# AATN6385 Project 2 solution

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Original Work
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## Description

The theme of the project is to study experimentally how the network reliability depends on the individual link reliabilities, in the specific situation
described below.
Network topology: A complete undirected graph on n = 5 nodes. Complete means that every node is connected with every other one (parallel edges
and self-loops are excluded in this graph). Therefore, this graph has m = 10
edges, representing the links of the network.
Components that may fail: The links of the network may fail, the nodes
are always up. The reliability of the links is computed as follows. Index
the links with the numbers 1,…,10 (in arbitrary order). Take a parameter
p, 0 ≤ p ≤ 1, the same for every link. The parameter p will take different
values in the experiments. For link i, (i = 1, 2, . . . , 10), let its reliability be
pi
, which is given by the following formula
pi = p
ddi/3e
,
where di
is the i
th digit in your 10-digit student ID, assuming the ID consists
of the digits d1, d2, . . . , d10. The d…e sign means upper integer part, which
rounds up any non-integer number to the nearest larger integer. For example,
if your ID is 0123456789, then link 5 has reliability p5 = p
dd5/3e = p
d4/3e = p
2
,
and link 1 has reliability p1 = p
dd1/3e = p
0 = 1.
Reliability configuration: The system is considered operational, if the
network is connected.
1. Create an algorithm to compute the network reliability in the above
described situation, using the method of exhaustive enumeration (see
in the Lecture Notes). Note that the high level description given in the
notes is not enough, since you also have to specify how you actually
want to find the details, such as how to generate the possible states,
how to assign an up/down system condition to each, how to convert it
into a reliability value, etc.
1
IMPORTANT: Finding algorithmic solutions for these details
Describe how your algorithm works. First briefly explain informally the
ideas. Then provide pseudo code for the description of the algorithm,
by a human.
2. Write a computer program that implements the algorithm. You may
use any programming language under any operating system, this is
entirely of your choice. Make sure, however, that your program is well
structured to support finding potential errors (debugging), checking
correctness or trying out algorithm changes. Explain how your program
supports these goals. Include a section that tells how to run your
program (this is usually called ReadMe file).
3. Run the program for different values of p. Let the parameter p run over
the [0.05, 1] interval, in steps of 0.05. Show graphically in a diagram
how the obtained network reliability values depend on p.
4. Now fix the p parameter at p = 0.9, and do the following experiment.
Among the 210 = 1024 possible combinations of component states pick
k of the combinations randomly, and flip the corresponding system
condition. That is, if the system was up, change it to down, if it was
down, change it to up. This models the situation that there are some
random errors in the computation. Show in a diagram, how the reliability of the system changes due to this alteration. With this we
want to investigate how the result depends on random errors. Specifically, show in a diagram how the change depends on k, in the range
k = 0, 1, 2, 3, . . . , 20. During this experiment keep the value of the parameter p fixed at p = 0.9. To reduce the effect of randomness, run
several experiments for each value of k, and average them out,
5. Provide a short (1-2 paragraph) explanation why the obtained diagrams
look the way they look. In other words, try to argue that they exhibit
a reasonable behavior that one could intuitively expect, so the program
is likely to work correctly.
2
Note: If something is not specified in this project description, that means it
Submission guidelines
Describe everything, including algorithms, program, sources, results and figures neatly and clearly in a study. Include everything in a single document
that can be read as a report. It should have a professional appearance,
scanned handwriting is not acceptable! The preferred file type is pdf. Do
not submit executable code, but include the source code as an Appendix in
the document. The project report will be read as a document and not run
as a program (but there are two exceptions, see them under Evaluation).
Submit the document through eLearning. Do not send it via e-mail!
Notes:
• The work should be fully individual and original. Any form of cheating
is a serious violation of University policies and can lead to serious consequences. Note that some of the data depend on the student ID, which
is unique for everybody, so no two projects can generate the exact same
results, even if the same random number generator is used.
• It may be helpful to think about the whole project presentation that
your task is not only to solve a technical problem, but you also have
to “sell” the results. Try to look at your work from the viewpoint of a
potential customer, to whom you want to sell such a software product.
How convincing would your presentation look for a customer?
Evaluation
The evaluation will focus on how well each of the specific tasks have been
carried out. Even though the submission will not be run, only read as a
document, there are two exceptions. You will be asked to demonstrate on
a computer how your program actually runs, if any of the following cases
occur:
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1. You do not agree with the grade and want to improve it. In this case
the demonstration should show that your work is actually better than