The validity of IEEE 802.11 MAC modeling hypothesesdwmalone/p/macom2010.pdf · Talk outline. I DCF...

The validity of IEEE 802.11 MAC modelinghypotheses

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.

I DCF — the IEEE 802.11 CSMA/CA MAC.

I Mathematical modeling of 802.11 MAC.

I Implicit approximations made to make modeling practical.

I Directly testing these hypotheses with test-bed data.

I Summary, thoughts and conclusions.


The 802.11 DCF

DataData

SIFS DIFS Decrement counter

Select Random Number in [0,31]

SIFS DIFS

CounterExpires;Transmit

Pause CounterResumeAck Ack

Data

Figure: 802.11 MAC operation (not to scale)


The 802.11 MAC flow diagram

(0, W−2)(0,1)

(1,1)(1,0)

Collision

Collision

(2,0) (2,1)

Collision

(0,0)

No collision

No collision

No collision

(0, W−1)

(1, 2W−1)

(2, 4W−1)(2, 4W−2)

(1, 2W−2)

Figure: Saturated 802.11 MAC operation


Popular mathematical modeling approaches

I P-persistent:approximate the back-off distribution be ageometric with the same mean. E.g. work by Marco Contiand co-authors (F Cali, M Conti, E Gregori, P AlephIEEE/ACM ToN 2000).

I Mean-field Markov models: seminal work by Bianchi (IEEEComms L. 1998, IEEE JSAC 2000).


Bianchi’s approach

Observation: each individual station’s impact on overall networkaccess is small.Mean field approximation: assume a fixed probability of collision ateach attempted transmission p, irrespective of the past.Each station’s back-off counter then a Markov chain.


Mean-field Markov Model’s Chain

(2, 4W−2)

(0,1)

(1,1)(1,0)

(0,0)

1−p

(2,0) (2,1)

111

1 1 1

11

p

p

p

1−p

1−p

1(2, 4W−1)

(1, 2W−1)

(0, W−1)(0, W−2)

(1, 2W−2)

Figure: Individual’s Markov Chain if p known


Mean-field Markov OverviewStationary distribution gives the probability the station attemptstransmission in a typical slot

τ(p) =2(1− 2p)

(1− 2p)(W + 1) + pW (1− (2p)m).

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0 0.1 0.2 0.3 0.4 0.5p

tau(p)

Figure: Attempt probability τ(p) vs p


The self-consistent equation

Network of N stations. Mean field decoupling idea: the impact ofevery 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∗.

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5

(1-ta

u(p)

)^{N

-1}

p

1-pN=2N=4N=8

N=16

Figure: 1− p and (1− τ(p))N for N = 2, 4, 8 &16


Example developments

I Unsaturated 802.11, Small buffer: Ahn, Campbell, Veres andSun, IEEE Trans. Mob. Comp., 2002; Ergen, Varaiya,ACM-Kluwer MONET, 2005; Malone, Duffy, Leith,IEEE/ACM Trans. Network., 2007.

I Unsaturated 802.11, Big buffer: Cantieni, Ni, Barakat andTurletti, Comp. Comm., 2005; Park, Han and Ahn,Telecomm. Sys., 2006; Duffy. and Ganesh, IEEE Comm.Lett., 2007.

I 802.11e, Saturated: Kong, Tsang, Bensaou and Gao, IEEEJSAC, 2004; Robinson and Randhawa, IEEE JSAC, 2004.Unsaturated: Zhai, Kwon and Fang, WCMC, 2004. Chen,Xhai, Tian and Fang, IEEE Trans. W. Commun., 2006.

I 802.11s, unsaturated: Duffy, Leith, Li and Malone, IEEEComm. Lett., 2006.


Standard approach to model verification

ASK: Do the model throughput and delay predictions match wellwith results from simulated system?

NOT: Make the approximations explicit hypotheses and checkthem directly.

Why do these models produce good predictions?Is there a Therom we should know?


Why is this important?


Test bed

Figure: PC as AP, 1 PC and 9 PC-based Soekris Engineering net4801 asclients. All with Atheros AR5215 802.11b/g PCI cards. ModifiedMADWiFi wireless driver for fixed 11 Mbps transmissions and specifiedqueue-size.


A first look at the data

0

0.01

0.02

0.03

0.04

0.05

0.06

100 200 300 400 500 600 700 800

Pro

babi

lity

Offered Load (per station, pps, 496B UDP payload)

Average P(col)P(col on 1st tx)

P(col on 2nd tx)1.0/321.0/64

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 kth transmission results in collision.• Ck = 0 if kth transmission results in success.Assumptions:

I (A1) {Ck} is an independent sequence;

I (A2) {Ck} are identically distributed with P(Ck = 1) = p.


Testing (A1): {Ck} independent

0 5 10 15 20−0.1

−0.05

0

0.05

0.1

0.15

0.2

Lag

Aut

oCov

aria

nce

Coe

ffici

ent

Saturated

N=2 λ=750N=5 λ=300N=10 λ=150

Figure: Saturated C1, . . . ,CK normalized auto-covariances. Experimentaldata, N = 2, 5, 10, K = 2500k, 1200k, 711k.


Testing (A1): {Ck} pairwise independent

0 5 10 15 20−0.02

0

0.02

0.04

0.06

0.08

0.1

Lag

Aut

oCov

aria

nce

Coe

ffici

ent

Unsaturated, Big Buffer

N=2 λ=250N=5 λ=100N=10 λ=50

Figure: Unsaturated, big buffer C1, . . . ,CK normalized auto-covariances.Experimental data, N = 2, 5, 10, K = 1800k, 750k, 380k.


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 185attempted transmissions at backoff stage i .



0 2 4 6 8 10 120

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Backoff Stage

Col

lisio

n P

roba

bilit

y

Saturated

N=2 λ=750N=5 λ=300N=10 λ=150Bianchi

Figure: Saturated collision probabilities. Experimental data.



0 2 4 6 8 10 120

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Backoff Stage

Col

lisio

n P

roba

bilit

y


N=2 λ=250N=5 λ=100N=10 λ=50

Figure: Unsaturated, big buffer collision probabilities. Experimental data.


What are the big-buffer hypotheses?

Big-buffer models:• Qk = 1 if packet waiting after kth successful transmission.• Qk = 0 if no packet waiting after kth successful transmission.Assumptions:

I (A3) {Qk} is an independent sequence;

I (A4) {Qk} are identically distributed with P(Qk = 1) = q.


Testing (A3): {Qk} pairwise independent

0 5 10 15 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Lag

Aut

oCov

aria

nce

Coe

ffici

ent


N=2 λ=250N=5 λ=100N=10 λ=50

Figure: Unsaturated, big buffer queue-non-empty sequence normalizedauto-covariances. Experimental data. K = 1700k, 720k, 360k.


Testing (A4): {Qk} identically distributed

0 2 4 6 8 10 120

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Backoff Stage

P(Q

>0)


N=2 λ=250N=5 λ=100N=10 λ=50

Figure: Unsaturated, big buffer queue-non-empty probabilities.Experimental data. (Note the large y-range!)


What about 802.11e?

DataData

SIFS DIFS Decrement counter

Select Random Number in [0,31]

SIFS DIFS

CounterExpires;Transmit

Pause CounterResumeAck Ack

Data

Figure: 802.11 MAC operation (not to scale)


What are the 802.11e hypotheses?

Models with different AIFS values:• Hk is length of kth period we spend in hold-states.Assumptions:

I (A5) {Hk} is an independent sequence;

I (A6) {Hk} are identically distributed and if we know silenceprobability distribution can be determined from Markov chain.


Testing (A5): {Hk} pairwise independent

0 10 20 30 40 50

0

0.05

0.1

0.15

0.2

Lag

Aut

oCov

aria

nce

Coe

ffici

ent

D=2D=4D=8

Figure: Hold state normalized auto-covariances. 5 class 1, 5 class 2stations, D = 2, 4 &8. K = 1700k, 1200k, 850k. ns-2 data


Testing (A6): {Hk} specific distribution

0 2 4 6 8 10 12 14 160

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

i

P(H

=i)

D=2

SimTheory

0 10 20 30 40 50 60 70 80

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

i

P(H

=i)

D=12

SimTheory

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.


What are the 802.11s hypotheses?

Mesh model(s) assume:• Dk is kth inter-departure time.Assumptions:

I (A7) {Dk} is an independent sequence;

I (A8) {Dk} are exponentially distributed.


Testing (A7): {Dk} pairwise independent

0 5 10 15 20−0.1

−0.05

0

0.05

0.1

0.15

0.2

Lag

Aut

oCov

aria

nce

Coe

ffici

ent

Unsaturated, Small Buffer

N=2 λ=400N=5 λ=160N=10 λ=80

Figure: Inter-departure time normalized auto-covariances. Experimentaldata data


Testing (A8): {Dk} exponentially distributed

0 2 4 6 8 10 12 14x 104

10−6

10−5

10−4

10−3

10−2

10−1

100

Inter−departure Time, t (µs)

P(D

>t)

Unsaturated, Big Buffer, N=5 !=100

Experimental DataTheoretical Data

0 1 2 3 4 5 6x 104

10−6

10−5

10−4

10−3

10−2

10−1

100

Inter−departure Time, t (µs)

P(D

>t)

Saturated, N=5 !=300

Experimental DataTheoretical Data

Figure: Inter-departure time distribution. 5 stations, small buffer. Lowload, Big Biffer and Saturated. Experimental data


Summary

Assumption Sat. Small buf. Big buf.

(A1) {Ck} indep. X X X(A2) {Ck} i. dist. X X ×(A3) {Qk} indep. - - X/×(A4) {Qk} i. dist. - - ×(A5) {Hk} indep. X - -

(A6) {Hk} dist. X - -

(A7) {Dk} indep. X X X(A8) {Dk} exp. dist. × light load light load

Table: {Ck} collision sequence; {Qk} queue-occupied sequence; {Hk}hold sequence; {Dk} inter-departure time sequence.


What to do?

I Collision probability assumption pretty good.I Full Markov chain?

I Modeling variable queue more tractable.I Arrival process structure.I Can also build queue into Markov chain.

R.P. Liu, G.J. Sutton, I.B. Collings, IEEE TWC, To Appear.

I 11e assumptions look OK, for moderate AIFS.I More specialized.

I When network is busy Poisson not that good.I Insensitive to distribution?


Impact of incorrect hypotheses?

0 200 400 600 800 1000 1200 1400 1600 1800 20000

10

20

30

40

50

60

70

Network Input (Packets/s)

Indi

vidu

al T

hrou

ghpu

t (P

acke

ts/s

)

Sim.Var−qConst−q

0 200 400 600 800 1000 1200 1400 1600 1800 20000

50

100

150

200

250

300

350

400

Network Input (Packets/s)

Indi

vidu

al T

hrou

ghpu

t (P

acke

ts/s

)

λ1/λ

2=30

Sim. Class1Sim. Class2Var−q Class1Var−q Class2Const−q Class1Const−q Class2

Figure: Theory & ns-2 data.

K.D. Huang & K.R. Duffy IEEE Comms Letters 2009.


Conclusions

I Some of our assumptions are good,

I Some are not so good,

I Our results are usually good, but not always.

I Possible to provide any analysis?

I Other assumptions: slottedness and channel.

Thanks! Questions?


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