ECSE4963: Experimental Networking Exam 1: SOLUTIONS

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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

• 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)

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• 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) ??xi yj Pxi , yj ??xi yj Pxi Pyj
  due to independence
• ?xi Pxi ? yj Pyj E(X)E(Y)
• The reverse argument cannot be made generally
  because the terms Pxi , yj , Pxi, Pyj are
  inside the summations (I.e. within the ?).
• Many counter examples can also be given Eg X
  Cos u Y Sin u

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• 2. 10 pts Given n6 random RTT samples (in
  ms)
• 31, 42, 28, 51, 28, 40
• 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
• s2 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
• gt 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 /- t1- 0.1/2 5 s/(n)0.5
• 36.667 /- 2.015 9.243/(6)
  0.5 29.07, 44.27
• 95 CI Use t0.975 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

• II. 10 pts Experiment Design Analyze the 23
  design
• Quantify all the main effects and all
  interactions 5 pts
• Quantify percentages of variations explained
  3 pts
• Sort the variables in the order of decreasing
  importance 2 pts

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Full Factorial Sign Table

• I A B C AB AC BC ABC y
• 1 -1 -1 -1 1 1 1 -1 90
• 1 1 -1 -1 -1 -1 1 1 100
• 1 -1 1 -1 -1 1 -1 1 35
• 1 1 1 -1 1 -1 -1 -1 30
• 1 -1 -1 1 1 -1 -1 1 20
• 1 1 -1 1 -1 1 -1 -1 20
• 1 -1 1 1 -1 -1 1 -1 30
• 1 1 1 1 1 1 1 1 45
• 370 20 90 140 0 10 160 30 Total
• 46.25 2.5 11.25 17.5 0 1.25 20 3.75 Total/8
• SST 23 (2.52 11.252 17.52 02 1.252
  202 3.752 ) 6837.5
• Portion of variation explained by seven effects
  are
• A 8 2.52/ 6837.5 7.31, B 14.81, C
  35.83,
• AB 0, AC 0.1828,
• BC 46.8, ABC 1.64
• Order BC, C, B, ABC, A, AC, AB
• Interesting that the interaction between B and C
  has the largest effect!

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• 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).
• Discuss the design issues and tradeoffs for this
  problem 4 pts
• 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
• What metrics would you use to test/validate your
  protocol explain why your set of metrics is a
  complete and meaningful set. 3 pts
• 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?
• 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.

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• 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 dont relate to this problem)
• 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