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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?
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).
- Spring '10
- The Land