The management and allocation of health resources, in particular equipment such as ventilators, has been the object of significant interest by a health community that is concerned to avoid new shortages. In this article, we develop a Markov chain based model considering random arrivals and discharges of patients in an intensive care unit requiring ventilator support. We provide a methodology in order to compute the exact probability distribution of the time-shortage, which is the moment where no more ventilators are available. We propose two applications of this model: a preventive traffic signal and a tool to evaluate purchasing decisions. A calibration of parameters based on real empirical data from a French hospital is carried out in order to test the operational use of the model.
