# The authors of the article “Stationarity of the Transition Probabilities in the Markov Chain…

The authors of the article “Stationarity of the Transition Probabilities in the Markov Chain…
The authors of the article “Stationarity of the Transition Probabilities in the Markov Chain Formulation of Owner Payments on Projects” (ANZIAM J., v. 53, 2012: C69-C89) studied payment delays in road construction in Australia. States for any payment were defined as follows: k weeks late for k =0, 1, 2, 3; paid (pd), an absorbing state; and “to be resolved” (tbr), meaning the payment was at least 1 month late, which the authors treated as another absorbing state. For one particular project, the following Q and R matrices were given for the canonical form of the one-step transition matrix: (a) Construct the complete 6 x 6 transition matrix P for this Markov chain. (b) Draw the state diagram of this Markov chain. c) Determine the mean time to absorption for payment that is about to come due (i.e., one that is presently 0 weeks late). (d) What is the probability a payment is eventually made, as opposed to being classified as “to be resolved”?  (e) Consider the two probabilities P(0 ->1) and P(3 ->pd). What is odd about each of these values? (The authors of the article offer no explanation for the irregularity of these two particular probabilities.) Apr 08 2022 03:26 PM

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