The authors of the article “Pavement Performance Modeling Using Markov Chain” (Proc. ISEUSAM, 2012:.
The authors of the article “Pavement Performance Modeling Using Markov Chain” (Proc. ISEUSAM, 2012: 619–627) developed a system for classifying pavement segments into five categories: (1) Very good, (2) Good, (3) Fair, (4) Bad, and (5) Very bad. Analysis of pavement samples led to the construction of the following transition matrix for the Markov chain Xn pavement condition n years from now: Notice that a pavement segment either maintains its condition or goes down by one category each year. (a) The evaluation of one particular stretch of road led to the following initial probability vector (what the authors call a “condition matrix”): [.3307 .2677 .2205 .1260 .0551]. Use the Markov chain model to determine the condition matrix of this same road section 1, 2, and 3 years from now. (b) “Very bad” road segments require repairs before they are again usable; the authors’ model applies to unrepaired road. What is the average time (number of years) that a very good road can be used before it degrades into very bad condition? Make the same determination for good, fair, and bad roads. (c) Suppose one road segment is randomly selected from the area to which the condition matrix in (a) applies. What is the expected amount of time until this road segment becomes very bad? [Hint: Use the results of part (b).] Apr 08 2022 03:26 PM
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