Centralized vs. Decentralized Ambulance Diversion: A Network Perspective

Abstract

In recent years, growth in the demand for emergency medical services along with decline in the number of hospitals with emergency departments (EDs) has led to overcrowding. In periods of overcrowding, an ED can request the Emergency Medical Services (EMS) agency to divert incoming ambulances to neighboring hospitals, a phenomenon known as “ambulance diversion”. The EMS agency will accept this request provided that at least one of the neighboring EDs is not on diversion. From an operations perspective, properly executed ambulance diversion should result in resource pooling and reduce the overcrowding and delays in a network of EDs. Recent evidence indicates, however, that this potential benefit is not always realized. In this paper, we provide one potential explanation for this discrepancy and suggest potential remedies. Using a queueing game between two EDs that aim to minimize their own waiting time, we find that decentralized decisions regarding diversion explain the lack of pooling benefits. Specifically, we find the existence of a defensive equilibrium, wherein each ED does not accept diverted ambulances from the other ED. This defensiveness results in a de-pooling of the network and, in turn, in delays that are significantly higher than when a social planner coordinates diversion. The social optimum is, itself, difficult to characterize analytically and has limited practical appeal as it depends on problem parameters such as arrival rates and length of stay. Instead, we identify an alternative solution that is more amenable to implementation and can be used by the EMS agencies to coordinate diversion decisions even without the exact knowledge of these parameters. We show that this solution is approximately optimal for the social planner’s problem. Moreover, it is Pareto improving over the defensive equilibrium whereas the social optimum might not be.

Keywords: emergency department, ambulance diversion, game theory, queueing networks, admission control