County Bank has several branch locations. At one of these locations, customers arrive at a Poisson rate of 150 per hour. The branch employs 6 tellers. Each teller takes, on average, 2 minutes to serve...

County Bank has several branch locations. At one of these locations, customers arrive at a Poisson rate of 150 per hour. The branch employs 6 tellers. Each teller takes, on average, 2 minutes to serve a customer, and service times are exponentially distributed. Also, all tellers perform all tasks, so that customers can go to any of the 6 tellers. Customers who arrive and find all 6 tellers busy join a single queue and are then served in FCFS fashion. As a first step, the bank manager wants to develop a queueing model of the current system. Then he wants to find the “best” number of tellers, given that tellers are paid $8 per hour.

Objective To develop an M/M/s queueing model for the bank and examine its steadystate properties, and then to find the number of tellers that is best from an economic point of view.