Abstract: In this talk I will sketch a body of recent results obtained in the context of a stochastic network of dependently operating resources. These could be thought of to represent real-life networks of all sorts, such as traffic or communication networks, but I will point out that this setup is also highly relevant in economic and biological applications. For such large networks, one would typically like to describe their dynamic behavior, and to devise procedures that can deal with various undesired events (link failures, sudden overload, etc.). I will show how for systems that do not allow explicit analyses, various parameter scalings help shedding light on their behavior. More specifically, I discuss situations in which the time-scale corresponding to the fluctuations of the available resources differs from that of the fluctuations of the customer's demand, leading to various appealing limit results.