Question ONE Consider the narrative below and use it to answer the questions that will follow: At the British Grand Prix's Silverstone Circuit's 3 July 2022 race, it was another battle royal of sorts as the Formula 1 drivers battled for maximum points in the series. The fans seeking to purchase tickets started arriving from 10:00 am running all through 1:30 pm, when the gates closed in readiness for the race. The fans were observed to arrive at an average of 2,048 each hour, and were being served at a rate of 533 every fourteen minutes. Some fans had already purchased their tickets earlier via the ticket sales agency e-commerce portal. The Silverstone gallery has a 150,000 seating capacity. The gallery was 95% full for this grace. Given the enthusiasm of the fans that were trickling in, this was going to be the race of the month. Required, assuming an M/M/1 system configuration: a) Derive the formulae for the various performance measures: i). The probability that there are n fans in the circuit ticketing system. ii). The average number of fans in the circuit ticketing system. iii). The average number of fans awaiting service. iv). The average time a fan spends in the circuit ticketing system. v). The average time a fan has to wait.
Question ONE Consider the narrative below and use it to answer the questions that will follow: At the British Grand Prix's Silverstone Circuit's 3 July 2022 race, it was another battle royal of sorts as the Formula 1 drivers battled for maximum points in the series. The fans seeking to purchase tickets started arriving from 10:00 am running all through 1:30 pm, when the gates closed in readiness for the race. The fans were observed to arrive at an average of 2,048 each hour, and were being served at a rate of 533 every fourteen minutes. Some fans had already purchased their tickets earlier via the ticket sales agency e-commerce portal. The Silverstone gallery has a 150,000 seating capacity. The gallery was 95% full for this grace. Given the enthusiasm of the fans that were trickling in, this was going to be the race of the month. Required, assuming an M/M/1 system configuration: a) Derive the formulae for the various performance measures: i). The probability that there are n fans in the circuit ticketing system. ii). The average number of fans in the circuit ticketing system. iii). The average number of fans awaiting service. iv). The average time a fan spends in the circuit ticketing system. v). The average time a fan has to wait.
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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Transcribed Image Text:Question ONE
Consider the narrative below and use it to answer the questions that will follow:
At the British Grand Prix's Silverstone Circuit's 3 July 2022 race, it was another battle royal of sorts
as the Formula 1 drivers battled for maximum points in the series.
The fans seeking to purchase tickets started arriving from 10:00 am running all through 1:30 pm,
when the gates closed in readiness for the race. The fans were observed to arrive at an average of
2,048 each hour, and were being served at a rate of 533 every fourteen minutes.
Some fans had already purchased their tickets earlier via the ticket sales agency e-commerce
portal. The Silverstone gallery has a 150,000 seating capacity. The gallery was 95% full for this
grace.
Given the enthusiasm of the fans that were trickling in, this was going to be the race of the month.
Required, assuming an M/M/1 system configuration:
a)
Derive the formulae for the various performance measures:
i). The probability that there are n fans in the circuit ticketing system.
ii).
The average number of fans in the circuit ticketing system.
iii). The average number of fans awaiting service.
iv). The average time a fan spends in the circuit ticketing system.
v). The average time a fan has to wait.
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Step 1 Given the following information in the question:
VIEWStep 2 i) The probability that there are n fans in the circuit ticketing system:
VIEWStep 3 ii) Average number of fans in the circuit ticketing system:
VIEWStep 4 iii) Average number of fans awaiting service:
VIEWStep 5 iv) Average time a fan spends in the circuit ticketing system:
VIEWStep 6 v) Average time a fan has to wait
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