ECEN4533 Data Communications Lecture #1511 February 2013 Dr. George Scheets n Review C.1 - C.3 n Problems: Web 7, 8, & 9 n Quiz #1 < 11 February (Async DL) u Corrected quizzes due 13 February (Live) u 1 week after you get them back (DL) n Corrected Design #1 u Due 17 February (Live) u 1 week after you get them back (DL) n Exam #1: 22 February (Live), < 1 March (DL)

ECEN4533 Data Communications Lecture #1613 February 2013 Dr. George Scheets n Problems: Web n Quiz #1: Corrected quizzes Today (Live) u 1 week after you get them back (DL) u Uncorrected Scores F Hi = 18.1, Low = 13.3, Ave = 14.98, σ = 2.08 n Corrected Design #1 u Due 18 February (Live) u 1 week after you get them back (DL) n Exam #1: 22 February (Live), < 1 March (DL)

ECEN4533 Data Communications Lecture #1715 February 2013 Dr. George Scheets n Read 7.1 n Problems: 2010 Exam #1 n Corrected Design #1 u Due 18 February (Live) u 1 week after you get them back (DL) n Exam #1: 22 February (Live), < 1 March (DL)

Probability & Statistics n P(A + B + C) = P(A) + P(B) + P(C) + ??? n P(AB) = P(A)P(B) if Statistically Independent n P(A | B) = P(AB)/P(B) n Gaussian PDF u Q function tables available online n Binomial PDF u Two state experiments u S.I. experiments u # of successes important, not order n Gaussian ≈ Binomial iff N(θ) >> 1 & N(1-θ) >> 1 u Gaussian Mean = Nθ, variance = Nθ(1-θ)

Flip coin 50 times, repeat 400x

Packet Switched StatMux Router or Switch 100 Mbps Trunk Mbps Connections P(Access Line is Active) = 10% n Number of Active Inputs is Binomially Distributed n Can be approximated by Gaussian PDF u Define X to be # of input lines active u X has Mean of 55.9 & Variance 50.31

Moments n 1st Moment E[X] u Mean n 2nd Moment E[X 2 ] u Useful for calculating Variance n Variance = E[X 2 ] - E[X] 2 u Standard Deviation (square root of Variance) ≈ Average deviation from the Mean

Autocorrelation n How alike is a waveform & shifted version of itself? n Given an arbitrary point on the waveform, how predictable is a point τ seconds away? n R X (τ) = 0? u Not alike. Uncorrelated. n R X (τ) > 0? u Alike. Positively correlated. n R X (τ) < 0? u Opposite. Negatively correlated.

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 tau (samples) Rxx 0

255 point Noise Waveform (Low Pass Filtered White Noise) Time Volts 23 points 0

Autocorrelation Estimate of Low Pass Filtered White Noise tau samples Rxx 0 23

Autocorrelation in ATM Cell Stream Each cell slot randomly On or Off (Empty) rx j 600j

Autocorrelation in ATM Cell Stream On & Off bursts average 20 cells rx j 600j

Queue Size: 71% vs 100% Load Average Load impacts Queue Sizes.

mean(queue)=43.59 Queue Size: σ 2 = 5.8 vs σ 2 = 2.9 ρ = 0.99 mean(queue)=20.08 Load Variation impacts Queue Sizes.

Queue Size: Correlated vs Uncorrelated σ 2 = 4.93 & ρ = 0.99 mean(queue)=135.6 mean(queue)=32.80 in(i) = 0.64in(i-1) + random # in(i) = random # Time Correlation impacts Queue Sizes.

Packet Switched StatMux Router or Switch 100 Mbps Trunk ?? 1.54 Mbps Connections P(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 Switch Router or Switch Trunk Multiple Input Switch QueueServer can be modeled by... Switch Memory Trunk NIC

Exponentially Distributed Inter-Arrival Time (Not a good fit to real world traffic) Time Between packet Arrivals (sec) Bin Count Results from Statistically Independent Packet Arrivals.