Question: Two customers move about among three servers. Upon completion of service at server i, the customer leaves that server and enters service at whichever of

Two customers move about among three servers. Upon completion of service at server i, the customer leaves that server and enters service at whichever of the other two servers is free. (Therefore, there are always two busy servers.) The service times at server i are exponential with rate μi, i = 1, 2, 3. If μ1 = 7, μ2 = 3 and μ3 = 5, what proportion of time is each server idle?

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