Problems DTMC Models
 Discrete Time Markov Chain Models - Printer Repair

The Mechanical Engineering Department has three printers. The probability that a printer will fail during a given week is 0.2. With the assumption that printers fail independently, we compute the probabilities below. The probabilities are based on the number of printers in the repair shop at the beginning of the week.

 Failures 0 in shop 1 in shop 2 in shop 3 in shop 0 0.73 0.81 0.90 1 1 0.24 0.18 0.10 0 2 0.03 0.01 0 0 3 0 0 0 0

In each case below construct the DTMC matrix when the time interval is one week and the states describe the number of printers in the repair shop at the beginning of the week.

Using the Stochastic Analysis Add-in compute the steady-state distribution of the number of printers in operation at the beginning of each week.

a. When one or more printer is in the shop at the beginning of the week, exactly one is repaired during the week.

b. Each printer in the shop at the beginning of the week will be repaired during the week with a probability of 0.5. With the assumption that printers are repaired independently, the number repaired during the week is governed by Binomial distribution.

c. Assume that only one printer can be repaired at a time and it takes exactly two weeks to repair a printer. A failed printer must be in the shop at the beginning of the week in order for repair to begin.

Operations Research Models and Methods
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by Paul A. Jensen