Transient Queueing Analysis for Emergency Hospital Management

Strategic and tactical capacity planning are critical decisions faced by hospitals. While these problems have received significant attention, current queueing-based approaches do not address realistic healthcare constraints such as blocking, transient arrivals, transient capacity assignments, and surge capacities. A queueing methodology is developed to extend the analysis of these constructs. The methodology developed is generic for hospitals responding to demand surges during epidemics and pandemics such as the recent COVID-19, and in other application areas in manufacturing, supply chain management, and logistics. The medical staff and patient chairs in the emergency room, beds in the operating theater, ICU, and medical/surgical care units are used in patient treatment at a hospital. They can be considered as servers in a system, where capacity and operational policies affect performance measures such as patient throughput. The methodology develops the probabilities from which system performance measures can be estimated for a serial queueing network with blocking. Transient analysis is employed, due to the time varying nature of the patient arrival patterns. The methodology has the capability to analyze different interventions such as increasing and decreasing capacities, and ambulance diversion. In order to handle typical hospital sized problems that result in thousands of ordinary differential equations defining the system probabilities, a transient version of Kanban queueing network decomposition is developed along with procedures for dealing with the discontinuities that arise at capacity changes. Verification/validation is presented along with several scenarios that illustrate the potential application of this methodology in emergency hospital management.