Unformatted text preview: et from (11), j
j = 0
Now, e = 1 is j = 1 2 :::
+ 2 + ::: = 1:
0 1 +
P
For convergence in this case, we need the condition =j
1. Since this is a geometric series,
convergence condition is satisﬁed by the requirement that = 1. We, thus, have
" 0 = 1 , :
j
j = 1 ,
and hence, If we write j = 1 2 ::: = =, which is known as utilization or trafﬁc intensity, then
j = 1 , j : The convergence condition also has a simple physical interpretation. Since = =
1, this means the
average arrival rate should be less than the average service rate; if it is other way around, the system will
overﬂow.
What has the M/M/1 queue anything to do with network design and analysis? We have mentioned
earlier that to get a handle on network modeling and performance, we have to have some idea about trafﬁc.
The simplest network we can think of is just a network link. So, here would refer to the arrival rate
to a network link while will refer to the average service rate of the link with the link being one server.
Speciﬁcally,...
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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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