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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

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Numerical Results

Basic Mode RTS/CTSBasic Mode RTS/CTS

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»

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