Hospital care facilities often make use of non-interoperable devices produced by many different vendors to monitor the state of patients. The heterogeneity of these devices makes it difficult to synthesize multivariate monitoring data into a unified array of real-time information regarding the state of patients in a care unit. Without an infrastructure for data integration, the assignment of caregivers to patients cannot be optimized to reflect the relative urgency of patient needs. This is an especially serious issue in critical care units (CCU). In this work, we evaluate the hypothesis that the integration of vital sign data can yield a significant positive impact on the efficiency and outcomes of critical care delivery, via a computer simulation of a CCU. Within our simulated CCU, an infinitely replenishable finite set of patients are being monitored, while a small set of caregivers is addressing patient alarm conditions. Patients who experience an alarm accumulate injury exponentially during the time that they are without care. Once a caregiver arrives at a patient, the time it takes to treat the underlying disturbance is assumed linear in the patient's accumulated injury. If a patient accumulates more than a threshold level of injury, a fatality occurs. Fatalities require the execution of close out procedures, which take a specified period of time (and must be given precedence over living patients). Through simulation we compare the current defacto scheduling processes in use within CCUs, against a new scheduling algorithm that makes use of an integrated array of patient information collected by a hypothetical vital sign integration infrastructure. Our simulation study provides quantitative evidence from which we can measure the extent to which such an infrastructure reduces risk to CCU patients and lowers operational personnel costs.