Etn 1np so if p 1 n x etn 1mp p1 m1 this implies

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Unformatted text preview: ther examples: Example 4.3. M/M/s queue. Imagine a bank with s 1 tellers that serve customers who queue in a single line if all of the servers are busy. We imagine that customers arrive at times of a Poisson process with rate , and that each service time is an independent exponential with rate µ. As in Example 4.2, q (n, n + 1) = . To model the departures we let ( nµ 0 n s q (n, n 1) = sµ n s To explain this, we note that when there are n s individuals in the system then they are all being served and departures occur at rate nµ. When n > s, all s servers are busy and departures occur at sµ. Example 4.4. Branching proceess. In this system each individual dies at rate µ and gives birth to a new individual at rate so we have q (n, n + 1) = n q (n, n 1) = µn A very special case called the Yule process occurs when µ = 0. Having seen several examples, it is natural to ask: Given the rates, how do you construct the chain? P Let i = j 6=i q (i, j ) be the rate at which Xt leaves i. If i = 1, th...
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This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).

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