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## Problem 1

Consider the mix of jobs with parameters described in Table 1. Assume that ties (if any) are broken by
scheduling jobs with lower ID first. Compute the following:
a) The schedule produced by SRT. Try to use the same notation as in the lecture notes.
b) The schedule produced by HSN. Try to use the same notation as in the lecture notes.
c) The schedule produced by SJN. Try to use the same notation as in the lecture notes.
d) The schedule produced by Round-Robin with a quantum of 1 time unit. Try to use the same notation
as in the lecture notes.
e) Which algorithm achieves better performance in terms of average response time? Motivate your answer.
f) Which algorithm achieves better fairness? Motivate your answer.
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CS-350 – Fundamentals of Computing Systems::Homework Assignment #5 Problem 2
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
j1
j2
j3
j4
j5
Figure 1: Schedule produced by an unknown scheduler.

## Problem 2

Consider the schedule in Figure 1 and answer the following questions. The “dot” in the figure indicates
completion of a job, while an up-arrow indicates arrival.
a) What are the parameters (e.g. arrival time, length) of the jobs in this system. Use the task/job
notation provided in class and in the notes.
b) What scheduling algorithm is being used to produce the schedule in Figure 1? Motivate your answer.
c) Provide a step-by-step explanation of the decision made by the scheduler at time 11.
d) Use the same job parameters derived above and plot the schedule that would be produced by SJN on
the same job parameters.
e) Use the same job parameters derived above and plot the schedule that would be produced by HSN on
the same job parameters.
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CS-350 – Fundamentals of Computing Systems::Homework Assignment #5 Problem 3
Website 1 Website 2 Website 3

Index Arrival Length Arrival Length Arrival Length
1 0 3 1 4 2 2
2 9 2 9 5 9 3
3 15 4 18 3 16 2
4 28 2 25 2 23 1
5 37 2 30 3 30 3
6 – – 37 4 37 2
Table 2: List of requests with arrival times and processing time.

## Problem 3

A single-cpu web server is trying to be smart about the way it schedules processing for incoming page
requests. The web server is running a sharing hosting service with three websites deployed on it. As page
requests come in for the three websites, the web server classifies the requests depending on the page they
target.

It then tries to schedule the pending requests for each of the websites using Shortest Job Next. But
the server does not know the future! This means that it needs to estimate, for each class of requests, how
long the next request will last based on what it observed in the past.

Table 2 reports the ground truth on the actual runtime of a series of about 6 requests per website and their
arrival times. Remeber: the webserver scheduler does not know the exact length of a job reported in the
table until the job has completed.

Also assume that when the scheduler has no knowledge of the requests
at all, it will default to schedule a request for website 1 first, then website 2, and so on. This is also the
priority ordering in case of any tie. Remeber also that if at any time there is more than one ready request
for the same website that is ready, the FIFO ordering is followed.

a) Assume an impossible webserver that is able to foresee the future (the oracle server!), what would be
the order in which the various requests are processed? Produce a time plot of the resulting schedule
that goes until the last request has been completed.

b) Now consider a realistic scheduler without clairvoyance capabilities. What is the resulting schedule if
the server tries to predict the length of the next request directed to each website using an exponentially
weighted moving average with parameter α = 0.5? Show your work where it is clear at every step of
the way how the scheduler it making predictions and taking decisions.

c) Compare now the two schedules produced above. Did not knowing the future caused a performance
degradation in terms of average response time?
d) Once again compare the two schedules and focus on the website that statistically receives shorter-lived
requests. How was the slowdown of the requests for this website impacted by the scheduler’s inability
to predict the future?

e) Without repeating the steps above, and focusing only on the difference between predictions and ground
truth (prediction error), can we find a better value for α? Analyze the average prediction error for
the case considered above, and then for 0.3 and 0.8. Which one of the three cases you expect to be in
closer match with what you drew in Part a)
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CS-350 – Fundamentals of Computing Systems::Homework Assignment #5 Problem 4

## Problem 4

Code: In this problem you will write two functions to work with MD5 hashes. The first function takes a
number and computes a MD5 hash. The second function takes a MD5 hash and returns the number that,
when hashed, produces the hash in input.

a) Start by writing a Java class namely Hash.java that implements number hashing logic. The class
should have a method with the following prototype: String hash(int to hash), produces the MD5
hash string for the integer number provided in input. Internally, the integer should be converted to a
string that represents the number in decimal format, and then hashed using the MD5 cryptographic
hash.

For instance, the return value of hash(12345) should be “827ccb0eea8a706c4c34a16891f84e7b”. You
are allowed to use Java libraries for the computation of MD5 hashes.
Next, write a Java class namely UnHash.java that implements number de-hashing (a.k.a. hash
cracking) logic. The class should have a method with the following prototype: int unhash(String
to unhash), produces an integer from a hash string in input. The integer produced in output should
be such that its MD5 hash corresponds to the hash string to unhash.

For instance, the return value of unhash(‘‘01cfcd4f6b8770febfb40cb906715822’’) should be 54321.
You are allowed to use Java libraries for the computation of MD5 hashes.
Apart from implementing the unhash(…) method, the class should also include a public static
void main(String [] args) function.

The main(…) function should accept 1 parameter from the
calling environment. The parameter is a string that contains an hash string to crack.
It is responsibility of the main(…) function to internally invoke the implemented unhash(…)
function only once and print its result in decimal format.

b) Using the code written in the previous part, work on being able to crack a list of MD5 hashes from a
file. For this part, write a Java class called Dispatcher.java. The input data (list of hashes to crack)
is given in a file. The path to the file is passed as the only parameter by the calling environment. The
input file is structured as a list of MD5 hashes to crack, one per line, with each line terminated with
a newline (\n) character.

It is the job of the dispatcher to (1) read the input file; (2) invoke the unhash(…) procedure written
for the first part for each of the hashes in the input file. The result of each of the unhash operations,
i.e. the cracked hashes, should be printed in output, with a single line per decoded hash. Apart from
the list of decoded hashes, nothing else should be printed in output.
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CS-350 – Fundamentals of Computing Systems::Homework Assignment #5 Problem 5

### Submission Instructions:

in order to submit this homework, please follow the instructions below for
exercises and code.
The solutions for Problem 1-3 should be provided in PDF format, placed inside a single PDF file named
hw5.pdf and submitted via Gradescope. Follow the instructions on the class syllabus if you have not received
an invitation to join the Gradescope page for this class. You can perform a partial submission before the
deadline, and a second late submission before the late submission deadline.

The solution for Problem 4 should be provided in the form of Java source code. To submit your code,
place all the .java files inside a compressed folder named hw5.zip. Make sure they compile and run correctly according to the provided instructions. The first round of grading will be done by running your code.

Use CodeBuddy to submit the entire hw5.zip archive at https://cs-people.bu.edu/rmancuso/courses/
cs350-fa22/codebuddy.php?hw=hw5. You can submit your homework multiple times until the deadline.
Only your most recently updated version will be graded. You will be given instructions on Piazza on how
to interpret the feedback on the correctness of your code before the deadline.
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