Question

The Bijou Theater shows vintage movies. Customers arrive at the theater line at the rate of 80 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.)

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 λ/µ value . Do not round intermediate calculations. Round your answer to 3 decimal places.)

Answer 1

a)

Arrival rate=80 per hour

Service rate=3600/30=120 per hour

Average number in the system= Arrival rate/( Service rate- Arrival rate)=80/(120-80)=2

Average customer time in the system= Average number in the system/ Arrival rate=2/80=1/40 hours =1.5 Minutes

b)

Here, service time is reduced to 20 seconds and customer time will also reduce.

Service rate=3600/20=180

Average number in the system= Arrival rate/( Service rate- Arrival rate)=80/(180-80)=80/100

Average customer time in the system= Average number in the system/ Arrival rate=0.8/80=0.6 Minutes

Average customer time in the system has reduced from 1.5 Minutes to 0.6 Minutes.

c)

As, each server will be doing all three tasks, so 80 customers will be divided by 3, 80/3=26.67

Service rate=3600/30=120

Average number in the system= Arrival rate/( Service rate- Arrival rate)=26.67/(120-26.67)=0.286

Average customer time in the system= Average number in the system/ Arrival rate=0.286/26.67= 0.011 Minutes