This paper explains the observed hospital congestion by physicians' decision to unconditionally refer patients to hospitals, and explain why such a choice is rational when congestion deteriorates the efficiency of the tirage process at the hospital level. In an imperfect information environment, physicians might refer to top-tier hospitals patients with mild diseases that could be properly addressed by regular hospitals, just to fulfill patients' demand for the best care. Yet, the tirage capability of top-tier hospitals declines if the hospital is subject to congestion, which, in turn, provides incentives to physicians to refer more patients to these hospitals. The model presents two equilibria, one with perfect triage, and another with triage errors and hospital congestion. In this last equilibrium, a higher hospital size raises the likelihood of congestion. Public policies strategies to overcome this issue are discussed. © 2021 Editions Dalloz Sirey. All rights reserved.