Flow in networks with random capacities

We study the problem of finding the maximum flow through a capacitated network in which the set of capacities is a collection of independent random variables, drawn from some known distribution. We find limit theorems when the underlying graph is either a branching tree or a complete graph. Finally, we discuss the difficulty of the problem of finding the expected maximum flow, using the language of computational complexity, and propose an easy approximate solution to the closely related reliability problem.

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