Planning of Instance-based state Representation for Network Repair by Aggelos Aggelidakis Aggelos Aggelidakis Department ECE– Technical University of Crete

CSFR Model(Cost-Sensitive Fault Remediation) Failure Mode Take action Gain information Repair actions Detect when correct functioning has been restored Aggelos Aggelidakis Department ECE– Technical University of Crete

Aggelos Aggelidakis Department ECE– Technical University of Crete CSFR Definition S, fault states Pr, prior probability of fault states AT , test actions AR, repair actions C(s,a), cost functions O(s,a), observation model Aggelos Aggelidakis Department ECE– Technical University of Crete

Finding Optimal Policy We can find an optimal repair policy via dynamic programming. Let B be the power set of S, which is the set of belief states of the system. For each b ∈ B and a ∈ AT ∪ AR, define the expected value of action a in belief state b as the expected cost of the action plus the value of the resulting belief state Aggelos Aggelidakis Department ECE– Technical University of Crete

Value of resulting belief state Where bi = {s ∈ b|o(s, a) = i} is the belief state resulting from taking action a in belief state band obtaining outcome i V (b) = min a∈At∪Ar Q(b, a) Pr(b)=∑ Pr(s), s∈B c(b)=∑ Pr(s)*c(s,a)), s∈B, a∈At∪Ar These equations can be evaluated in time proportional to 2|S| (|AT | + |AR |)(|S| + |AT | + |AR |), at which point the optimal policy can be extracted by choosing the action a in belief state b that minimizes Q(b, a). Such a policy will opti- mally trade off actions to gain information, actions to repair, and the information gained from a failed attempt at repair, in a way that minimizes the total expected cost of repair Aggelos Aggelidakis Department ECE– Technical University of Crete