most recent 30 from http://mathoverflow.net 2013-05-20T17:46:16Z http://mathoverflow.net/feeds/question/20380 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/20380/probability-queue-theory-m-m-1 Dave Grear 2010-04-05T11:43:44Z 2010-04-05T11:48:45Z

<p>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. </p> <p>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 </p> <pre><code>E(N) = p / (1 - p) </code></pre> <p>provides the expected number of users in a system?</p> <p>Where p is the utilisation of the queue, given by</p> <pre><code>p = arrival rate / service rate </code></pre> <p>Am I right in assuming that p is also the probability that the system is not empty?</p>