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Unformatted text preview: hine formula (3.7), since a key
ingredient in the derivation is false: arriving customers who enter the system
do not see the time average queue length.
By our fourth queueing equation, (3.6), the server’s busy periods have mean
which agrees with the computation in Example 4.21. Multiple servers
Our next example is queue with s servers with an unlimited waiting room, a
system described more fully in Example 4.3.
Example 4.25. M/M/s queue. Imagine a bank with s
1 tellers that
serve customers who queue in a single line if all servers are busy. We imagine
that customers arrive at the times of a Poisson process with rate , and each
requires an independent amount of service that has an exponential distribution
with rate µ. As explained in Example 1.3, the ﬂip rates are q (n, n + 1) = and
if n s
q (n, n 1) =
if n s
The conditions that result from using the detailed balance condition are
⇡ (j 1) = µj ⇡ (j )
1) = µj ⇡ (j...
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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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