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$54$min$49$ secs

A Ticket counter has four $(4)$ systems. The arrival rate of the machine is $3$ per hour $($Poisson distributed$)$ and it can serve an average of $4$ per hour $($Poisson distributed$).$ Assuming the repairing capacity is one system a week, the repairing time being exponentially distributed.

Find the Probability that the service for be exactly

II$.$ Find the probability that there she repaired

III. Find the expected length of queue $($number of machines in the Queve$)$

IV$.$ Find the expected number of machines waiting to be and being, repaired. $($number of machines in the system$)$

V$.$ Find the expected time a machine shall wait in the queue to be repaired, and $($Average time in the Queue$)$

VI$.$ Find the expected time that a machine shall spend in the system that is waiting for and getting repaired. $($Average time in the system$)$