The validity of IEEE 802.11 MAC modeling
hypotheses
David Malone
Joint work with Kaidi Huang and Ken Duffy
Hamilton Institute, National University of Ireland Maynooth
MACOM, Barcelona, September 14th 2010
David Malone
The validity of IEEE 802.11 MAC modeling hypotheses
Talk outline.
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DCF — the IEEE 802.11 CSMA/CA MAC.
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Mathematical modeling of 802.11 MAC.
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Implicit approximations made to make modeling practical.
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Directly testing these hypotheses with test-bed data.
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Summary, thoughts and conclusions.
David Malone
The validity of IEEE 802.11 MAC modeling hypotheses
The 802.11 DCF
Select Random Number in [0,31]
Data
Ack
SIFS
Pause Counter
Ack
Data
DIFS
Counter
Expires;
Transmit
Resume
Data
Decrement counter
SIFS
DIFS
Figure: 802.11 MAC operation (not to scale)
David Malone
The validity of IEEE 802.11 MAC modeling hypotheses
The 802.11 MAC flow diagram
No collision
(0,0)
(0,1)
(0, W−2)
(0, W−1)
(1,1)
(1, 2W−2)
(1, 2W−1)
(2,1)
(2, 4W−2)
(2, 4W−1)
Collision
No collision
(1,0)
Collision
No collision
(2,0)
Collision
Figure: Saturated 802.11 MAC operation
David Malone
The validity of IEEE 802.11 MAC modeling hypotheses
Popular mathematical modeling approaches
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P-persistent:approximate the back-off distribution be a
geometric with the same mean. E.g. work by Marco Conti
and co-authors (F Cali, M Conti, E Gregori, P Aleph
IEEE/ACM ToN 2000).
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Mean-field Markov models: seminal work by Bianchi (IEEE
Comms L. 1998, IEEE JSAC 2000).
David Malone
The validity of IEEE 802.11 MAC modeling hypotheses
Bianchi’s approach
Observation: each individual station’s impact on overall network
access is small.
Mean field approximation: assume a fixed probability of collision at
each attempted transmission p, irrespective of the past.
Each station’s back-off counter then a Markov chain.
David Malone
The validity of IEEE 802.11 MAC modeling hypotheses
Mean-field Markov Model’s Chain
1−p
1
(0,0)
1
(0,1)
1
(0, W−2)
(0, W−1)
p
1−p
1
(1,0)
1
(1,1)
1
(1, 2W−2)
(1, 2W−1)
p
1−p
1
(2,0)
1
(2,1)
1
(2, 4W−2)
(2, 4W−1)
p
Figure: Individual’s Markov Chain if p known
David Malone
The validity of IEEE 802.11 MAC modeling hypotheses
Mean-field Markov Overview
Stationary distribution gives the probability the station attempts
transmission in a typical slot
2(1 − 2p)
.
(1 − 2p)(W + 1) + pW (1 − (2p)m )
τ (p) =
0.07
tau(p)
0.06
0.05
0.04
0.03
0.02
0.01
0
0
0.1
0.2
0.3
0.4
0.5
p
Figure: Attempt probability τ (p) vs p
David Malone
The validity of IEEE 802.11 MAC modeling hypotheses
The self-consistent equation
Network of N stations. Mean field decoupling idea: the impact of
every station on the network access of the others is small, so that
1 − p = (1 − τ (p))N−1 .
(1)
Solution of equation (1) determines the network’s “real” p ∗ .
1
0.9
(1-tau(p))^{N-1}
0.8
0.7
0.6
0.5
1-p
N=2
N=4
N=8
N=16
0.4
0.3
0
0.1
0.2
0.3
0.4
0.5
p
Figure: 1 − p and (1 − τ (p))N for N = 2, 4, 8 &16
David Malone
The validity of IEEE 802.11 MAC modeling hypotheses
Example developments
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Unsaturated 802.11, Small buffer: Ahn, Campbell, Veres and
Sun, IEEE Trans. Mob. Comp., 2002; Ergen, Varaiya,
ACM-Kluwer MONET, 2005; Malone, Duffy, Leith,
IEEE/ACM Trans. Network., 2007.
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Unsaturated 802.11, Big buffer: Cantieni, Ni, Barakat and
Turletti, Comp. Comm., 2005; Park, Han and Ahn,
Telecomm. Sys., 2006; Duffy. and Ganesh, IEEE Comm.
Lett., 2007.
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802.11e, Saturated: Kong, Tsang, Bensaou and Gao, IEEE
JSAC, 2004; Robinson and Randhawa, IEEE JSAC, 2004.
Unsaturated: Zhai, Kwon and Fang, WCMC, 2004. Chen,
Xhai, Tian and Fang, IEEE Trans. W. Commun., 2006.
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802.11s, unsaturated: Duffy, Leith, Li and Malone, IEEE
Comm. Lett., 2006.
David Malone
The validity of IEEE 802.11 MAC modeling hypotheses
Standard approach to model verification
ASK: Do the model throughput and delay predictions match well
with results from simulated system?
NOT: Make the approximations explicit hypotheses and check
them directly.
Why do these models produce good predictions?
Is there a Therom we should know?
David Malone
The validity of IEEE 802.11 MAC modeling hypotheses
Why is this important?
David Malone
The validity of IEEE 802.11 MAC modeling hypotheses
Test bed
Figure: PC as AP, 1 PC and 9 PC-based Soekris Engineering net4801 as
clients. All with Atheros AR5215 802.11b/g PCI cards. Modified
MADWiFi wireless driver for fixed 11 Mbps transmissions and specified
queue-size.
David Malone
The validity of IEEE 802.11 MAC modeling hypotheses
A first look at the data
0.06
0.05
Average P(col)
P(col on 1st tx)
P(col on 2nd tx)
1.0/32
1.0/64
Probability
0.04
0.03
0.02
0.01
0
100
200
300
400
500
600
700
800
Offered Load (per station, pps, 496B UDP payload)
Figure: Collision probability at backoff stages versus load. 2 stations.
Also checked with simulations.
David Malone
The validity of IEEE 802.11 MAC modeling hypotheses
What are the hypotheses?
Common assumptions to all:
• Ck = 1 if k th transmission results in collision.
• Ck = 0 if k th transmission results in success.
Assumptions:
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(A1) {Ck } is an independent sequence;
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(A2) {Ck } are identically distributed with P(Ck = 1) = p.
David Malone
The validity of IEEE 802.11 MAC modeling hypotheses
Testing (A1): {Ck } independent
Saturated
0.2
N=2 λ=750
N=5 λ=300
N=10 λ=150
AutoCovariance Coefficient
0.15
0.1
0.05
0
−0.05
−0.1
0
5
10
Lag
15
20
Figure: Saturated C1 , . . . , CK normalized auto-covariances. Experimental
data, N = 2, 5, 10, K = 2500k, 1200k, 711k.
David Malone
The validity of IEEE 802.11 MAC modeling hypotheses
Testing (A1): {Ck } pairwise independent
Unsaturated, Big Buffer
0.1
N=2 λ=250
N=5 λ=100
N=10 λ=50
AutoCovariance Coefficient
0.08
0.06
0.04
0.02
0
−0.02
0
5
10
Lag
15
20
Figure: Unsaturated, big buffer C1 , . . . , CK normalized auto-covariances.
Experimental data, N = 2, 5, 10, K = 1800k, 750k, 380k.
David Malone
The validity of IEEE 802.11 MAC modeling hypotheses
Testing (A2): {Ck } identically distributed
Record the backoff stage at which the attempt was made.
Probability pi of collision given backoff stage i.
Assumption (A2): pi = p for all i.
MLE
p̂i =
#collisions at back-off stage i
.
#transmissions at back-off stage i
Hoeffding’s inequality (1963):
P(|p̂i − pi | > x) ≤ 2 exp (−2x(#transmissions at back-off stage i)) .
To have 95% confidence that |p̂i − pi | ≤ 0.01 requires 185
attempted transmissions at backoff stage i .
David Malone
The validity of IEEE 802.11 MAC modeling hypotheses
Testing (A2): {Ck } identically distributed
Saturated
0.5
N=2 λ=750
N=5 λ=300
N=10 λ=150
Bianchi
0.45
0.4
Collision Probability
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0
2
4
6
Backoff Stage
8
10
12
Figure: Saturated collision probabilities. Experimental data.
David Malone
The validity of IEEE 802.11 MAC modeling hypotheses
Testing (A2): {Ck } identically distributed
Unsaturated, Big Buffer
0.16
N=2 λ=250
N=5 λ=100
N=10 λ=50
0.14
Collision Probability
0.12
0.1
0.08
0.06
0.04
0.02
0
0
2
4
6
Backoff Stage
8
10
12
Figure: Unsaturated, big buffer collision probabilities. Experimental data.
David Malone
The validity of IEEE 802.11 MAC modeling hypotheses
What are the big-buffer hypotheses?
Big-buffer models:
• Qk = 1 if packet waiting after k th successful transmission.
• Qk = 0 if no packet waiting after k th successful transmission.
Assumptions:
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(A3) {Qk } is an independent sequence;
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(A4) {Qk } are identically distributed with P(Qk = 1) = q.
David Malone
The validity of IEEE 802.11 MAC modeling hypotheses
Testing (A3): {Qk } pairwise independent
Unsaturated, Big Buffer
1
N=2 λ=250
N=5 λ=100
N=10 λ=50
0.9
AutoCovariance Coefficient
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
5
10
Lag
15
20
Figure: Unsaturated, big buffer queue-non-empty sequence normalized
auto-covariances. Experimental data. K = 1700k, 720k, 360k.
David Malone
The validity of IEEE 802.11 MAC modeling hypotheses
Testing (A4): {Qk } identically distributed
Unsaturated, Big Buffer
0.9
N=2 λ=250
N=5 λ=100
N=10 λ=50
0.8
0.7
P(Q>0)
0.6
0.5
0.4
0.3
0.2
0.1
0
0
2
4
6
Backoff Stage
8
10
12
Figure: Unsaturated, big buffer queue-non-empty probabilities.
Experimental data. (Note the large y-range!)
David Malone
The validity of IEEE 802.11 MAC modeling hypotheses
What about 802.11e?
Select Random Number in [0,31]
Data
Ack
SIFS
Pause Counter
Ack
Data
DIFS
Counter
Expires;
Transmit
Resume
Data
Decrement counter
SIFS
DIFS
Figure: 802.11 MAC operation (not to scale)
David Malone
The validity of IEEE 802.11 MAC modeling hypotheses
What are the 802.11e hypotheses?
Models with different AIFS values:
• Hk is length of k th period we spend in hold-states.
Assumptions:
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(A5) {Hk } is an independent sequence;
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(A6) {Hk } are identically distributed and if we know silence
probability distribution can be determined from Markov chain.
David Malone
The validity of IEEE 802.11 MAC modeling hypotheses
Testing (A5): {Hk } pairwise independent
AutoCovariance Coefficient
0.2
D=2
D=4
D=8
0.15
0.1
0.05
0
0
10
20
Lag
30
40
50
Figure: Hold state normalized auto-covariances. 5 class 1, 5 class 2
stations, D = 2, 4 &8. K = 1700k, 1200k, 850k. ns-2 data
David Malone
The validity of IEEE 802.11 MAC modeling hypotheses
Testing (A6): {Hk } specific distribution
D=2
0.8
0.7
Sim
Theory
0.35
0.6
0.3
0.5
0.25
P(H=i)
P(H=i)
D=12
0.4
Sim
Theory
0.4
0.2
0.15
0.3
0.1
0.2
0.05
0.1
0
0
0
2
4
6
8
i
10
12
14
16
0
10
20
30
40
i
50
60
70
80
Figure: Hold state distributions, D = 2, 12. ns-2 data.
Kolmogorov-Smirnov test accepts fit for K of the order 10, 000;
rejects it for K of the order 1, 000, 000.
David Malone
The validity of IEEE 802.11 MAC modeling hypotheses
What are the 802.11s hypotheses?
Mesh model(s) assume:
• Dk is k th inter-departure time.
Assumptions:
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(A7) {Dk } is an independent sequence;
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(A8) {Dk } are exponentially distributed.
David Malone
The validity of IEEE 802.11 MAC modeling hypotheses
Testing (A7): {Dk } pairwise independent
Unsaturated, Small Buffer
0.2
N=2 λ=400
N=5 λ=160
N=10 λ=80
AutoCovariance Coefficient
0.15
0.1
0.05
0
−0.05
−0.1
0
5
10
Lag
15
20
Figure: Inter-departure time normalized auto-covariances. Experimental
data data
David Malone
The validity of IEEE 802.11 MAC modeling hypotheses
Testing (A8): {Dk } exponentially distributed
Unsaturated, Big Buffer, N=5 !=100
0
Saturated, N=5 !=300
0
10
10
Experimental Data
Theoretical Data
Experimental Data
Theoretical Data
−1
−1
10
10
−2
−2
10
P(D>t)
P(D>t)
10
−3
10
−4
−4
10
10
−5
−5
10
10
−6
10
−3
10
−6
0
2
4
6
8
10
Inter−departure Time, t (µs)
12
14
4
x 10
10
0
1
2
3
4
Inter−departure Time, t (µs)
5
6
4
x 10
Figure: Inter-departure time distribution. 5 stations, small buffer. Low
load, Big Biffer and Saturated. Experimental data
David Malone
The validity of IEEE 802.11 MAC modeling hypotheses
Summary
Assumption
(A1) {Ck } indep.
(A2) {Ck } i. dist.
(A3) {Qk } indep.
(A4) {Qk } i. dist.
(A5) {Hk } indep.
(A6) {Hk } dist.
(A7) {Dk } indep.
(A8) {Dk } exp. dist.
Sat.
X
X
X
X
X
×
Small buf.
X
X
X
light load
Big buf.
X
×
X/×
×
X
light load
Table: {Ck } collision sequence; {Qk } queue-occupied sequence; {Hk }
hold sequence; {Dk } inter-departure time sequence.
David Malone
The validity of IEEE 802.11 MAC modeling hypotheses
What to do?
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Collision probability assumption pretty good.
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Modeling variable queue more tractable.
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I
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Arrival process structure.
Can also build queue into Markov chain.
R.P. Liu, G.J. Sutton, I.B. Collings, IEEE TWC, To Appear.
11e assumptions look OK, for moderate AIFS.
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Full Markov chain?
More specialized.
When network is busy Poisson not that good.
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Insensitive to distribution?
David Malone
The validity of IEEE 802.11 MAC modeling hypotheses
Impact of incorrect hypotheses?
400
60
350
1
2
300
50
Individual Throughput (Packets/s)
Individual Throughput (Packets/s)
λ /λ =30
70
40
30
20
250
200
Sim. Class1
Sim. Class2
Var−q Class1
Var−q Class2
Const−q Class1
Const−q Class2
150
100
Sim.
Var−q
Const−q
10
0
0
200
400
600
800
1000
1200
1400
Network Input (Packets/s)
1600
1800
2000
50
0
0
200
400
600
800
1000
1200
Network Input (Packets/s)
1400
1600
1800
2000
Figure: Theory & ns-2 data.
K.D. Huang & K.R. Duffy IEEE Comms Letters 2009.
David Malone
The validity of IEEE 802.11 MAC modeling hypotheses
Conclusions
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Some of our assumptions are good,
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Some are not so good,
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Our results are usually good, but not always.
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Possible to provide any analysis?
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Other assumptions: slottedness and channel.
Thanks! Questions?
David Malone
The validity of IEEE 802.11 MAC modeling hypotheses