Priority, Capacity Rationing, and Ambulance Diversion in Emergency Departments

44 Pages Posted: 3 Jun 2019

See all articles by Opher Baron

Opher Baron

University of Toronto - Operations Management

Tianshu Lu

University of Toronto - Operations Management

Jianfu Wang

Nanyang Technological University (NTU) - Nanyang Business School

Date Written: May 13, 2019

Abstract

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.

Keywords: healthcare operation, non-preemptive priority queue, capacity rationing, ambulance diversion, heavy traffic, numerical algorithm

Suggested Citation

Baron, Opher and Lu, Tianshu and Wang, Jianfu, Priority, Capacity Rationing, and Ambulance Diversion in Emergency Departments (May 13, 2019). Available at SSRN: https://ssrn.com/abstract=3387439 or http://dx.doi.org/10.2139/ssrn.3387439

Opher Baron

University of Toronto - Operations Management ( email )

105 St. George st
Toronto, ON M5S 3E6
Canada

Tianshu Lu (Contact Author)

University of Toronto - Operations Management ( email )

105 St. George st
Toronto, ON M5S 3E6
Canada

Jianfu Wang

Nanyang Technological University (NTU) - Nanyang Business School ( email )

Singapore, 639798
Singapore

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