We introduce a novel generic algorithmic problem in directed acyclic graphs,
motivated by our train delay research. Roughly speaking, an arc is
admissible or not subject to the value of a random variable at its
tail node. The core problem is to precompute data such that a walk along
admissible arcs will lead to one of the target nodes with a high probability.
In the motivating application scenario, this means
to meet an appointment with a high chance even if train
connections are broken due to train delays.
We present an efficient dynamic-programming algorithm for the generic
case. The algorithm allows us to maximize the probability of success
or, alternatively, optimize other criteria subject to a guaranteed
probability of success.
Moreover, we customize this algorithm to the application scenario.
For this scenario, we present computational results based on real
data from the national German railway company. The results
demonstrate that our approach is superior to the natural approach,
that is, to find a fast and convenient connection and to
identify alternative routes for all tight train changes
where the probability that the change breaks due to delays is not negligible
