The Bijou Theater shows vintage movies. Customers arrive at the theater line at
ID: 379099 • Letter: T
Question
The Bijou Theater shows vintage movies. Customers arrive at the theater line at the rate of 70 per hour. The ticket seller averages 32 seconds per customer, which includes placing validation stamps on customers’ parking lot receipts and punching their frequent watcher cards. (Because of these added services, many customers don’t get in until after the feature has started.) .
a. What is the average customer time in the system? (Round your answer to 2 decimal places.)
b. What would be the effect on customer time in the system of having a second ticket taker doing nothing but validations and card punching, thereby cutting the average service time to 20 seconds? (Round your answer to 3 decimal places.)
c. What would be the customer time in the system if a second window was opened with each server doing all three tasks? (Use closest /µ value from Exhibit 10.9. Do not round intermediate calculations. Round your answer to 3 decimal places.)
http://lectures.mhhe.com/connect/0077535111/exhibit_10.9.jpg
Explanation / Answer
Arrival rate, = 70 per hour
Service rate, µ = =3600 seconds per hour / 32 seconds per customer = 112.5 per hour
a) Average customer time in the system, W = 1/(µ - ) = 1/(112.5-70) = 0.0235 hours = 84.71 seconds
b) New service rate, µ = 3600/20 = 180 per hour
Customer time in system = 1/(µ - ) = 1/(180-70) = 0.0091 hour = 32.73 seconds
c) /µ = 70/112.5 = 0.6222
Corresponding to /µ and s = 2, from the table, Lq = 0.0667
L = Lq + /µ = .0667 + 70/112.5 = 0.68892
Average customer time in system, W = L/ = 0.68892/112.5 = 0.0098 hour = 35.43 seconds
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