Distributional Properties of Stochastic Shortest Paths for Smuggled Nuclear Material

The shortest path problem on a network with fixed weights is a well studied problem with applications to many diverse areas such as transportation and telecommunications. We are particularly interested in the scenario where a nuclear material smuggler tries to succesfully reach her/his target by identifying the most likely path to the target. The identification of the path relies on reliabilities (weights) associated with each link and node in a multi-modal transportation network. In order to account for the adversary's uncertainty and to perform sensitivity analysis we introduce random reliabilities. We perform some controlled experiments on the grid and present the distributional properties of the resulting stochastic shortest paths.