A Queueing Theoretic Approach to Gridlock Prediction in Emergency Departments
When an emergency department (ED) decides that it is not going to be able to serve any more newly arriving patients, it declares "diversion". When an ED is on diversion, it suspends arrivals that can be controlled by forcing some or all of the incoming emergency medical system (EMS) transport units to search for alternate treatment facilities for their patients. This search causes both patients and EMS crew to loose valuable time. Contrary to the general belief that suggests diversions are not very common, the results of the American Hospital Association survey present an example where one third of the studied hospitals were on diversion more than 20% of the three-day study period.
Past research indicates that the lack of critical care beds in the hospital is the primary contributor to ambulance diversion. When patients need to be transferred from the ED to the hospital with no available beds in the hospital, they continue occupying their beds (i.e. the patient is boarding). While they are boarding in the ED, the associated staff is idle, and their bed cannot be used to treat other patients. Boarders in the ED lead to gridlock, which is defined as the situation when no new patient can be accepted to the ED until a hospital bed becomes available.
In this research, we developed a predictive model to provide probabilities of entering gridlock within a time horizon, given the current state of the system. These real-time predictions are provided for a relatively short time horizon, and in order to be useful, they need to be used in conjunction with effective preventive measures that can be applied quickly. The predictive model is based on a queueing theoretic approach and encapsulated in a user-friendly Visual Basic program in order to calculate and provide gridlock probabilities. Two systems, one with low (24% - System 1), and one with high (81% - System 2) gridlock probability were simulated in conjunction with our predictive model and preventive measures. When a gridlock was found imminent, the number of ED beds was temporarily increased, attempting to prevent gridlock. With only 3 additional beds, the probability of gridlock decreased to 6% in System 1 and 58% in System 2. With 5 additional beds, gridlocks in System 1 were almost eliminated while System 2 entered gridlock only 34% of the time. Our results indicate that by temporarily increasing the number of ED beds in the event of an imminent gridlock, the proportion of time that system enters gridlock can be significantly reduced.