The Security & Trust Bank employs 4 tellers to serve its customers. Customers arrive according to a Poisson process at a mean rate of 2 per minute. However, business is growing and management projects that the mean arrival rate will be 3 per minute a year from now. The transaction time between the teller and customer has an exponential distribution with a mean of 1 minute.
Management has established the following guidelines for a satisfactory level of service to customers. The average number of customers waiting in line to begin service should not exceed 1. At least 95 percent of the time, the number of customers waiting in line should not exceed 5. For at least 95 percent of the customers, the time spent in line waiting to begin service should not exceed 5 minutes.
(a) Use the M/M/s model to determine how well these guidelines are currently being satisfied.
(b) Evaluate how well the guidelines will be satisfied a year from now if no change is made in the number of tellers.
(c) Determine how many tellers will be needed a year from now to completely satisfy these guidelines.