Question

Prob.3 In a relay network, the relay components are arranged in the configuration shown in the diagram below. Assume that each relay component fails randomly and with probability p. (a) Find the probability that a signal sent from point a arrives at point b successfully. (b) Find the value of p so that the probability that a signal sent from point a arrives at point b successfully is 0.9375. R. R ob R R,

I really need help to understand this Stochastic Models problem.

Answer 1

The circuit will be complete from a->b in case, either of the line is working

P(fail) = p

P(success) = 1 - p

P(R1 works).P(R2 works) S1 (Combination of R1 and R2) 1- p).(1- p) (1 -p)2

P(R3 works).P(R4 works) S2 (Combination of R3 and R4) (1 p)2

P(System Works) = P(S1 works or S2 works) = P(S1 works) + P(S2 works) - P(S1 works and S2 works)

P(system works) (1-p(1-p-(1-p-2(1-p-(1-p

b)

Equating the formula to 0.9375 we get

2(1 p)-(1-p = 0.9375

p= 0.134

Note - Post any doubts/queries in comments section