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Suppose I have M/M/1 system with $\lambda = 4$ per hour and $\mu = 5$ per hour. How can I find out if all jobs have been served after, say, 8 hours? At first I thought about doing $P(n > 40)$ since $\mu = 5$ means 5 arrive, on average, per hour but I'm pretty sure that's not the right way to do it. I don't know how it actually goes, however.

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$\mu=5$ means 5 are served every hour, not arrived –  Alex Dec 31 '12 at 23:50
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up vote 2 down vote accepted

What is the probability that the queue is empty?

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It starts empty. If you mean at the end, then that's what I want to know, but after some time has passed (in my initial post, that time is 8 hours). –  mr chibobo May 9 '11 at 0:33
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Oooooh. I get it. –  mr chibobo May 9 '11 at 0:43
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