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inﬁnite number of servers available. CS 522, v 0.94, d.medhi, W’99 21 16. M/M/1/ /K model: single server, ﬁnite population In this case, we have a ﬁnite population, K . The statetransition diagram is:
Κλ
0 1
µ 3 2
µ λ 2λ (Κ−2)λ (Κ−1)λ •• • Κ−1
µ µ Κ
µ In this case, 8 j = : K , j if 0 j 0 otherwise. j =
0 if 1 j K K otherwise. Steadystate probabilities are given by K ! j
j = K , j ! 0
where 0jK 2 K j
3 ,1
X
K! 5
0 = 4
K , j ! :
j =0 This model is often applicable for performance evaluation of a computer system where ﬁnite population
is a good assumption. 17. Inverse ErlangB: given a and blocking, ﬁnd the number of channels
This is another inverse design problem for a network link where the offered load is given in erlangs
and the acceptable blocking level is also given, and we are to ﬁnd the number of channels required in the
link to meet the acceptable level of blocking (known as gradeofservice).
The problem is to ﬁnd an integral minimum m for given a and acceptable blocking b: min fm E a m bg:
In this case, the inverse is not easy to calculate as in the M/M/1 case with delay. Thus, an algorithmic
approach is needed. We provide below a rough sketch:
Given offered_load and b_goal, estimate number of trunks
======================================================== CS 522, v 0.94, d.medhi, W’99 22 assign tolerance
estimated_trunk = (int) offered_load
b_test = erlangb(o...
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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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