Consider two machines that are maintained by a single repairman. Each machine functions for an exponentially distributed amount of time with rate λ=2 before it fails. The repair times for each unit are exponential with rate μ=1. The Markov chain model for this situation has state space indicating the number of machines that are in the repair shop: S={0,1,2}. Notice that you move from 0 to 1 if one of the two machines breaks down. You move from 1 to 0 when the machine in the repair room is repaired.

Consider two machines that are maintained by a single repairman. Each machine functions for an exponentially distributed amount of time with rate λ=2 before it fails. The repair times for each unit are exponential with rate μ=1. The Markov chain model for this situation has state space indicating the number of machines that are in the repair shop: S={0,1,2}. Notice that you move from 0 to 1 if one of the two machines breaks down. You move from 1 to 0 when the machine in the repair room is repaired.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Matrices

Section2.5: Markov Chain

Problem 33E

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