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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. 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. 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 I 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). I 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 I 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. I 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. I 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. I 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: I (A1) {Ck } is an independent sequence; I (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: I (A3) {Qk } is an independent sequence; I (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: I (A5) {Hk } is an independent sequence; I (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: I (A7) {Dk } is an independent sequence; I (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? I Collision probability assumption pretty good. I I Modeling variable queue more tractable. I I I 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. I I Full Markov chain? More specialized. When network is busy Poisson not that good. I 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 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? David Malone The validity of IEEE 802.11 MAC modeling hypotheses