Hospitals are experiencing increased congestion due to population growth, an aging population, and the nationwide closure of hospitals. Hospitals are complex flow systems whose internal components interact with each other, yet there are almost no operations research models (as opposed to financial models) of whole hospitals in the literature. This dissertation develops three methodologies to capacitate and potentially control whole hospitals. An analytical probabilistic approach, rather than an experimental simulation approach, is employed. First, the spatial distribution of inpatient (IP) department beds in a hospital is improved by quantifying true patient demand from all sources and properly allocating capacity among the different levels of care present. This formulation relies on the splitting property of Poisson processes and queuing. Next, a computational approach to generalize and optimize a new paradigm of patient flow in hospital emergency departments (ED) is derived based on multiple-entity type, Jackson open-queuing network theory. This formulation includes IP access delays as an important interaction. Finally, the ED and IP departments are joined together with surgery in a unified framework that aims to control whole hospital behaviors by prioritizing and timing patient flows. A control theoretic approach is taken and model predictive control (MPC) is used as a basis for determining tactical decision policies that will help a hospital best achieve healthcare delivery and profitable capacity goals. The MPC models require non-standard model developments in their formulation.