Assignment 2: Non-Homogeneous Poisson Process
Simulation
FEB22013(X)
Deadline: 17:00 January 31, 2023
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Assignment2.pdf and the following .java files:
• MainStudentRoom.java
• MainElevators.java
• ElevatorPolicy1State.java
• ElevatorPolicy2State.java
• ElevatorPolicy3State.java
• Utils.java
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1
Question 1 Student Room Search
You are looking for a room via Stadswonen. You replied to many advertisements
and now received invitations to visit m of these rooms. When you visit the room,
you immediately have to decide whether you want that room or not, before viewing
the other rooms. A well known strategy for this problem is to visit the first r rooms
without taking any of them, and to then take the first room that exceeds the best
rooms out of the first r rooms. Since you really want to have a room in Rotterdam,
you do always take the last room you visit, regardless of its quality.
Assume there exists a preference ranking of all m rooms that you are allowed to
visit, i.e., there are no two rooms that you like equally well. Let the nicest room
have rank 1 and the worst room have rank m.
a. Give the pseudocode of a Monte Carlo Algorithm to determine the probability
that you end-up with the nicest room if you use the above described strategy.
b. Give the pseudocode of a Monte Carlo Algorithm to determine the expected
rank of the room that you end-up with if you use the above described strategy.
c. Implement the above described Monte Carlo Algorithms. If you can visit
m = 12 rooms, what level of r would you use if you want to maximise the
probability of obtaining the nicest room, and what level of r would you use if
you want to minimise the expected rank of the room? Provide the output in
a table.
2
Question 2 Office Elevators
An investor of a tall office building with 2 elevators wants to analyse the effect of
different elevator policies on the average time waiting for an elevator, the average
number of employees waiting for an elevator, and the average time spend in an
elevator. He is specifically interested in this during the morning peak, which lastst
for one hour, when employees arrive at the office. He is considering the following
three policies:
1. Both elevators visit all floors
2. One elevator visits the odd numbered floors and the other elevator visits the
even numbered floors.
3. One elevator visit the bottom half of the building (floors 1-6) and the other
elevator visit the remaining, top part, of the building (floors 7-12).
To compare the two policies, you are asked to implement a simulation and provide
the company with an advice for their elevator policy. You can make use of the
following assumptions:
• During the morning peak, employees arrive at the ground floor and take the
elevator to the floor that contains their office. There are no employees that
take the elevator from another floor than the ground floor.
• Employees arrive according to a non-homogeneous Poisson process with rate
100 + 50 cos{2πt − π}
for 0 ≤ t ≤ 1.
• The offices of the employees are evenly spread over all floors and all employees
take the elevator.
• For policy 1, when both elevators are at the ground floor and have capacity,
employees choose an elevator at random.
• For policy 1 and 2, when an elevator departs from the ground floor and needs
to stop at n floors, it takes the elevator 30 + 20n seconds to stop at those
floors and be back at the ground floor. For policy 3, it takes an elevator for
the bottom part of the building 20 + 20n seconds to stop at n floors be back
at the ground floor and 40 + 20n seconds to stop at n floors from the top part
of the building and be back at the ground floor.
• Each elevator has a capacity of 10 people.
• An elevator departs 10 seconds after the first employee enters the elevator, regardless of the number of employees in the elevator and time the last employee
entered the elevator.
3
a. Define the relevant state variables, counter variables and events when using
policy 1. Explain how all variables are updated (i.e., when and how do the
values change). Moreover, show how the simulation is initialised, and for each
event when it is generated. Explain how the required performance measures
can be calculated.
b. Program the DES using the variables and events defined.
c. Program the DES for policy 2. Explain briefly what changes compared to the
scenario with policy 1 (i.e., explain what parts are different compared to a.,
you do not have to repeat the elements that remain the same).
d. Program the DES for policy 3. Explain briefly what changes compared to the
scenario with policy 1 (i.e., explain what parts are different compared to a.,
you do not have to repeat the elements that remain the same).
e. Give a recommendation to the investor regarding the elevator policy in his
building. Explain differences you find in the performance measures for the
different policies.