Question

The Bijou Theater shows vintage movies. Customers arrive at the theater line at the rate of 80 per hour. The ticket seller averages 36 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 the Excel spreadsheet Queue Models.)

a. What is the average customer time in the system? (Round your answer to 2 decimal places.)

	Average customer time      minutes

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 25 seconds? (Round your answer to 3 decimal places.)

Average time in system ________ minutes

c. What would be the customer time in the system if instead of the change in Part b, a second window was opened with each server doing all three tasks? (Do not round intermediate calculations. Round your answer to 3 decimal places.)

	Average time in system      minutes

d. Would system waiting time which is obtained in part (c) be less than you found in (b)?

• Yes

• No

Answer 1

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This is M/M/1 queue system with following characteristics

Arrival rate, λ = 80 per hour

Service rate, μ = 3600 seconds per hour / 36 seconds per customer = 100 customers per hour

(a) Average customer time in system, W = 1/(μ-λ) = 1/(100-80) = 0.05 hour = 3 minutes

(b) New service rate = 3600/25 = 144

Average time in system = 1/(144-80) = 0.0156 = 0.928 minutes

(c) This becomes M/M/s queue system , with s = 2

Calculation of queue characteristics is done using table in excel as below.

Average time in system = 0.0119 hour = 0.714 minute

Formula: B12 =($B$4/$B$5)^A12/FACT(A12) copy to B13

C13 =SUM(B$11:$B12)

D13 =+B13/(1-$B$4/(A13*$B$5))

E13 =1/(C13+D13)

F13 =$B$4/($B$5*A13)

G13 =+E13*B13*F13/(1-F13)^2

H13 =G13+$B$4/$B$5

I13 =G13/$B$4

J13 =I13+1/$B$5

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