Question

The First American bank is trying to determine whether it should install one or two drive-through windows. The following probability distributions for arrivals and service times have been developed from historical data

Time between
Automobile arrivals in (min) Probability
1 .20
2 .60
3 .10
4 .10
1.00

Service Time (min) Probability
2 .10
3 .40
4 .20
5 .20
6 .10
1.00

Assume that in the two-server system an arriving car will join the shorter queue. When queues are of equal length there is a 50-50 chance the driver will enter the queue for either window.

a. Simulate both the one- and the two-teller systems. Compute the average queue length, waiting time, and percentage of utilization for each system.