At the Forrester Manufacturing Company, one repair technician has been assigned the responsibility of maintaining four machines. For each machine, the probability distribution of the running time before a breakdown is exponential, with a mean of 8 hours. The repair time also has an exponential distribution, with a mean of 4 hours.
(a) Which queueing model fits this queueing system?
(b) Use this queueing model to find the probability distribution of the number of machines not running, and the mean of this distribution.
(c) Use this mean to calculate the expected time between a machine breakdown and the completion of the repair of that machine.
(d) What is the expected fraction of time that the repair technician will be busy?