1. Consider two machines that are maintained by a single repairman. Each machine functions for an exponentially distributed amount of time with rate A=2 before it fails. The repair times for each unit are exponential with rate u=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. 2. Same as above but now machines are repaired in the order in which they fail. Each machine functions for an exponentially distributed amount of time with rate Aj before it fails. A1 = 2, A 2 = 3. The repair times for each unit are exponential with rate u j, with u 1=.5 and u 2=1 . The state space has nodes that keep track of the machine that is at the repair shop (in case there is only one) and keeps track of which machine is worked on in case there are two machines at the repair shop. That is the state space is S={0, 1, 2, 12, 21}.
1. Consider two machines that are maintained by a single repairman. Each machine functions for an exponentially distributed amount of time with rate A=2 before it fails. The repair times for each unit are exponential with rate u=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. 2. Same as above but now machines are repaired in the order in which they fail. Each machine functions for an exponentially distributed amount of time with rate Aj before it fails. A1 = 2, A 2 = 3. The repair times for each unit are exponential with rate u j, with u 1=.5 and u 2=1 . The state space has nodes that keep track of the machine that is at the repair shop (in case there is only one) and keeps track of which machine is worked on in case there are two machines at the repair shop. That is the state space is S={0, 1, 2, 12, 21}.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1. Consider two machines that are maintained by a single repairman. Each machine functions for an exponentially distributed amount of time with rate A=2 before it fails. The repair times for each unit are exponential with rate u=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.
2. Same as above but now machines are repaired in the order in which they fail. Each machine functions for an exponentially distributed amount of time with rate Aj before it fails. A1 = 2, A 2 = 3. The repair times for each unit are
exponential with rate u j, with u 1=.5 and u 2=1 . The state space has nodes that keep track of the machine that is at the repair shop (in case there is only one) and keeps track of which machine is worked on in case there are two machines
at the repair shop. That is the state space is S={0, 1, 2, 12, 21}.
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