Stochastic bounds on distributions of optimal value functions with applications to pert,network flows and reliability

In various network models the quantities of interest are optimal value functions of the form max X _i , min X _i , min maxX _i , max minX _i , where the inner operation is on the nodes of a path/cut and the outer operation on all paths/cuts, e.g. shortest path of a project network, maximal flow of a flow network or lifetime of a reliability system. ForX _i random with given marginal distributions, we obtain bounds for the optimal value functions, based on common and on antithetic joint distributions.This work was carried out during a visit to RWTH Aachen, supported by DAAD.