Unformatted text preview: CTMC Modeling Exercises 1. Consider a machine that operates for an exp( μ ) amount of time and then fails. Once it fails, it gets repaired. The repair time is an exp( λ ) random variable, and is independent of the past. The machine is as good as new after the repair is complete. Let X ( t ) be the state of the machine at time t , 1 if it is up and 0 if it is down. Model this as a CTMC. 2. There are two identical photocopy machines in our department. The up times of each machine is exponentially distributed with mean up time 1 /μ days. As soon as a machine breaks down, a repariperson is called from the company. The repair times of each machine is exponentially distributed with mean 1 /λ days. It is possible that both machines are down and we have 2 repairpersons from the company taking care of them. Assume that the repairpersons are independent. Let X ( t ) be the number of machines that are up at time t . Model the { X ( t ) , t ≥ } process as a CTMC. What if there was a single repairperson?there was a single repairperson?...
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This note was uploaded on 09/18/2011 for the course ISEN 609 taught by Professor Klutke during the Spring '08 term at Texas A&M.
 Spring '08
 Klutke

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