8. A single repairperson looks after the two machines 1 and 2. Each time it is repaired, machine i stays up for an exponential time with rate 2, , where i = 1,2. When machine i fails, it requires an exponentially distributed amount of work with rate u, to complete its repair. The repairperson will always service machine 1 when it is down. For instance, if machine 1 fails while 2 is being repaired, then the repairperson will immediately stop work on machine 2 and start on 1. (i) Write down all the states. (ii) What is the probability that the machine 2 is down.
8. A single repairperson looks after the two machines 1 and 2. Each time it is repaired, machine i stays up for an exponential time with rate 2, , where i = 1,2. When machine i fails, it requires an exponentially distributed amount of work with rate u, to complete its repair. The repairperson will always service machine 1 when it is down. For instance, if machine 1 fails while 2 is being repaired, then the repairperson will immediately stop work on machine 2 and start on 1. (i) Write down all the states. (ii) What is the probability that the machine 2 is down.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:A single repairperson looks after the two machines 1 and 2. Each time it is repaired, machine i stays up for an
exponential time with rate a,, where i = 1,2. When machine i fails, it requires an exponentially distributed
8.
amount of work with rate u, to complete its repair. The repairperson will always service machine 1 when it
is down. For instance, if machine 1 fails while 2 is being repaired, then the repairperson will immediately stop
work on machine 2 and start on 1.
(i) Write down all the states.
(ii) What is the probability that the machine 2 is down.
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