A switchboard has two outgoing lines serving four customers who never call each other. When a customer is not talking on the phone, he or she generates calls according to a Poisson process with rate λ calls per minute.

Call lengths are exponentially distributed with a mean of 1/μ minutes.

If a customer finds the switchboard blocked (i.e., both lines are busy) when attempting to make a call, he or she never tries to make that particular call again; that is, the call is lost.

a. Give the state-transition-rate diagram of the process.

b. What is the fraction of time that the switchboard is blocked?