# Question

A computer is inspected at the end of every hour. It is found to be either working (up) or failed (down). If the computer is found to be up, the probability of its remaining up for the next hour is 0.95. If it is down, the computer is repaired, which may require more than 1 hour. Whenever the computer is down (regardless of how long it has been down), the probability of its still being down 1 hour later is 0.5.

(a) Construct the (one-step) transition matrix for this Markov chain.

(b) Use the approach described in Sec. 29.6 to find the µij (the expected first passage time from state i to state j) for all i and j.

(a) Construct the (one-step) transition matrix for this Markov chain.

(b) Use the approach described in Sec. 29.6 to find the µij (the expected first passage time from state i to state j) for all i and j.

## Answer to relevant Questions

Read Selected Reference A13 that describes an OR study done for Intel that won the 2011 Daniel H. Wagner Prize for Excellence in Operations Research Practice. (a) What is the problem being addressed? What is the objective of ...Read Selected Reference A7 that describes an OR study done for TNT Express that won the 2012 Franz Edelman Award for Achievement in Operations Research and the Management Sciences. This study led to a worldwide global ...A manufacturer has a machine that, when operational at the beginning of a day, has a probability of 0.1 of breaking down sometime during the day. When this happens, the repair is done the next day and completed at the end of ...Consider the following gambler’s ruin problem. A gambler bets $1 on each play of a game. Each time, he has a probability p of winning and probability q = 1 p of losing the dollar bet. He will continue to play until he ...A particle moves on a circle through points that have been marked 0, 1, 2, 3, 4 (in a clockwise order). The particle starts at point 0. At each step it has probability 0.5 of moving one point clockwise (0 follows 4) and 0.5 ...Post your question

0