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One of the most important operational challenges faced by emergency departments (EDs) in the United States is patient 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 may 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 depooling of the network and, subsequently, 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 because it depends on problem parameters such as arrival rates and length of stay. Instead, we identify an alternative solution that does not require the exact knowledge of the parameters and may be used by the EMS agencies to coordinate diversion decisions when defensive diversion is present. 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, in general, might not be. This paper was accepted by Yossi Aviv, operations management.
Deo et al. (Tue,) studied this question.