A shop contains three identical machines that are subject to a failure of a certain kind. Therefore, a maintenance system is provided to perform the maintenance operation (recharging) required by a failed machine. The time required by each operation has an exponential distribution with a mean of 30 minutes. However, with probability 1/3, the operation must be performed a second time ( with the same distribution of time) in order to bring the failed machine back to a satisfactory operational state. The maintenance system works on only one failed machine at a time, performing all the operations (one or two) required by that machine, on a first-come-firstserved basis. After a machine is repaired, the time until its next failure has an exponential distribution with a mean of 3 hours.
(a) How should the states of the system be defined in order to formulate a model for this queueing system in terms of transitions that only involve exponential distributions?
(b) Construct the corresponding rate diagram.
(c) Develop the balance equations.