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dtmc_analysis - Class Problems DTMC analysis 1 A company...

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Class Problems: DTMC analysis 1. A company uses two forecasting tools to predict the demand of its product. Tool i is effective w.p. p i (for i = 1 , 2). If the n th prediction uses tool i and it is observed to be effective, then the ( n + 1) st prediction is also done using the same tool; if it is observed to be ineffective, then the ( n + 1) st prediction is made using the other tool. Let X n be the tool used for the n th prediction. In steady- state what is the probability that tool 1 is used for prediction? What is the long run fraction of predictions made by tool 2? 2. Students switch between 3 phone companies A , V , and S according to the following transition probability matrix 0 . 4 0 . 2 0 . 4 0 . 6 0 . 4 0 0 . 3 0 . 5 0 . 2 . What is the steady state market share for the 3 phone companies if all the students behaved according to the above matrix. 3. Consider a machine tool that is used on an NC-machine. The time to produce a part and inspect it is 1 hour. If the tool has produced i parts, it fails w.p. p i
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