An consulting firm has 2 consultants in the office. The consultants service time is exponentially distributed with mean of 12 minutes. Customers arrive to the office according to a Poisson process with rate of 10 per hour. When the customer arrives, if there is a free consultant, the customer is served immediately by the consultant. the office is space limited; there is only 1 additional chair in the office. When both consultants are busy, a new customer will wait for the next available consultant if there is a spare chair; otherwise the customer will leave.

1. Make transition diagram, with clearly specified states and transition rates, and identify the queuing model.

2. What is the probability that a customer will be served (will not leave) when she comes to the office?

3. How long is the average time tat a served customer spends in office