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Unformatted text preview: nding the probability of failure of the upper branch by p1 + p2 and the lower branch
by p3 + p4 and multiplying these bounds because the branches are independent. The numerical
value is 0.000004 in case pi = 0.001 for 1 ≤ i ≤ 4.
For network D, F = F1 F3 ∪ F2 F4 . The union bound for two events yields P (F ) ≤ p1 p3 + p2 p4 .
The numerical value is 0.000002 in case pi = 0.001 for 1 ≤ i ≤ 4.
Fo network E, F = F1 F3 ∪ F2 F4 ∪ F1 F5 F4 ∪ F3 F5 F2 . The union bound for four events yields
P (F ) ≤ p1 p3 + p2 p4 + p1 p5 p4 + p3 p5 p2 . The numerical value is 0.000002002 in case pi = 0.001 for
1 ≤ i ≤ 5, which is approximately 0.000002.
Note that for all four networks, B through E, the numerical value of the union bound, in case
pi = 0.001 for all i, is close to the exact value of network outage computed above.
Calculation by exhaustive listing of network states Another way to calculate the outage
probability of an s − t network is to enumerate all the possible network states, determine which
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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
- The Land