2. The Bijou Theater shows vintage movies. Customers arrive at the theater line

Question

2. The Bijou Theater shows vintage movies. Customers arrive at the theater line at the rate of 100 per hour. The ticket seller averages 30 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.) (USE MODEL 1)

a. What is the average customer time in the system?

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?

c. Would system waiting time be less than you found in ( b) if a second window was opened with each server doing all three tasks?

Explanation / Answer

A. Service rate = 60*60 / 30 = 120 per hour = u

Lambda = 100 per hour

Average customer time in the system = 1 / (u - lambda)

= 1 / (120 - 100) = 0.5 hour or 3 minutes.

B. u(new) = 60*60 / 20 = 180 per hour

Average time = 1 / (180 - 100)

= 0.0125 hour or 0.75 minutes.

C. For n = 2

P = lambda / u = 100 / 120 = 0.833 or 0.8 approx

From table Lq for 0.80 = 0.1523.

L = Lq + p = 0.1523 + 0.8 = 0.9523

Ws = L / lambda = 0.9523 / 100 = 0.01058 hour or 0.634 minutes

Average time will be 0.634 which is lower than found in part B.

Do give a positive rating if you think this answer helped

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.