At the start of football season, the ticket office gets busy the day before the first game. Customers arrive at the rate of four every ten minutes. A ticket seller can service a customer in four minutes
Traditionally, there are two ticket sellers working. The university is considering an automated ticket machine similar to the airlines' e-ticket system. The automated ticket machine can service a customer in 2 minutes.
(a) What is the average length of the queue for the in-person model?
(b) What is the average length of the queue for the automated system model?
(c) What is the average time in the system for the in-person model?
(d) What is the average time in the system for the automated system model?
(e) Assume the ticket sellers earn $8 per hour and the machine costs $20 per hour (amortized over 5 years). The wait time is only $4 per hour because students are patient. What is the total cost of each model?
(a) Lq = 2.844
(b) Lq = 1.6
(c) W = 0.1852 hour or 11.11 minutes
(d) W = 0.1 hour or 6 minutes
(e) Total cost (in-person) = (2 ? $8/hour) + (24/hour ? .1852 hours) ($4/hour) = $33.78
Total cost (automated) = (1 ? $20/hour) + (24/hour ? .1 hour) ($4/hour) = $29.60
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