Question

he 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.) What is the system waiting time if a second window was opened with each server doing all three tasks?

Answer 1

Solution:

We have λ = 100 and µ = 120

1. Average customer time in the system is given by:-

W. =anu)

      
| 11 100 (120 - 100)

| 11 100 (120 - 100)

       = 0.05/hour

      = 3minutes

b)
W, = 12

W, = 12

          
10 100 (180 - 100)

10 100 (180 - 100)

           = 0.0125/hour

           = 0.0125*3600seconds

            = 45 seconds

3. Yes, system waiting would be less than about 36 seconds.

W. =anu)

          
200 200 - 100)

200 200 - 100)

           = 0.01/hour

            = 0.01*3600 seconds

            = 36 seconds