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Macca's Arcade provides an opportunity for patrons to step into a batting cage and hit against a pitching machine that throws 90-mile-per-hour fastballs. Patrons purchase a token and then join the line. Once a batter leaves the cage, the attendant quickly adjusts the pitching machine to match the next batter's height while that batter steps into the cage. Once the batter is ready, the attendant drops the token into a slot on the side of the pitching machine and the batter receives exactly 15 pitches (each delivered 24 seconds apart) at which to swing. (a) Using Kendall notation, specify the appropriate queuing model for this problem. (b) Specify the probability that the batting cage is in use at any time during business hours. (c) Specify the number of customers on average that are waiting in line to hit in the cage at Macca's Arcade. (d) How many minutes on average does a customer wait from the time when he or she gets their token until the time that he or steps into the cage?

Macca's Arcade provides an opportunity for patrons to step into a batting cage and hit against a pitching machine that throws 90-mile-per-hour fastballs. Patrons purchase a token and then join the line. Once a batter leaves the cage, the attendant quickly adjusts the pitching machine to match the next batter's height while that batter steps into the cage. Once the batter is ready, the attendant drops the token into a slot on the side of the pitching machine and the batter receives exactly 15 pitches (each delivered 24 seconds apart) at which to swing. (a) Using Kendall notation, specify the appropriate queuing model for this problem. (b) Specify the probability that the batting cage is in use at any time during business hours. (c) Specify the number of customers on average that are waiting in line to hit in the cage at Macca's Arcade. (d) How many minutes on average does a customer wait from the time when he or she gets their token until the time that he or steps into the cage?

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Macca's Arcade provides an opportunity for patrons to step into a batting cage and hit against a pitching machine that throws 90-mile-per-hour fastballs. Patrons purchase a token and then join the line. Once a batter leaves the cage, the attendant quickly adjusts the pitching machine to match the next batter's height while that batter steps into the cage. Once the batter is ready, the attendant drops the token into a slot on the side of the pitching machine and the batter receives exactly 15 pitches (each delivered 24 seconds apart) at which to swing. (a) Using Kendall notation, specify the appropriate queuing model for this problem. (b) Specify the probability that the batting cage is in use at any time during business hours. (c) Specify the number of customers on average that are waiting in line to hit in the cage at Macca's Arcade. (d) How many minutes on average does a customer wait from the time when he or she gets their token until the time that he or steps into the cage?
Transcribed Image Text:Macca's Arcade provides an opportunity for patrons to step into a batting cage and hit against a pitching machine that throws 90-mile-per-hour fastballs. Patrons purchase a token and then join the line. Once a batter leaves the cage, the attendant quickly adjusts the pitching machine to match the next batter's height while that batter steps into the cage. Once the batter is ready, the attendant drops the token into a slot on the side of the pitching machine and the batter receives exactly 15 pitches (each delivered 24 seconds apart) at which to swing. (a) Using Kendall notation, specify the appropriate queuing model for this problem. (b) Specify the probability that the batting cage is in use at any time during business hours. (c) Specify the number of customers on average that are waiting in line to hit in the cage at Macca's Arcade. (d) How many minutes on average does a customer wait from the time when he or she gets their token until the time that he or steps into the cage?
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