-1,0)
(m,0) (m,1) (m,2) (m,CWm-2) (m,CWm-1)
(m-1,0)
1 1 1 1
1-p
1 1 1 1
1 1 1 1
p
1/CW0
p/CW1
p/CWi
p/Cwi+1
p/CWm
1/CWm
, lim ( ) , ( ) , (0, ), (0, 1)i k t ib P s t i b t k i m k CW Stationary distribution:
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Bianchi’s Model: Two Dimensional Markov chain
(0,0) (0,1) (0,2) (0,CW0-2) (0,CW0-1)
(i,0) (i,1) (i,2) (i,CWi-2) (i,CWi-1)
(i-1,0)
(m,0) (m,1) (m,2) (m,CWm-2) (m,CWm-1)
(m-1,0)
1 1 1 1
1-p
1 1 1 1
1 1 1 1
p
1/CW0
p/CW1
p/CWi
p/Cwi+1
p/CWm
1/CWm
SuccessfulTransmission
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Bianchi’s Model: Two Dimensional Markov chain
(0,0) (0,1) (0,2) (0,CW0-2) (0,CW0-1)
(i,0) (i,1) (i,2) (i,CWi-2) (i,CWi-1)
(i-1,0)
(m,0) (m,1) (m,2) (m,CWm-2) (m,CWm-1)
(m-1,0)
1 1 1 1
1-p
1 1 1 1
1 1 1 1
p
1/CW0
p/CW1
p/CWi
p/Cwi+1
p/CWm
1/CWm
Collision
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Bianchi’s Model: Stationary Distribution of Chain
bi,0 = p bi-1,0
(i,0) (i,1) (i,2) (i,CWi-2) (i,CWi-1)
(i-1,0)
1 1 1
p/CWi
bm,0 = p bm-1,0 + p bm,0
(m,0) (m,1) (m,2) (m,CWm-2) (m,CWm-1)
(m-1,0)
1 1 1
p
p/CWm
1/CWm
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Bianchi’s Model: Solution for p and
After some derivations system of two nonlinear equations with two variables p and :
Can be solved numerically to obtain p and
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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
[ ]
[ ] (1 ) (1 )s tr
is tr s tr s c tr id
PP LE Payload Transmitted by user i in a slot time
E Duration of slot time P P T P P T P T
1
1 (1 )
(1 )
1 (1 )
Ntr
N
s N
s H L ACK
c H L
P
NP
T t t SIFS t DIFS
T t t DIFS