Patients admitted to a hospital's intensive care unit (ICU) often endure excessive wait times for bed assignment due to capacity shortages, and prolonged transfer times following receipt of ICU care. Many admitted ICU patients should instead be treated in an intermediate care unit, or step-down unit (SDU), to free up acute-care beds for more critically ill patients. When ICU utilization levels are high, patients experience shorter lengths of stay (LOS), as staff accelerate patient transfers to other areas of the hospital. In this paper, we propose an econometric model to investigate the impact of patient census levels on ICU LOS, which is divided into two components: active care ("service" time) and inactive care prior to transfer ("non-service" time). Using a logistic regression, we test whether bed transfer during higher census levels impacts 30-day readmission rates. We use nine months of patient-level data for Yale-New Haven Hospital, a tertiary care hospital with a large (51-bed) Medicine ICU. We also develop a four-class priority queuing model with multiple-server types and state-dependent service times, which we simulate using our empirical data. We consider alternative bed allocation policies that are presently under consideration, and examine their impact on projected wait times.