A switchboard has two outgoing lines and is concerned only w

A switchboard has two outgoing lines and is concerned only with servicing the outgoing calls of three customers who never call each other. When a customer is not on a line, each potential caller generates calls at a Poisson rate lambda. Call lengths are exponentially distributed, with a mean call length of If a caller finds the switchboard blocked, he never tries to retry that particular call. All call initiations and durations are independent of each other. Determine the fraction of time that the switchboard is saturated. Determine the fraction of outgoing calls which encounter a saturated switchboard.

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