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Unformatted text preview: rk A has two
links, link 1 and link 2, in parallel. Network B has two links in series. Network C has two parallel
paths, with each path consisting of two links in series. Network D has two stages of two parallel
links. Network E has ﬁve links.
Suppose each link i fails with probability pi . Let Fi be the event that link i fails. So pi = P (Fi ).
Assume that for a given network, the links fail independently. That is, the Fi ’s are independent
events. Network outage is said to occur if at least one link fails along every s − t path, where an
s − t path is a set of links that connect s to t. Let F denote the event of network outage. We will 62 CHAPTER 2. DISCRETETYPE RANDOM VARIABLES Figure 2.12: Five s − t networks with associated outage probabilities.
ﬁnd P (F ) for each of the ﬁve networks, and then apply the union bound to get a simple upper
bound to P (F ) for networks B through E.
Exact calculation of network outage Network A has two s − t paths: the path consisting of
link 1 alone, and the path consisting of link 2 alone. Therefore, network outage happens if and
only if both links fail. Thus, for network A, F = F1 F2 . By the assumption that F1 and F2 are
independent, P (F ) = p...
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This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Institute of Technology.
 Spring '08
 Zahrn
 The Land

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