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Unformatted text preview: spond to network outage, and then add together the probabilities of those states. The 64 CHAPTER 2. DISCRETETYPE RANDOM VARIABLES method becomes intractable for large networks,3 but it is often useful for small networks and it
sharpens intuition about most likely failure modes.
For example, consider network C. Since there are four links, the network state can be represented
by a length four binary string such as 0110, such that the ith bit in the string is one if link i fails,
This computation is illustrated in Table 2.3, where we let qi = 1 − pi . For example, if the network
Table 2.3: A table for calculating P (F ) for network C .
State
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111 Network fails?
no
no
no
no
no
yes
yes
yes
no
yes
yes
yes
no
yes
yes
yes probability q1 p2 q3 p4
q1 p 2 p 3 q4
q1 p2 p3 p4
p 1 q2 q3 p 4
p 1 q2 p 3 q4
p1 q2 p3 p4
p1 p2 q3 p4
p1 p2 p3 q4
p1 p2 p3 p4 state is 0110, meaning that links 2 and 3 fail and links 1 and 4 don’t, then...
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 Spring '08
 Zahrn
 The Land

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