Unformatted text preview: the network fails. The
probability of this state is q1 p2 p3 q4 . For given numerical values of p1 through p4 , numerical values
can be computed for the last column of the table, and the sum of those values is P (F ). 2.12.3 Distribution of the capacity of a ﬂow network An s − t ﬂow network is an s − t network such that each link has a capacity. Two s − t ﬂow
networks are shown in Figure 2.13. We assume as before that each link i fails with probability pi .
If a link fails, it cannot carry any ﬂow. If a link does not fail, it can carry ﬂow at a rate up to
the link capacity. Link capacities and ﬂows are given in units of some quantity per unit time. For
example, the units could be gallons per minute (for an irrigation system), packets per second (for
a communication network), or vehicles per hour (for a highway transportation system).
3 From a computational complexity point of view, the problem of computing the outage probability, also called the
reliability problem, has been shown to be P space complete, meaning ex...
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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 Tech.
 Spring '08
 Zahrn
 The Land

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