Problem definition: This research focuses on elderly patients who have been hospitalized and are ready to be discharged, but they must remain in the hospital until a bed in a geriatric institution becomes available; these patients block a hospital bed. Bed blocking has become a challenge to healthcare operators because of its economic implications and the quality-of-life effect on patients. Indeed, hospital-delayed patients who do not have access to the most appropriate treatments (e.g., rehabilitation) prevent new admissions. Moreover, bed blocking is costly, because a hospital bed is more expensive to operate than a geriatric bed. We are thus motivated to model and analyze the flow of patients between hospitals and geriatric institutions to improve their joint operation. Academic/practical relevance: Practically, our joint modeling of hospital-institution is necessary to capture blocking effects. In contrast to previous research, we address an entire time-varying network, which enables an explicit consideration of blocking costs. Theoretically, our fluid model captures blocking without the need for reflection, which simplifies the analysis as well as the convergence proof of the corresponding stochastic model. Methodology: We develop a mathematical fluid model, which accounts for blocking, mortality, and readmissionall significant features of the discussed environment. Then, for bed allocation decisions, the fluid model and especially, its offered load counterpart turn out insightful and easy to implement. Results: The comparison between our fluid model, a two-year data set from a hospital chain, and simulation results shows that our model is accurate and useful. Moreover, our analysis yields a closed form expression for bed allocation decisions, which minimizes the sum of underage and overage costs. Solving for the optimal number of geriatric beds in our system shows that significant reductions in cost and waiting list length are achievable compared with current operations. Managerial implications: Our model can support healthcare managers in allocating geriatric beds to reduce operational costs. Moreover, our model facilitates three extensions: a periodic reallocation of beds, incorporation of setup costs into bed allocation decisions, and accommodating home care (or virtual hospitals) when feasible.