a consulting firm has two consultants. customers arrive according to a Poisson process with rate 10 per hr. the consultants service time is exponentially distributed with mean 12 mins. when a customer arrives , if there is a free consultant, the customer is served immediately by the consultant. the office is space limited and 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 he will leave.

1. show transition diagram, specify states and transition rates, also identify queuing model

2. what is the probability that a customer will be served when he comes to the office

3. how long is the average time that a served customer spends in office.