Each entering customer must be served first by server 1, then by server 2, and finally by server 3. The amount of time it takes to be served by server i is an exponential random variable with rate μi, i = 1, 2, 3. Suppose you enter the system when it contains a single customer who is being served by server 3.

(a) Find the probability that server 3 will still be busy when you move over to server 2.

(b) Find the probability that server 3 will still be busy when you move over to server 3.

(c) Find the expected amount of time that you spend in the system. (Whenever you encounter a busy server, you must wait for the service in progress to end before you can enter service.)

(d) Suppose that you enter the system when it contains a single customer who is being served by server 2. Find the expected amount of time that you spend in the system.