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Be sure to check the list of worksheet functions that are needed for the homework assignments, to see which new functions (if any) might help with this assignment.
Since macros aren’t permitted in this homework assignment, be certain that the workbook you submit for grading has no macros. Read about how to check your workbooks for macros.
Remember that some problems are slight extensions of what we show you in class, in the demonstrations and in the session notes, and some problems are somewhat ambiguous. This is intended to parallel what you’ll frequently encounter at work. If you feel a bit confused, there are some things you can do to help clarify things.
Before attempting this homework, you might find it helpful to read about:
Numbers in square brackets to the right of the problem numbers indicate point values.
Having originally positioned itself as an upscale burger chain, Windy’s has a number of outlets that do not have drivethrough service. To meet competitive pressures, Windy’s has decided to install drivethrough service throughout its operations. They estimate that drivethrough customers will arrive, on average, every 2.8 minutes, and that the time to service them will be exponentially distributed with a rate of one every 2.4 minutes.
Find the average number of cars in the drivethrough, including both the number in line and the one being served. Your result should be a single cell.
Find the average number of cars in line. Your result should be a single cell.
Find the average time (in minutes) that it takes a car to move through the line and arrive at the service window. Your result should be a single cell.
Find the average time (in minutes) that a car takes to move through the entire drivethrough system. Your result should be a single cell.
Find the probability that there are 6 cars in the drivethrough, either waiting to be, or being, served. Your result should be a single cell.
Find the probability that there are 10 cars in the drivethrough, either waiting to be served, or being served. Your result should be a single cell.
You’ve procrastinated yet again, and you’re standing in line at the post office to mail your income tax form on the due date. There’s only one service window open. When you arrive in the line there are 6 people in front of you, so you have some time to kill, and you try to apply what you know about service lines. As time passes, you observe that the average service time is about 1.75 minutes, and new people come into the line, on average, one every 2.0 minutes.
Find the average number of people in the system including both the number in line and the one being served. Your result should be a single cell.
Find the average length of lines when there actually is a line. Your result should be a single cell.
Last Modified: Wednesday, 27Apr2016 04:15:26 EDT
Modeling service systems in general is extraordinarily complex, but as we’ve seen, if we make reasonable approximations, we can gain powerful tools that are very easy to apply. In the case of service systems, we assumed that the system was at equilibrium or close to it. Analogously, we can make simplifying assumptions for many other complex questions. Examples are process control, resource scheduling, resource allocation, cost allocation, vehicle routing, and many more.