## Probability Queue Theory M/M/1 [closed]

After not doing any maths for quite a while I am more then a little rusty when it comes to probability, so I was wondering if you guys could help me.

I understand that P(A and B) = P(A) * P(B) So what is achieved by P(A)/P('A) ? I am currently trying to understand why

E(N) = p / (1 - p)


provides the expected number of users in a system?

Where p is the utilisation of the queue, given by

p = arrival rate / service rate


Am I right in assuming that p is also the probability that the system is not empty?

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Ask on one of the websites mentioned here: mathoverflow.net/faq – rgrig Apr 5 2010 at 13:49
en.wikipedia.org/wiki/Geometric_series#Formula – Steve Huntsman Apr 5 2010 at 14:51
To expand on what rgrig said: your question probably isn't at the right level for Math Overflow, and you're likely to get better responses at some of the sites listed in the FAQ (under mathoverflow.net/faq#whatnot ). Good luck. – Tom Leinster Apr 5 2010 at 17:16