# If s t t then p yst j ys i p xt p xt st

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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 ✓ ◆ ✓ ◆ 1 1 65 19 1 1= 1= EB = ⇡ (0) 2 27 27 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 ( µn if n s q (n, n 1) = µs if n s The conditions that result from using the detailed balance condition are ⇡ (j ⇡ (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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