Conditional expected time

Reference no: EM131005873

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 Pi Pijtij/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?

Reference no: EM131005873

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