Customers can be served by any of three servers, where the service times of server i are exponentially distributed with rate μi, i = 1, 2, 3. Whenever a server becomes free, the customer who has been waiting the longest begins service with that server.

(a) If you arrive to find all three servers busy and no one waiting, find the expected time until you depart the system.

(b) If you arrive to find all three servers busy and one person waiting, find the expected time until you depart the system.