Maximum Flow and Critical Cutset as Descriptors of Multi-State Systems with Randomly Capacitated Components.
NORTH CAROLINA UNIV AT CHAPEL HILL CURRICULUM IN OPERATIONS RESEARCH AND SYSTEMS ANALYSIS
Pagination or Media Count:
Let G V,E,s,t denote a directed network with node set V, arc set E 1,...,n, source node s and sink node t. Let gamma denote the set of all minimal s-t cutsets and B1 tau, ..., Bntau, the random arc capacities at time tau with known joint probability distribution function. Let lambda tau denote the maximum s-t flow at time tau and Dtau, the corresponding critical minimal s-t cutset. Let omega denote a set of minimal s-t cutsets. This paper describes a comprehensive Monte Carlo sampling plan for efficiently estimating the probability that D tau epsilon omega subset of gamma and x lambda tau or y at time tau and the probability that D tau epsilon omega given that x lambda tau or y at time tau. The proposed method makes use of a readily obtainable upper bound on the probability that lambda tau x to gain its computational advantage. Techniques are described for computing confidence intervals and credibility measures for assessing that specified accuracies have been achieved. The paper includes an algorithm for performing the Monte Carlo sampling experiment, an example to illustrate the technique and a listing of all steps needed for implementation. Author
- Operations Research