Write down the markov chain and the generator matrix for, Project Management

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Write down the markov chain and the generator matrix for

(a) We consider a system of n identical failure-prone machines. A repairman is assigned to repair the broken machines. The mean normal time and the repair time of a machine are exponentially distributed with means λ-1 and μ-1 respectively. The system is said to be in state i(i = 0, 1, . . . , n) if there are i broken machines.

(a) Write down the Markov chain and the generator matrix for the states of this machine repairing model.

(b) Find the steady-state probability pi that there are Pi broken machines in the system.

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