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Unformatted text preview: cation networks is m parallel servers. This model comes up in
the case of a communication link which is divided into m circuits or channels. An arriving customer can take any of the circuits on arrival, OR, has to wait if all the servers (circuits) are busy. Inﬁnite population
assumption is made here. [this model is close to a telephone network link, but not quite; we’ll see later
where the difference is].
This is again a BD model, where j = and j = j if 1 j m m for j m. The statetransition diagram is
λ
0 λ λ λ
1 3 2 µ 2µ • • m • m+1 mµ 3µ mµ • • • mµ Note that for M/M/m model, the utilization, , is
= m 1:
Here, we can show (from BD model) that 8 j
1
j ! 0 for 1 j m!mj,m 0 for j j = j
: Further, 2
0 = 4 1 =m m m. 3
m,1 =j ,1
X m!1 , =m + j=0 j! 5: Given ’s, different performance measures can be derived. CS 522, v 0.94, d.medhi, W’99 18 14. M/M/m/m model: m parallel servers, loss system In this case, the buffer size is m (including for servers) with m para...
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This document was uploaded on 03/19/2014 for the course CS 6030 at Western Michigan.
 Fall '08
 Staff
 Computer Networks

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