Intensive Care Units (ICUs) provide care for the most critical patients in a hospital. Due to high staffing requirements and specialized equipment, they are very expensive to operate. As such, patient demand for critical care often exceeds bed availability. In such cases, current ICU patients may be discharged early in order to accommodate new, more urgent patients. Such a discharge increases the likelihood of physiologic deterioration resulting in readmission to the ICU. We model such an ICU as a state‐ dependent queuing network where patient service times and readmission probabilities depend on the overloaded or under loaded state of the ICU. We refer to the reduction in Length‐of‐Stay due to incoming critical patients during overloaded periods as speedup. We use fluid models to examine how different definitions of overload affect the steady‐state behavior of the ICU and provide insight into capacity management of such systems. Readmissions can potentially increase the aggregate load on the ICU, and so we identify scenarios where speedup should never be used as well as scenarios where it can be helpful to increase service accessibility.

Joint work with Carri W. Chan (Columbia Business School) and Gabriel Escobar (Kaiser Permanente)