The service counter at Southwest Montana Airlines has a single queue for waiting customers and two ticket agents. One of the agents is on duty at all times; the other agent goes on duty whenever the...

The service counter at Southwest Montana Airlines has a single queue for waiting customers and two ticket agents. One of the agents is on duty at all times; the other agent goes on duty whenever the queue of customers becomes too long. Suppose that customer arrivals to the counter are well modeled as a Poisson process with rate 45/hour. The agents both work at rate 30 customers/hour, and the second agent goes on duty if there are 3 or more customers at the counter (including the ones being served). Service times are modeled as exponentially distributed.

(a) Develop a queueing model capable of answering the questions below. Carefully state all of your modeling approximations.

(b) Determine the fraction of time that the second agent is on duty.

(c) Determine the average length of the queue, not including those being served.

(d) Now treat the number of customers that trigger the second agent to go on duty as a decision variable. When should the second agent go on duty to keep the expected number in the system under 5?