The reservation office for Central Airlines has two agents answering incoming phone calls for flight reservations. In addition, one caller can be put on hold until one of the agents is available to take the call. If all three phone lines (both agent lines and the hold line) are busy, a potential customer gets a busy signal, in which case the call may go to another airline. The calls and attempted calls occur randomly (i.e., according to a Poisson process)

at a mean rate of 15 per hour. The length of a telephone conversation has an exponential distribution with a mean of 4 minutes.

(a) Construct the rate diagram for this queueing system.

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(b) Find the steady-state probability that

(i) A caller will get to talk to an agent immediately,

(ii) The caller will be put on hold, and

(iii) The caller will get a busy signal.