Modeling and analysis of high risk patient queues

For many medical procedures, patients face substantial risk of complication or death when treatment is delayed. When a queue is formed in such a situation, it is imperative to assess the suffering and risk faced by patients in queue and plan adequate medical capabilities in advance to address the concerns. We develop in this paper a patient queue model that considers the condition and its changes over time for a patient in a queue. The risk faced by a patient is characterized under this model as a function of the arrival rate, the service capacity and the hazard rate of the disease. This characterization provides an approach to the planning and management of medical services based on the risk faced by patients. When the condition of patients is heterogeneous, a priority patient queue model is developed to minimize the overall risk for all patients. The operational characteristics of the priority queue, particularly the risk faced by different groups of patients, are derived. Managerial issues induced by prioritization are also addressed. In general, patients of heterogeneous condition should be prioritized in as many urgency classes as possible to maximize survival.