First American Bank is trying to determine whether it should install one or two drive-through teller windows. The following probability distributions for arrival intervals and service times have been developed from historical data:
Time Between
Automobile Arrivals (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 the 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 two-teller systems. Compute the average queue length, waiting time, and percentage utilization for each system.
b. Discuss your results in (a) and suggest the degree to which they could be used to make a decision about which system to employ.