develop a discrete event simulation of a bank operation using the Arena simulation tool.

Customers arrive at the bank and enter a queue to wait for a single teller. When the customer reaches the teller, the teller performs her transaction. When the initial transaction is completed, the teller determines if the customer must see the supervisor. If this is the case, the customer moves to the single supervisor; when finished, the customer returns to the teller queue to re-do her transaction. If the customer is not required to see the supervisor, she leaves the bank.

The time between customer arrivals is exponentially distributed with a mean of 5 minutes. The travel times from the entrance to the teller queue and from the teller to the exit are both 1 minute. All teller transaction times are normally distributed with a mean of 3 minutes and a standard deviation of 1 minute. Ten percent of the customers are required to see the supervisor. It is possible for a customer to see the supervisor several times. Travel time to and from the supervisor takes 1.5 minutes, and the supervisor service time follows a triangular distribution with parameters (12, 15, 20) minutes.

The simulation is to be run for an 8.5 hour day. Statistics are to be gathered on the teller utilization, the supervisor utilization, the customer flow time, the customer delay in queue, and the number of customers in the teller queue.