A stochastic control approach to avoiding Emergency Department overcrowding

Emergency Department (ED) overcrowding is a common problem in hospitals in the United States. Presenting a barrier to safe delivery of healthcare, hospitals address ED overcrowding by diverting ambulances to the nearest available facility, leading to delays in healthcare delivery and losses in revenue. Control policies on hospital resources could greatly improve healthcare delivery by preventing overcrowding and ambulance diversion. In this paper, we use Petri-nets (PNs) to model patient and resource flow in a hospital system. Simulating these PNs, we can observe changes in the availability of resources over time and obtain a stochastic differential equation (SDE) which models the hospitals proximity to entering a divert state (in a Euclidean sense). Likening the resource allocation problem to a stochastic control problem, we derive the related free-boundary problem. The solution of this problem is the optimal control policy that dictates when and how many resources should be added or removed.