Maximum Flow and Critical Cutset as Descriptors of Multi-State Systems with Randomly Capacitated Components.
Abstract
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), ..., Bn(tau), 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 D(tau), 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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1986
- Accession Number
- ADA169959
Entities
People
- George S. Fishman
Organizations
- University of North Carolina at Chapel Hill