Modular decomposition and reliability computation in stochastic transportation networks having cutnodes

Abstract

AbstractConsider a flow network having random arc capacities and having associated with each node n a “supply‐demand random variable” Yn whose absolute value equals the supply available at the node when Yn assumes a non‐negative value and the demand required by the node when Yn assumes a nonpositive value. A fundamental problem is the computation of the reliability R, that is, the probability that the random variables will assume values that permit a feasible flow. Upon adapting the graph‐theoretic concepts of “cutnode” and “block,” it is possible to identify a “block‐module,” an independent, nontrivial subnetwork that has one and only one node (the “cutnode”) connected to nodes outside the subnetwork. The reliability of the network will increase by a known factor after a “block‐modular decomposition” that consists of a transformation of the cutnode's supply‐demand random variable and the deletion of the remainder of the block module. Provided the original network possesses at least one block module, R can be determined from a sequence of block‐modular decompositions that reduce the original network to a single node whose reliability is easily computed. Computational experience with a computer implementation of such a decomposition method is reported, and the application of the method to the analysis of electrical power networks is included.