A group of n processors is arranged in an ordered list. When ajob arrives, the first processor in line attempts it; if it isunsuccessful, then the next in line tries it; if it too isunsuccessful, then the next in line tries it, and so on. When thejob is successfully processed or after all processors have beenunsuccessful, the job leaves the system. At this point we areallowed to reorder the processors, and a new job appears. Supposethat we use the one-closer reordering rule, which moves theprocessor that was successful one closer to the front of the lineby interchanging its position with the one in front of it. If allprocessors were unsuccessful (or if the processor in the firstposition was successful), then the ordering remains the same. Suppose that each time processor i attempts a job then, independently of anything else, it is successful with probabilitypi.(a) Define an appropriate Markov chain to analyze thismodel.(b) Show that this Markov chain is time reversible.(c) Find the long-run probabilities.