36. Consider a system of n components such that the working times of component , are exponentially...

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36. Consider a system of n components such that the working times of component , are exponentially distributed with rate .

When a component fails, however, the repair rate of component i depends on how many other components are down. Specifically, suppose that the instantaneous repair rate of component

, when there are a total of k failed components, is .

(a) Explain how we can analyze the preceding as a continuous-time Markov chain. Define the states and give the parameters of the chain.

(b) Show that, in steady state, the chain is time reversible and compute the limiting probabilities.

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Introduction To Probability Models

ISBN: 9780128143469

12th Edition

Authors: Sheldon M Ross

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Question Posted: Sep 18, 2024 11:01 AM

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36. Consider a system of n components such that the working times of component , are exponentially...

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Introduction To Probability Models

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