47. In a semi-Markov process, let tij denote the conditional expected time that the process spends in

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47. In a semi-Markov process, let tij denote the conditional expected time that the process spends in state i given that the next state is j.

(a) Present an equation relating μi to the tij .

(b) Show that the proportion of time the process is in i and will next enter j is equal to PiPijtij/μi .

Hint: Say that a cycle begins each time state i is entered. Imagine that you receive a reward at a rate of 1 per unit time whenever the process is in i and heading for j.
What is the average reward per unit time?

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Introduction To Probability Models

ISBN: 9780123756862

10th Edition

Authors: Sheldon M Ross

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Question Posted: Sep 16, 2024 04:01 AM

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47. In a semi-Markov process, let tij denote the conditional expected time that the process spends in

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Introduction To Probability Models

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