- #1
allamar2012
- 2
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Homework Statement
I design a markov model to study the availability of a node which will not work unless the network work: I make the following matrix. In which (i,j) means i is node up /down and j is network up/down. R1,R2 means the repair rate for node and network. F1,F2 means the failure rate for node and network.
(0,0) (1,0) (0,1) (1,1)
(0,0) 0 R1 R2 0
(1,0) F1 0 0 R2
(0,1) F2 0 0 R1
(1,1) 0 F2 F1 0
Homework Equations
I do the following equations to detemine the P(1,1)
(R1+R2)P(0,0)= F1 P(1,0) + F2 P(0,1)
(F1+R2)P(1,0) = R1 P(0,0) +F1 P(1,1)
(F2+R1)P(0,1) = R2 P(0,0) +F1 P(1,1)
(F2+F1)P(1,1) = R2 P(1,0) +R1 P(0,1)
P(0,0) + P(1,0) + P(0,1) + P(1,1) = 1
I do this symbolically in which it gives me long recursive and I couldn't complete it.
The Attempt at a Solution
is my equation right or wrong?
I need advise in how to solve this equations to get P(1,1).
I try MATLAB to calculate this equations as linear system
it gives me
[ 0
0
0
0 ]
Thanks