The Smalltown Credit Union experiences its greatest congestion on paydays from 11:30 A.M. until 1:00 P.M. During these rush periods, customers arrive according to a Poisson process at rate 2.1 per minute. The credit union employs 10 tellers for these rush periods, and each takes 4.7 minutes to service a customer. Customers who arrive to the credit union wait in a single queue, if necessary, unless 15 customers are already in the queue. In this latter case, arriving customers are too impatient to wait, and they leave the system. Simulate this system to find the average wait in queue for the customers who enter, the average number in queue, the percentage of time a typical teller is busy, and the percentage of arrivals who do not enter the system. Try this simulation under the following conditions and comment on your results. For each condition, make three separate runs, using a different random number seed on each run.
a. Try a warm-up time of two hours. Then try no warm-up time. Use exponentially distributed service times for each.
b. Try exponentially distributed service times. Then try gamma-distributed service times, where the standard deviation of a service time is 2.4 minutes. Use a warm-up period of one hour for each.
c. Try 10 tellers, as in the statement of the problem. Then try 11, then 12. Use exponentially distributed service times and a warm-up period of one hour for each.
d. Why might the use of a long warm-up time bias the results toward worse system behavior than would actually be experienced? If you could ask the programmer of the simulation to provide another option concerning the warm-up period, what would it be? (Hint: The real rush doesn’t begin until 11:30.)