WiFi MAC Models
David Malone
November 2006, MACSI
Hamilton Institute, NUIM, Ireland
Talk outline
•
•
•
•
•
•
Introducing the 802.11 CSMA/CA MAC.
Finite load 802.11 model and its predictions.
Issues with standard 802.11, leading to 802.11e.
Finite load 802.11e model and its predictions.
Beyond infrastructure mode networks.
Why do these models work?
Hamilton Institute, NUIM, Ireland
1
The 802.11 MAC
Select Random Number in [0,31]
Pause Counter
Data
Resume
Counter
Expires;
Transmit
Ack
Decrement counter
SIFS
DIFS
SIFS
DIFS
Figure 1: 802.11 MAC operation
Hamilton Institute, NUIM, Ireland
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802.11 MAC Summary
•
•
•
•
•
After transmission choose rand(0, CW − 1).
Wait until medium idle for DIFS(50µs),
While idle count down in slots (20µs).
Transmission when counter gets to 0, ACK after SIFS (10µs).
If ACK then CW = CWmin else CW∗ = 2.
Ideally produces even distribution of packet transmission.
Hamilton Institute, NUIM, Ireland
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Modelling approaches
• P-persistent: approximate the back-off distribution be a geometric with the
same mean. Exemplified by Marco Conti and co-authors.
• Asymptotic full system analysis: Bordenave, McDonald and Proutiere +
Sharma, Ganesh and Key.
• Bianchi’s mean-field Markov model: treat stations individually; network
relationship between stations gives a set of coupling equations.
In simplest form: constant transmission probability τ gives throughput
S = nτ (1 − τ )n−1 ,
(1)
1 − p = (1 − τ )n−1 .
(2)
and collision probability
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Mean-field Markov Overview
Mean field approximation: each individual station’s impact on overall network is
small. Assume a fixed probability of collision given attempted transmission p.
Each station’s back-off counter then a Markov chain. Stationary distribution
gives the probability the station attempts transmission in a typical slot τ (p).
Network coupling then gives a system of equations relating all stations’ p and τ ,
which determines everything.
Real-time quantities determined through a relation involving the average real-time
that passes during a counter decrement.
Following to appear in IEEE/ACM ToN (Duffy, Leith, Malone).
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Mean-field Markov Model’s Chain
(1−q)(1−p)
(1−q)(1−p)
(1−q)
q(1−p)(1−p)(1−q)
(1−q)
(1−q)
(0,0)e
(0,1)e
qp
q(1−p)
(1−q)
(0, CW−2)e
q
q
(0, CW−1)e
q
q(1−p)p
1
1
(0,0)
(0,1)
1
(0, CW−2)
(0, CW−1)
q(1−p)
p
(1,0)
1
1
(1,1)
1
(1, 2CW−2)
(1, 2CW−1)
p
Figure 2: Individual’s Markov Chain
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Mean-field Markov Model Solution
Stationary distribution of Markov chain gives:
τ (p, q, W0, m) = η
−1
2
2
q W0
q (1 − p)
−
,
(1 − p)(1 − q)(1 − (1 − q)W0 )
1−q
(3)
where
η
q(W0 +1)
q 2 W0 (W0 +1)
q 2 W0
= (1 − q) + 2(1−(1−q)W0 ) + 2(1−q) 1−(1−q)W0 + p(1 − q) − q(1
m−1
2
1−p−p(2p)
W0
pq
2
+1 .
+ 2(1−q)(1−p)
2W0
−
(1
−
p)
W
1−2p
1−(1−q) 0
Hamilton Institute, NUIM, Ireland
− p)2
7
Network coupling
For given loads q1, . . . , qn, define τj = τ (pj , qj , W0, m) and then n coupling
equations:
Y
1 − pi =
(1 − τj ).
j6=i
Solve to determine (p1, τ1), . . . , (pn, τn).
If all packets are the same length, L bytes taking TL time on the medium, then
τi(1 − pi)L
Qn
.
i=1(1 − τi )δ + (1 −
i=1(1 − τi ))TL
Si = Qn
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Relating q to offered load
• Taking lim models saturation.
q→1
• For small buffers, a crude approximation:
q = min(Expected slot length/mean inter-packet time, 1).
• If packets arrive a Poisson manner with rate λl , then ql is 1 −
exp(−λlExpected slot length).
• Possible to produce a relation of this sort that uses conditional information.
Hamilton Institute, NUIM, Ireland
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Model Predictions
0.35
normalised throughput
0.3
0.25
16 stations (sim)
(model unif)
(model Pois)
(model Cond)
20 stations (sim)
(model unif)
(model Pois)
(model Cond)
24 stations (sim)
(model unif)
(model Pois)
(model Cond)
0.2
0.15
0.1
0
0.2
0.4
0.6
0.8
1
1.2
normalised total offered load
1.4
1.6
Throughput as the traffic arrival rate is varied. Results for three load relationships
(uniform, Poisson and conditional) shown.
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Model Predictions
0.02
model class 1
model class 2
simulation
normalised per-node throughput
0.018
0.016
0.014
0.012
0.01
0.008
0.006
0.004
0.002
0
0
0.5
1
1.5
2
total offered normalised load
2.5
3
Normalized per-station throughput, where n1 = 12, n2 = 24. The offered load of
a class 2 station is 1/4 of a class 1 station.
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TCP Upload Scenario
Access Point
Stations with competing TCP uploads
Figure 3: Competing TCP uploads.
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TCP Uploads
1.8
1.6
TCP throughput (Mbps)
1.4
1.2
1
0.8
0.6
0.4
0.2
0
1
2
3
4
5
6
7
8
9
10
Number of the upstream connection
Figure 4: Competing TCP uploads, 10 stations (NS2 simulation, 802.11 MAC,
300s duration).
Hamilton Institute, NUIM, Ireland
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The 802.11e MAC
The three most significant 802.11e MAC parameters on traffic prioritization are
TXOP, W0 and AIFS.
•
•
•
•
Four traffic classes per station.
Station transmits for max duration TXOP (one packet without 802.11e).
Per class, W0 is 2n, n ∈ {0, 1, . . .}.
Per class, AIFS = DIFS + kδ, k ∈ {−2, −1, 0, 1, . . .}.
Hamilton Institute, NUIM, Ireland
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The 802.11 MAC
Select Random Number in [0,W−1]
0
Pause Counter
Data
Resume
Counter
Expires;
Transmit
Ack
Decrement counter
SIFS
AIFS
SIFS
AIFS
Figure 5: 802.11 MAC operation
Hamilton Institute, NUIM, Ireland
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Existing 802.11e models
Saturated 802.11e multi-class models.
• R. Battiti and Bo Li, University of Trento Technical Report DIT-03-024 (2003).
• J.W. Robinson and T.S. Randhawa, IEEE JSAC 22:5 (2004).
• Z. Kong, D. H.K. Tsang, B. Bensaou and D. Gao, IEEE JSAC 22:10 (2004).
Following (maybe!) to appear in IEEE Trans. Mob. Computing, with Clifford,
Duffy, Foy, Leith and Malone.
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Modelling 802.11e
Added complications: Need hold states for AIF S.
(1 −
Ph =
1 + (1 −
Hamilton Institute, NUIM, Ireland
(1)
Q n1
j=1(1 − τj )
Qn1
j=1(1 −
Q n2
(2)
j=1(1 − τj ))
(1) Qn2
τj ) j=1(1
(2)
D
X
PS−i
1
i=1
D
X
− τj ))
.
(4)
PS−i
1
i=1
17
New coupling equations
(1)
1 − pi
=
Y
(1)
(1 − τj )(Ph + (1 − Ph)
j6=i
1−
(2)
pi
(2)
(1 − τj ))
(5)
j=1
=
n1
Y
(1 −
j=1
Hamilton Institute, NUIM, Ireland
n2
Y
(1)
τj )
Y
(2)
(1 − τj ).
(6)
j6=i
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How good is it?
0.25
0.2
0.15
0.1
0.05
0.25
model class 1
model class 2
simulation
0.2
Per station throughput (Mbps)
model class 1
model class 2
simulation
Per station throughput (Mbps)
Per station throughput (Mbps)
0.25
0.15
0.1
0.05
0
5
10
15
20
Total offered load (Mbps)
(a) D = 0
25
30
0.2
0.15
0.1
0.05
0
0
model class 1
model class 2
simulation
0
0
5
10
15
20
Total offered load (Mbps)
(b) D = 2
25
30
0
5
10
15
20
Total offered load (Mbps)
25
30
(c) D = 4
Throughput for a station in each class vs. offered load. 10 class 1 stations offering
one quarter the load of 20 class 2 stations. Range of D values, the difference
in AIFS between class 2 and class 1 (NS2 simulation and model predictions,
802.11e MAC, 11Mbps PHY, 100s duration. ).
Hamilton Institute, NUIM, Ireland
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How good is it?
0.25
0.2
0.15
0.1
0.05
0.25
model class 1
model class 2
simulation
0.2
Per station throughput (Mbps)
model class 1
model class 2
simulation
Per station throughput (Mbps)
Per station throughput (Mbps)
0.25
0.15
0.1
0.05
0
5
10
(1)
(d) W0
15
20
Total offered load (Mbps)
(2)
= 32, W0
25
30
= 16
0.2
0.15
0.1
0.05
0
0
model class 1
model class 2
simulation
0
0
5
(1)
(e) W0
10
15
20
Total offered load (Mbps)
(2)
= 32, W0
25
30
= 64
0
5
(1)
(f) W0
10
15
20
Total offered load (Mbps)
(2)
= 32,W0
25
30
= 256
Throughput for a station in each class vs. offered load. There are 10 class 1
stations each offering one quarter the load of 20 class 2 stations. Range of W0
values (NS2 simulation and model predictions, 802.11e MAC 11Mbps PHY, 100s
duration).
Hamilton Institute, NUIM, Ireland
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How do you use it?
6
0.9
W1=1
W1=2
W1=4
W1=8
W1=16
W1=32
5
W1=1
W1=2
W1=4
W1=8
W1=16
W1=32
0.8
Ratio of lost traffic to offered load
Throughput of Data Stations (Mbps)
0.7
4
3
2
0.6
0.5
0.4
0.3
0.2
1
0.1
0
0
0
5
10
Difference in AIFS
(g) Data throughput
15
20
0
5
10
Difference in AIFS
15
20
(h) ACK loss
10 stations (1500 byte packets) and AP transmitting (60 byte packets) at half
achieved data rate.
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1.2
0.6
1
0.5
0.8
0.4
TCP Throughput (Mbps)
TCP Throughput (Mbps)
Does it work?
0.6
0.4
0.2
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
Number of the upstream connection
10
11
12
1
2
3
4
5
6
7
8
9
Number of the upstream connection
10
11
12
Competing TCP uploads, 12 stations experiment without and with prioritization
(802.11e MAC, 300s duration).
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Why stop with single infrastructure mode network?
Basic behavior of individual stations is independent of the network in which they
exist. Change the network coupling, change the network.
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Typical mesh issue
0.4
0.35
throughput (Mbs)
0.3
0.25
0.2
0.15
NS
0.05
1
0
2
r0
NS r
0.1
0
5
10
15
#conversations
20
25
Example of aggregate throughput vs number of voice calls for the multi-hop
2
802.11b WLAN topology. Voice packets are transported between l11 and l12 , ..., lN
by node r01/r02 which denotes a relay station with two radios.
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Mesh
Following in IEEE Comms. Letters (2006), (Duffy, Leith, Li and Malone).
M distinct local zones on common frequency. For n ∈ {1, . . . , M } local stations
Ln = {l1n, . . .} and relay stations Rn = {r0n, . . .}. Mean field gives for each
station c ∈ Rn ∪ Ln:
1 − pc =
Y
(1 − τb).
(7)
b∈Rn ∪Ln , b6=c
Q
The stationary probability the medium is idle is pidle = b∈Rn∪Ln (1 − τb). The
mean state length is En = pidleσ + L(1 − pidle), where each packet takes L
seconds and idle slot-length is σ seconds.
Added difficulty: for each n, l ∈ Ln, ql is given, but qr is not known a priori for
each relay station.
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Mesh
The parameter qr is determined through relay traffic.
• For each n, l ∈ Ln, a fixed route fl from its zone to a destination zone.
fl = {l, s1 . . . , sm, d}.
• If m = 0, then l and d are in the same zone and no relaying occurs.
• We assume routes are predetermined by an appropriate wireless routing
protocol.
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Mesh
For each s ∈ Ln ∪ Rn, let E(s) = En. For k ∈ {1, . . . , m} Let Ql,sk be offered
load from l arriving at sk and Qsk be the total load offered to sk . From these we
calculate:
τs (1 − psk )
S sk = k
En
and then assume:
X Ql,s
k
Ss
Qsk+1 =
Qsk k
to calculate the load in the next network.
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Buffering
• Limitations of small buffers particularly apparent in mesh.
• Need to introduce queue empty probability to model queue: rn.
• Model queues as M/G/1.
W0
E(B(p)) =
(1 − p − p(2p)m).
2(1 − 2p)
(8)
rn = min(1, −B(pn) log(1 − qn))
(9)
Simply replaces τ (p) relation.
To appear, IEEE Comms. Letters (2007), (Duffy, Ganesh).
Seeing some interaction between buffering and service.
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Unfairness
One conversation, N data stations
500
400
Conv. throughput, small buffer
Data throughput, when conversation has small buffer
Conv. throughput, large buffer
Data throughput, when conversation has large buffer
64 kbps
350
400
250
300
200
200
<-- Mean delay, conv., large buffer
150
Delay (milli seconds)
Throughput (kbps)
300
100
100
50
0
0
0
5
10
15
Number of data stations, N
20
25
Figure 6: N S packet-level simulation results and model predictions
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Understanding the Models
•
•
•
•
Models are inexact in several ways.
Constant p replaces complex Markov chain with direct sum.
Throughput relationship assumes independent.
Do assumptions hold or are stationary distributions similar?
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Is p constant?
0.06
0.05
0.3
Average P(col)
P(col on 1st tx)
P(col on 2nd tx)
1.0/32
1.0/64
0.25
0.2
Probability
Probability
0.04
0.03
0.15
0.02
0.1
0.01
0.05
Average P(col)
P(col on 1st tx)
P(col on 2nd tx)
0
100
0
200
300
400
500
600
Offered Load (per station, pps, 496B UDP payload)
(a) 2 Stations
700
800
40
60
80
100
120
140
160
180
Offered Load (per station, pps, 486B UDP payload)
(b) 10 Stations
Figure 7: Measured collision probabilities as offered load is varied.
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Independence of Transmissions
4000
3500
Throughput (Kbps)
3000
2500
2000
1500
1000
500
Throughput (measured)
Throughput (model)
Throughput (model + measured Ts/Tc)
Throughput (model + measured Ts/Tc/p)
0
2
4
6
8
Number of STA(s)
10
12
14
Figure 8: Overall throughput in a network of saturated stations as the number of
stations is varied. The measured values are compared to model predictions.
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Conclusions
• 802.11/802.11e CSMA/CA models that are simple, solvable, yet complex
enough to predict data throughput.
• Model gives insight into 802.11 MAC behavior.
• Model gives insight into effect of 802.11e parameters.
• Prioritization schemes can now be designed quickly based on the model.
• Extensible to network scenarios.
• Interesting questions on buffering and foundations remain to be answered.
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