[10 pts.] Consider the network given below with twelve components. Suppose that

Question

[10 pts.] Consider the network given below with twelve components. Suppose that the components operate independently of each other. Assume that the components 1,2,3, and 4 ( Sub-Network A) allow a message with a failure rate of 10% (each one), while components 5,6,7,8 and 9 ( Sub-Network B) have a failure rate of 5%, 4%,4%,3%, and 2%, respectively. Finally the components 11, and 12 (Sub-Network C) allow a message with a rate of 98%, 95%, 95%. 2. 10 What is the probability that the message will find a route through the network? What is the probability that the message will not find a route through the network? a) b)

Explanation / Answer

probability subsystem 2-3 works =1-0.1*0.1=0.99

hence probability 1,2-3 and 4 works =0.9*0.99*0.9=0.8019

probability subsystem 6-7-8 works =1-0.04*0.04*0.03=0.999952

hence probability 5 ,6-7-8   works = 0.95*0.999952=0.949954

probbaility subsystem 1,2,3,4 or 5,6-7-8 works =1-(1-0.8019)*(1-0.949954)=0.990086

probability that subsystem 9-10 works =1-0.02*0.02 =0.9996

hence probability that message will find a route through the network =0.990086*0.9996*0.95*0.95 =0.893195

b) probability that message will not find a route through the network =1-0.893195 =0.106805

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