Path Planning under Time-Dependent Uncertainty

Standard algorithms for finding the short­ est path in a graph require that the cost of a path be additive in edge costs, and typically assume that costs are determinis­ tic. We consider the problem of uncertain edge costs, with potential probabilistic de­ pendencies among the costs. Although these dependencies violate the standard dynamic­ programming decomposition, we identify a weaker stochastic consistency condition that justifies a generalized dynamic-programming approach based on stochastic dominance. We present a revised path-planning algorithm and prove that it produces optimal paths under time-dependent uncertain costs. We test the algorithm by applying it to a model of stochastic bus networks, and present em­ pirical performance results comparing it to some alternatives. Finally, we consider ex­ tensions of these concepts to a more general class of problems of heuristic search under uncertainty.