This dissertation focuses on three issues that reflect some of the most important challenges facing both hospital administrators and healthcare policy makers. First, we present an empirical research study on the effects of ambulance diversion on patients' safety. To determine whether increased diversion activity is associated with poor patient outcomes, we analyze myocardial infarction deaths as a function of emergency department (ED) diversion status within the five boroughs of New York City. Negative binomial regressions are used to demonstrate a statistically significant association between the level and extent of ambulance diversions and increasing myocardial infarction deaths. The second project is dedicated to identifying effective nursing levels for specific hospital units. We represent the nursing system as a variable finite-source queuing model. An approximating assumption results in a reliable, tractable, easily parameterized two-dimensional model that represents the crucial interaction between the nurse and bed systems. We use this model to show how unit size, nursing intensity, occupancy levels and unit length-of-stay each affect the impact of nursing levels on responsiveness to patients' needs and thus how inflexible nurse-to-patient ratios can lead to either understaffing or overstaffing The model can also be used to determine the relative impact of lack of inpatient beds and nursing levels on ED delays for a particular unit. Finally, we examine the problem of capacity and admission decisions for a stroke unit. Access to a stroke unit with dedicated beds and staff decreases the mortality rate and the need for institutional long-term care after stroke. In recent years hospital utilization has reached levels at which the rationing of critical care beds has become unavoidable, so there is a need to support capacity and admission decisions. We present a two-dimensional queuing model and an iterative approximation for representing the flow of stroke patients in a hospital. We show how these models can help assess the impact of capacity and admission decisions on the performance of the medical units involved in the recovery of stroke patients.