Shortest paths and probabilities on time-dependent graphs — Applications to transport networks

In this paper, we focus on time-dependent graphs which seem to be a good way to model transport networks. In the first part, we remind some notations and techniques related to time-dependent graphs. In the second one, we introduce new algorithms to take into account the notion of probability related to paths in order to guarantee travelling times with a certain accuracy. We also discuss different probabilistic models and show the links between them.