In a network with capacity constraints congestion effects such as bottlenecks, spillbacks and gridlocks can be observed. These can be described with a queueing network model. The main challenge of such an approach lies in adequately capturing the between-queue correlation, which explains these congestion effects as well as their overall network impact. We present an analytic queueing network model, with finite capacity queues, where structural parameters are used to capture the between-queue correlation. We describe the methods validation versus both pre-existing methods and simulation runs. The method is then applied to study patient flow within a set of hospital units of the Geneva University Hospitals. In this context the main source of congestion is known as bed blocking. The model has allowed us to identify three main sources of bed blocking and to quantify their impact upon the different hospital units.