# Question

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.

(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.

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