Priority, Capacity Rationing, and Ambulance Diversion in Emergency Departments

We evaluate the practices of priority, capacity rationing, and ambulance diversion in emergency department management. We consider a two-class non-preemptive priority M/M/c queue where high- and low-priority customers correspond to acute and non-acute patients, respectively; the two classes have heterogeneous service time requirements. We model capacity rationing by reserving k servers (beds) to high priority customers, and ambulance diversion by balking acute customers from entering the system when the number of waiting acute patients is higher than m. We provide asymptotic result indicating that for a system with no ambulance diversion and a large number of servers, c, the non-degenerative capacity rationing level is of order O(√c). We also derive exact solutions for different performance measures of interest for this system using queueing Markov chain decomposition (QMCD). These performance measures include expected number of patients, distribution of waiting time, and the rate of ambulance diversion. These are the first exact results for a multi-server queue with non-preemptive priorities and heterogeneous service rates, and thus are of independent interest. We demonstrate numerically how system parameters impact these performance measures and provide insights on the control of capacity rationing and ambulance diversion in emergency departments. Specifically, we show that, as predicted by the asymptotic analysis, a low level of capacity rationing can significantly reduce the waits of high-priority customers with little effect on the waiting of low priority customers