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This article studies disruption tolerant networks (DTNs) where each node knows the probabilistic distribution of contacts with other nodes. It proposes a framework that allows one to formalize the behaviour of such a network. It generalizes extreme cases that have been studied before where (a) either nodes only know their contact frequency with each other or (b) they have a perfect knowledge of who meets who and when. This paper then gives an example of how this framework can be used; it shows how one can find a packet forwarding algorithm optimized to meet the 'delay/bandwidth consumption' tradeoff: packets are duplicated so as to (statistically) guarantee a given delay or delivery probability, but not too much so as to reduce the bandwidth, energy, and memory consumption.