2
$\begingroup$

Consider a set of n machines and a single repair facility to service these machines. Suppose that when machine i , i = 1,2, … n, fails, it requires an exponentially distributed amount of work with rate πœ‡π‘– to repair it. The repair facility divides its efforts equally among all failed machines in the sense that whenever there are k failed machines each one receives work at a rate of 1/k per unit time. If there are a total of r working machines, including machine i , then i fails at an instantaneous rate πœ†π‘–/r

(a) Find the instantaneous transition rates

The answer is as following, enter image description here

Okay, I can understand that qS,S-i = Β΅i / |S|. As far as I know, because the repair facility divides its efforts equally among all failed machines in the sense, we need to make Β΅i divided by |S|.

But I cannot understand that qS,S+j = πœ†π‘–.

In my opinion, since the sentence-"i fails at an instantaneous rate πœ†π‘–/r" should imply that the rate at which process makes a transition from state S into state S+j is πœ†j/r, then qS,S+j should be
πœ†j/|$S^c$|.

Do I misunderstand something?

$\endgroup$

0

Your Answer

By clicking β€œPost Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.