2008SimMidtermSols

2008SimMidtermSols - IEOR 4404 Simulation Prof Mariana...

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IEOR 4404 Midterm Exam Simulation October 23, 2008 Prof. Mariana Olvera-Cravioto Page 1 of 11 Midterm Exam Place all answers on the question sheet provided. The exam is open book/notes/handouts/homework. You are allowed to use a calculator, but not a computer. Write all answers clearly and in complete sentences. All answers should be supported by analysis or an argument. This exam has a total of 100 points. First Name: Last Name: 1(a) 1(b) 1(c) 1(d) 1(e) 1(f)(i) 1(f)(ii) 1(f)(iii) 1(g) 2 3(a) 3(b) Total Honor Code I resolve i ) not to give or receive aid during this examination, and ii ) to take an active part in seeing that other students uphold this Honor Code. Signature:
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2 IEOR 4404, Midterm Exam 1. Internet access during the INFORMS conference was available in a room with 10 desktop computers and 5 ethernet connections for laptops (there was no wireless signal during a couple of days). People wanting to check their e-mail or access the internet would line up in either of the two queues (one for the desktops and one for the ethernet connections). Assume that people with no laptops only go to the desktop line, while people who have laptops stand in the laptop line but might go to a desktop if one is available. See the diagram below. Ethernet connections Desktops 1 2 3 4 5 1 2 10 The specifics of the model are the following: Arrivals to the desktop queue and to the laptop queue occur according to nonhomoge- neous Poisson processes with rates λ D ( t ) and λ L ( t ), respectively. Customers in each queue are served in the order in which they arrive. At any moment in time, if a desktop computer is available (no people in the desktop line) and there are people in the laptop queue, the first person in the laptop queue takes the empty desktop. Users of both kinds have i.i.d. demands for internet time having distribution G (there is no difference between demand times of desktop users and laptop users). A member of the INFORMS keeps track of the amount of time that each person has been at a computer (desktop or laptop). If a person has been at a computer (desktop or laptop) for more than 30 min and there is somebody waiting to use the same kind of computer, the staff member will ask the person who is using the computer to leave. There is no limit to the number of people who can be in the queue, and no one abandons the queue until he/she gets to use the internet. (a) (8 pts) Suppose both lines are empty at time zero and you are given the following information about the arrival times and service times of the first 8 customers (measured in minutes): Customer 1 2 3 4 5 6 7 8 Arrival time 1 3 7 10 11 15 17 21 Service time 10 15 7 21 40 27 16 30 Type of customer L L D L D D L D where L represents a laptop user and D a desktop user. How many customers are in the laptop queue at time t = 16?
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IEOR 4404, Midterm Exam 3 (Use this page for computations of part (a)) Solution: No customers are in the laptop queue at time t = 16, since before t = 16, there are only three customers coming for laptop. Among those three customers, two leave after t = 16, and thus stay in the laptop station at t = 16.
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