Many intensive care units (ICUs) face overcrowding. One response to this overcrowding is to bump ICU patients to other departments of the hopsital to make room for new patient arrivals. Such bumping clearly has the potential to reduce quality care. In this paper we develop a stochastic model of a single ICU with patient bumping. The purpose of this model is to enable planners to predict performance, in terms of bumping, under differing capacity and arrival patterns. We develop a new aggregation-disaggregation algorithm for this problem that enables us to keep track of the time in system for each patient despite the high dimensionality of the problem. Our approach allows for more accurate modelling of the system. We demonstrate the superior computational efficiency of our approach over traditional Gaussian Elimination.