ECEN4533 Data CommunicationsLecture #15 11 February 2013Dr. George Scheets

ECEN4533 Data CommunicationsLecture #15 11 February 2013Dr. George Scheets Review C.1 - C.3Review C.1 - C.3 Problems: Web 7, 8, & 9Problems: Web 7, 8, & 9 Quiz #1 Quiz #1 << 11 February (Async DL) 11 February (Async DL)

Corrected quizzes due 13 February (Live)Corrected quizzes due 13 February (Live) 1 week after you get them back (DL)1 week after you get them back (DL)

Corrected Design #1Corrected Design #1 Due 17 February (Live)Due 17 February (Live) 1 week after you get them back (DL)1 week after you get them back (DL)

Exam #1: 22 February (Live), Exam #1: 22 February (Live), << 1 March (DL) 1 March (DL)

ECEN4533 Data CommunicationsLecture #16 13 February 2013Dr. George Scheets

ECEN4533 Data CommunicationsLecture #16 13 February 2013Dr. George Scheets Problems: Web 10 - 12Problems: Web 10 - 12 Quiz #1: Quiz #1: Corrected quizzes Today (Live)Corrected quizzes Today (Live)

1 week after you get them back (DL)1 week after you get them back (DL) Uncorrected ScoresUncorrected Scores

Hi = 18.1, Low = 13.3, Ave = 14.98, Hi = 18.1, Low = 13.3, Ave = 14.98, σσ = 2.08 = 2.08

Corrected Design #1Corrected Design #1 Due 18 February (Live)Due 18 February (Live) 1 week after you get them back (DL)1 week after you get them back (DL)

Exam #1: 22 February (Live), Exam #1: 22 February (Live), << 1 March (DL) 1 March (DL)

ECEN4533 Data CommunicationsLecture #17 15 February 2013Dr. George Scheets

ECEN4533 Data CommunicationsLecture #17 15 February 2013Dr. George Scheets

Read 7.1Read 7.1 Problems: 2010 Exam #1Problems: 2010 Exam #1 Corrected Design #1Corrected Design #1

Due 18 February (Live)Due 18 February (Live) 1 week after you get them back (DL)1 week after you get them back (DL)

Exam #1: 22 February (Live), Exam #1: 22 February (Live), << 1 March (DL) 1 March (DL)

Probability & StatisticsProbability & Statistics P(A + B + C) = P(A) + P(B) + P(C) P(A + B + C) = P(A) + P(B) + P(C) ++ ??? ??? P(AB) = P(A)P(B) if Statistically IndependentP(AB) = P(A)P(B) if Statistically Independent P(A | B) = P(AB)/P(B)P(A | B) = P(AB)/P(B) Gaussian PDFGaussian PDF

Q function tables available onlineQ function tables available online Binomial PDFBinomial PDF

Two state experimentsTwo state experiments S.I. experimentsS.I. experiments # of successes important, not order# of successes important, not order

Gaussian ≈ Binomial iff N(Gaussian ≈ Binomial iff N(θθ) >> 1 & N(1-) >> 1 & N(1-θθ) >> 1) >> 1 Gaussian Mean = NGaussian Mean = Nθθ, variance = N, variance = Nθθ(1-(1-θθ))

Flip coin 50 times, repeat 400xFlip coin 50 times, repeat 400x

Packet Switched StatMuxPacket Switched StatMux

Routeror

Switch 100 Mbps Trunk

559 1.54 Mbps ConnectionsP(Access Line is Active) = 10%

Number of Active Inputs is Binomially DistributedNumber of Active Inputs is Binomially Distributed Can be approximated by Gaussian PDFCan be approximated by Gaussian PDF

Define X to be # of input lines activeDefine X to be # of input lines active X has Mean of 55.9 & Variance 50.31X has Mean of 55.9 & Variance 50.31

MomentsMoments

1st Moment E[X]1st Moment E[X] MeanMean

2nd Moment E[X2nd Moment E[X22]] Useful for calculating VarianceUseful for calculating Variance

Variance = E[XVariance = E[X22] - E[X]] - E[X]22 Standard Deviation (square root of Variance)Standard Deviation (square root of Variance)

≈ Average deviation from the Mean≈ Average deviation from the Mean

AutocorrelationAutocorrelation

How alike is a waveform & shifted version of itself?How alike is a waveform & shifted version of itself? Given an arbitrary point on the waveform, how Given an arbitrary point on the waveform, how

predictable is a point predictable is a point ττ seconds away? seconds away? RRXX((ττ) = 0?) = 0?

Not alike. Uncorrelated.Not alike. Uncorrelated. RRXX((ττ) > 0?) > 0?

Alike. Positively correlated.Alike. Positively correlated. RRXX((ττ) < 0?) < 0?

Opposite. Negatively correlated.Opposite. Negatively correlated.

255 point zero mean discrete time White Noise waveform(Adjacent points are independent)

255 point zero mean discrete time White Noise waveform(Adjacent points are independent)

time

Volts

0

Autocorrelation Estimate of zero mean

Discrete Time White Noise

Autocorrelation Estimate of zero mean

Discrete Time White Noise

tau (samples)

Rxx

0

255 point Noise Waveform(Low Pass Filtered White Noise)255 point Noise Waveform(Low Pass Filtered White Noise)

Time

Volts

23 points

0

Autocorrelation Estimate of Low Pass Filtered White NoiseAutocorrelation Estimate of Low Pass Filtered White Noise

tau samples

Rxx

0

23

Autocorrelation in ATM Cell StreamEach cell slot randomly On or Off (Empty)Autocorrelation in ATM Cell StreamEach cell slot randomly On or Off (Empty)

0 20 40 60 80 1001

0

11.25

1

xi

1000 i

0 10 20 30 40 50 6020

0

20

4032

3

rxj

600 j

Autocorrelation in ATM Cell StreamOn & Off bursts average 20 cells Autocorrelation in ATM Cell StreamOn & Off bursts average 20 cells

0 50 100 150 200 250 300 350 4001

0

11.25

1

xi

4000 i

0 10 20 30 40 50 6020

0

20

4032

6

rxj

600 j

Queue Size: 71% vs 100% LoadQueue Size: 71% vs 100% LoadAverage

LoadimpactsQueueSizes.

mean(queue)=43.59

Queue Size: σ2 = 5.8 vs σ2 = 2.9ρ = 0.99

Queue Size: σ2 = 5.8 vs σ2 = 2.9ρ = 0.99

mean(queue)=20.08

LoadVariationimpactsQueueSizes.

Queue Size: Correlated vs Uncorrelated σ2 = 4.93 & ρ = 0.99

Queue Size: Correlated vs Uncorrelated σ2 = 4.93 & ρ = 0.99

mean(queue)=135.6

mean(queue)=32.80

in(i) = 0.64in(i-1) + random #

in(i) = random #

TimeCorrelation

impactsQueueSizes.

Packet Switched StatMuxPacket Switched StatMux

Routeror

Switch 100 Mbps Trunk

?? 1.54 Mbps ConnectionsP(Access Line is Active) = 10%

Trunk Bandwidth assigned based on average input rates. *Infinite Buffers? Can support 649 access lines. *Negligible Buffering? Can support 405 lines

w/P(input > 100 Mbps) = .0001

Statistical Multiplexed Packet SwitchStatistical Multiplexed Packet Switch

Routeror

Switch Trunk

Multiple Input Switch

Queue Server

can be modeled by...Switch Memory

Trunk NIC

Exponentially Distributed Inter-Arrival Time(Not a good fit to real world traffic)

Exponentially Distributed Inter-Arrival Time(Not a good fit to real world traffic)

Time Between packet Arrivals (sec)

BinCount

Results fromStatisticallyIndependent

Packet Arrivals.