In this manuscript we perform a rigorous mathematical investigation of the behavior opportunistic network models exhibit when two major real-world problems are taken into account. The first problem considered is obstruction. Here we model the network using an obstructed Gilbert graph which is a classical Gilbert graph but where there exist zones where no nodes are allowed to be placed. We take a look at percolation properties of this model, that is we investigate random graph configurations for which a component of infinite size has strictly positive probability to be created. The second problem considered in this thesis is mobility. Of course mobility in and of itself is not a problem but a feature in any network that follows the store-carry-forward paradigm. However it can be problematic to properly handle in a mathematical model. In the past this has been done by modelling movement by a series of static network configurations. However, with this technique it can be difficult to get a grasp on some of the time sensitive properties of the network. In this work we introduce the time bounded cylinder model which enables an analysis over a complete timeframe. We provide normal approximations for important properties of the model, like its covered volume and the number of isolated nodes. As we are using rigorous mathematics to tackle problems which computer scientists working in the field of distributed systems are faced with, we bring the two fields closer together.