In: Statistics and Probability
A Florida coastal community experiences a population increase during the winter months, with seasonal residents arriving from the Northern States and Canada. Staffing at a local post office is often in a state of change due to the relatively low volume of customers in the summer months and the relatively high volume in winter months. The service rate of a postal clerk is 0.75 customers per minute. The post office counter has a maximum of three workstations. The target maximum time a customer waits in the system is 5 minutes. For a particular Monday morning, the anticipated arrival rate is 1.3 customers per minute. Assume two out of three workstations are open.
A new population growth study suggests that over the next two years, the arrival rate at the postal office in the winter months can be expected to grow to 2.1 customers per minute. How many stations should be open to ensure that the maximum time a customer waits in the system is still 5 minutes or less?