1. Shivkumar Kalyanaraman Rensselaer Polytechnic Institute 1 ECSE-4963: Experimental Networking Exam 1: SOLUTIONS Time: 60 min (strictly enforced) Points: 50 YOUR NAME: Be brief, but DO NOT omit necessary detail {Note: Simply copying text directly from the slides or notes will not earn (partial) credit. Brief, clear and consistent explanation will.}

2. Shivkumar Kalyanaraman Rensselaer Polytechnic Institute 2 I. Quick questions on probability/experiment design 1. [5 pts] What is the difference between the cumulative distribution function (CDF) and probability density function (pdf)? State one purpose where CDF is easier to work with than the pdf ?(hint: mean vs median) Pdf is the derivative of the CDF. The median = F -1 (0.5)

3. Shivkumar Kalyanaraman Rensselaer Polytechnic Institute 3 I. [10 pts] Show (derive) that if two random variables are independent {I.e. P(XY) = P(X)P(Y)} they are uncorrelated {I.e. E(XY) = E(X)E(Y) }, but the reverse is not true. {assuming discrete r.v.s} E(XY) =  x i y j P[x i, y j ] =  x i y j P[x i ] P[y j ] {due to independence} =  x i P[x i ]  y j P[y j ] = E(X)E(Y) The reverse argument cannot be made generally because the terms P[x i, y j ], P[x i ], P[y j ] are inside the summations (I.e. within the  ). Many counter examples can also be given… {Eg: X = Cos u ; Y = Sin u }

4. Shivkumar Kalyanaraman Rensselaer Polytechnic Institute 4 2. [10 pts] Given: n=6 random RTT samples (in ms): {31, 42, 28, 51, 28, 40} q Find: sample mean (xbar), sample standard deviation (s), 90% confidence interval (CI) & 95% CI for the population mean xbar = 1/6 {31 + 42 + 28 + 51 + 28 + 40} = 36.67 s 2 = 1/(6-1) { (31-36.67) 2 + (42-36.67) 2 + (28-36.67) 2 + (51-36.67) 2 + (28-36.67) 2 + (40-36.67) 2 } = 85.467 => s = 9.243 Since we have only 6 samples, we cannot use normal distribution, but need to use the t distribution (not the z-distribution!) with n-1 = 5 degrees of freedom 90% CI: xbar +/- t [1- 0.1/2; 5] s/(n) 0.5 = 36.667 +/- 2.015* 9.243/(6) 0.5 = [29.07, 44.27] 95% CI: Use t [0.975; 5] : 36.667 +/- 2.571* 9.243/(6) 0.5 = [26.97, 46.37] Observe that the 95% CI is wider. If you had used z-tables (wrong in this case), you will have obtained a tighter CI…

5. Shivkumar Kalyanaraman Rensselaer Polytechnic Institute 5 II. [10 pts] Experiment Design: Analyze the 2^3 design a) Quantify all the main effects and all interactions [5 pts] b) Quantify percentages of variations explained [3 pts] c) Sort the variables in the order of decreasing importance [2 pts] A1A2 C1C2C1C2 B1902010020 B23530 45

6. Shivkumar Kalyanaraman Rensselaer Polytechnic Institute 6 Full Factorial Sign Table q I ABCABACBCABCy q 1-1-1-1111-190 q 11-1-1-1-111100 q 1-11-1-11-1135 q 111-11-1-1-130 q 1-1-111-1-1120 q 11-11-11-1-120 q 1-111-1-11-130 q 1111111145 q 370209014001016030Total q 46.252.511.2517.501.25203.75Total/8 q SST = 2 3 (2.5 2 + 11.25 2 + 17.5 2 + 0 2 +1.25 2 +20 2 +3.75 2 ) = 6837.5 q Portion of variation explained by seven effects are: q A: 8* 2.5 2 / 6837.5 = 7.31%, B: 14.81%, C: 35.83%, q AB: 0%, AC: 0.1828%, q BC: 46.8%, ABC: 1.64% q Order: BC, C, B, ABC, A, AC, AB q Interesting that the interaction between B and C has the largest effect!

7. Shivkumar Kalyanaraman Rensselaer Polytechnic Institute 7 I. [15 pts] DESIGN WALK-THROUGH: We learnt about animation, simulation (ns-2), graphing tools, and click modular router toolkit. Assume that you are given the following design problem: to design a new error resilience protocol for overlay networks that involves a mix of forward error correction (FEC) and automatic repeat request (ARQ) to be implemented at the IP-layer (I.e. layer 3). a) Discuss the design issues and tradeoffs for this problem [4 pts] b) Walk me through how you would systematically use the above tools (in the right sequence) to help design and incrementally refine your design. [5 pts] c) What metrics would you use to test/validate your protocol & explain why your set of metrics is a complete and meaningful set. [3 pts] d) What set of workloads would you use to test such a system & explain why it is meaningful, and yet helps you make quick progress in your design process. [3 pts] a) Issues: FEC overhead vs ARQ delay, impact on delay (for interactive apps) and goodput (for bulk apps). Can the FEC coding/decoding be done in real time (implementation issue)? Any interaction between the FEC/ARQ provided in the overlay vs the ARQ provided by TCP? b) Use ns-2, animation and graphing tools to validate the behavior and study the tradeoffs. Implementation issues (eg: real-time FEC, residual effects on interactive/bulk applications) resolved through Click implementation and testing.

8. Shivkumar Kalyanaraman Rensselaer Polytechnic Institute 8 b) Metrics: goodput (measure of overhead), latency (measure of impact on interactive apps), utilization (measure of link-efficiency). Secondary: TCP window/sequence number behavior. Why? Directly relates to the issues under consideration. Non-metrics: queuing delay, buffer size (they don’t relate to this problem) c) Workloads: TCP bulk, interactive and web traffic; Lossy/congested links; UDP streaming/conferencing traffic. Lossy/congested links are two ways to “stress” the resilience mechanisms. Various forms of TCP/UDP workloads are representative of a majority of legacy applications – we would like to study the impact/performance-gains of the overlay FEC/ARQ on these applications…