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(Solved): A certain shop has four identical machines that are operated continuously except when they are bro ...



A certain shop has four identical machines that are operated continuously except when
they are broken down. Because they brea

A certain shop has four identical machines that are operated continuously except when they are broken down. Because they break down fairly frequently, the top-priority assignment for a full-time maintenance person is to repair them whenever needed. The a time required to repair a machine has an exponential distribution with a mean of 1/8 day. Once the repair of a machine is completed, the time until the next breakdown of that machine has an exponential distribution with a mean of 1/4 day. These distributions are independent. (Modification of Example in page 752 of Hillier-Lieberman's Introduction to Operations Research, 9th edition) 1. Let each state of system represents the number of machines broken down. Now formulate the problem as a continuous-time Markov process, and draw its transition diagram. 2. Construct the steady-state equations using a) Balance equations b) Matrix A c) Streamlined equations for a birth-death process 3. Solve the system of equations in Question #2 for the steady-state probabilities. I


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