4 a table for calculating the distribution of

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Unformatted text preview: spond to network outage, and then add together the probabilities of those states. The 64 CHAPTER 2. DISCRETE-TYPE 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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