||Many applications in Stochastic Networks can be described in terms of many sources that all generate work, leading to arrival processes of work that needs to be matched with resources. There is growing evidence that many arrival processes observed in practice can only be described by sources that are highly correlated. A major questions is how to choose capacity in order to deal properly with correlation. To answer this question, this project is about developing stochastic models that describe and capture the essence of such correlated arrivals, as an input to a queueing network. Here the focus is on the analysis of the many-sources regimes, in scaling related to normal, moderate and large deviations (that arise by specific choices for the capacity). Models that most likely play are role are: Markov-modulated models, regime-switching models and factor models. Networks of (potentially infinite server) queues are a leading example here, where the input parameters (arrival rates, departure rates) react to a single external process. In these contexts questions on the optimization of capacities and routing strategies are highly relevant and challenging.