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Unformatted text preview: act solution for large networks is probably
not feasible. 2.12. RELIABILITY 65 Figure 2.13: Two s − t ﬂow networks.
For simplicity we have chosen to work with undirected links, and we assume that the ﬂow can
be in either direction on a link, up to the total capacity of the link. We assume that ﬂow can be
split among multiple paths. The capacity of an s − t ﬂow network is the maximum ﬂow rate from s
to t. The capacity is random because of the possible link failures. We will compute the pmf of the
capacity of each of the two networks.
We begin with Network F . If both of the links are working, then the capacity is 30, because the
top link can carry ﬂow at rate 20 and the bottom link can carry ﬂow at rate 10. If link 2 fails and
link 1 does not, then the total maximum ﬂow rate is 10. By considering all four network states, we
arrive at the following expression for the pmf of X , the capacity of Network F :
pX (0) = p1 p2 pX (10) = q1 p2 pX (20) = p1 q2 pX (30) = q1 q2 .
Let Y denote the capacit...
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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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