SolutionsPracticeMidterm

SolutionsPracticeMidterm - IEOR 4404 Simulation Prof...

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IEOR 4404 Solutions to the Practice Midterm Exam Simulation October 15, 2008 Prof. Mariana Olvera-Cravioto Page 1 of 10 Solutions to the Practice 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)(i) 1(a)(ii) 1(b) 1(c) 1(d) 1(e)(i) 1(e)(ii) 1(e)(iii) 1(e)(iv) 1(f) 2(a) 2(b) 3 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, Solutions to the Practice Midterm Exam 1. Consider the following simplified model of a supermarket checkout system. There are two identical checkout lines. Due to space constraints, at most two people can be waiting for service in each line. To make the system more efficient, the supermarket has hired a “coordi- nator” who uses the following rule to manage customer traffic at the checkout: If both lines are full, then turn the next customer away. If both lines have the same number of vacant spots, the coordinator flips a fair (i.e., 50-50) coin to determine which line to send the next customer to; if the toss is a head the customer is sent to line 1 and if it is a tail to line 2. If one line has fewer waiting customers than the other, the coordinator sends the next customer to the line with more vacant spots. Customers cannot enter the checkout area without first being routed by the coordinator. The diagram below illustrates the structure of the supermarket. Coordinator Line 1 Customers Line 2 (a) 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 7 customers (measured in minutes): Customer 1 2 3 4 5 6 7 Arrival time 1 5 8 9 11 14 16 Service time 6 5 5 7 4 6 5 You are also given the outcome of the first 10 tosses of the coin the coordinator used (you might not need all of them to answer the following questions): H, H, T, H, T, T, T, H, T, T i. (9 pts) What line did customer 4 go to?
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