Lecture 12

# J j k j 0 where 0jk 2 k j 3 1 x k 5 0 4 k

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Unformatted text preview: ls) if there were 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 state-transition 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. Steady-state probabilities are given by K !  j  j = K , j !  0 where 0jK 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 Erlang-B: 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 grade-of-service). 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.

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