[SOLVED] algorithm math theory BeijingDublin International College

BeijingDublin International College

SEMESTER I FINAL EXAMINATION20162017
School of Computer Science
BDIC Final Exam COMP3014J Performance of Computer Systems
HEAD OF SCHOOL: Padraig Cunningham MODULE COORDINATOR: Lina Xu
Time Allowed: 120 minutes
Instructions for Candidates
All questions carry equal marks. The distribution of marks in the right margin shown as a percentage gives an approximate indication of the relative importance of each part of the question.
BJUT Student ID:UCD Student ID:
I have read and clearly understand the Examination Rules of both Beijing University of Technology and University College Dublin. I am aware of the Punishment for Violating the Rules of Beijing University of Technology andor University College Dublin. I hereby promise to abide by the relevant rules and regulations by not giving or receiving any help during the exam. If caught violating the rules, I accept the punishment thereof.
Honesty Pledge: Signature
Instructions for Invigilators
Nonprogrammable calculators are permitted.
No roughwork paper is to be provided for candidates.

BDIC Semester One Academic Year 20162017
Obtained score
20
Question 1: General Theories on Performance
a. Whatarethethreecommonperformanceevaluationtechniquesandwhentouse them? Talk a little bit about their advantages and disadvantages. 5 Marks
b. Explainwhatisworkloadinyourownwords.IntheLEACHevaluation,whathas been used as workload to test the performance? 3 Marks
c. Workload Selection is essential for performance evaluation. Give your ideas and opinions on workload selection in terms of level of details. 4 Marks
d. Presentasystemandproposeaperformanceevaluationstrategyforit.Youneedto describe what is the system, evaluation methods, workload selection and other relevant information. 8 Marks
the x values have xthe mean of the x values of all the data points subtracted, and all the y values have ysubtracted from them. This produces a data set
Obtained score
20
Question 2: Workload Characterization whose mean is zero.
Step 3: Calculate the covariance matrix
This is done in exactly the same way as was discussed in section 2.1.4. Since
a. What arettheedadtiaffeisre2ndcimeesnsbioentawl,etehne cfoavcatroiarnsceamndatrmixewtrililcsbe?2Pre2s.eTnhtetrheearaensower in your
surprises here, so I will just give you the result:
own words and also give some examples for both. 5 Marks
cov .616555556 .615444444.615444444 .716555556
b. Whenanalysingdata,whatcanclusteringmethoddo?Writetheclustering
So, since the nondiagonal elements in this covariance matrix are positive, we should expect that both the x and y variable increase together.
algorithm based on minimal spanning tree in pseudocode. 7 Marks
Step 4: Calculate the eigenvectors and eigenvalues of the covariance matrix
c. What is the main advantages to apply Principal Component Analysis PCA when analysingShinicgehthdeimcoevanrsiaioncneamldataritxasisestq?uaGreiv,ewnetchanecfaollcluolwatientgheiegigenveactluoressanadnd
eigenvalues for this matrix. These are rather important, as they tell us useful
eigenvectors, which vector is the principle component of the dataset?
information about our data. I will show you why soon. In the meantime, here
8 Marks
It is important to notice that these eigenvectors are both unit eigenvectors ie. their lengths are both 1. This is very important for PCA, but luckily, most maths packages, when asked for eigenvectors, will give you unit eigenvectors.
are the eigenvectors and eigenvalues:
eigenvalues .0490833989
1.28402771 eigenvectors .735178656 .677873399
.677873399 .735178656
So what do they mean? If you look at the plot of the data in Figure 3.2
Page 2 of 6
then you can see how the data has quite a strong pattern. As expected from the
covariance matrix, they two variables do indeed increase together. On top of the data I have plotted both the eigenvectors as well. They appear as diagonal
dotted lines on the plot. As stated in the eigenvector section, they are perpen

BDIC Semester One Academic Year 20162017
Question 3: Summarize Measured Data
a. WhatisQQplotandwhatpurposeisitnormallyusedfor?Giveexamplestoclarify your point. 6 marks
b. Auniversitywantstoknowmoreabouttheknowledgeofstudentsregarding international events. They are concerned that their students are uninformed in regards to new from other countries. A standardized test is used to assess students knowledge of world events national reported mean65, S5. A sample of 30 students from this university are tested sample mean58, Standard Error3.2. Can Can we say with 99 confidence that the university result is below the national standard? What about 95 confidence? 6 Marks
c. Deduce the linear regression process with one dependent variable Y and one independent variable X. What is R2 indicating in linear regression and how to calculate it? 8 Marks
Question 4: Queuing Model
a. In queuing theory, what do the terms MM1, MMn, MMnK stand for?
3 Marks
b. In Beijing, supposedly the birth rate l and the death rate is . Both follow Poisson distribution. pn is referred as the possibility for the populationn. Deduce the value for pn if p0 is known. 6 marks
c. For an MM1 queue we know that the mean number of customers in the system L is equal to the utilization divided by one minus the utilization. Using basic laws and relationships, derive the mean wait in the system W, the mean number of customers in the queueing area Lq, and the mean wait in the queuing area Wq as a function of the utilization. 6 Marks
d. Customers arrive in a usual MM1 system, with an arrival rateand service rate . However, in some system, the customers in the queue are impatient: Each customer waiting in the queue will abandon the system without receiving service with a rate g. Draw the Markov Chain diagram for this queue and derive the stationary probability pi in this chain. 10 Marks
Obtained score
20
Obtained score
25
Page 3 of 6

BDIC Semester One Academic Year 20162017
Obtained score
15
Question 5: Simulation
a. We say a simulation evaluation is good if it is validated and verified. Explain in your own words what are validation and verification. 5 Marks
b. Supposedly you are a project manager in a car company and your team is going to test an auto driven system through simulation. Talk about the general approach you should follow in order to avoid common mistakes. 5 Marks
c. For simulation, random number generation is open required. LinearCongruential Generators are the popular ones that can be applied efficiently. Explain how can you obtain
a full period generator.
5 Marks
Page 4 of 6

BDIC Semester One Academic Year 20162017
Appendix :
Page 5 of 6

BDIC Semester One Academic Year 20162017
Page 6 of 6