Patient Flow Management in Emergency Departments

In this thesis, we consider the control of patient flow through physicians in emergency departments (EDs), which have attracted many researchers' attention. Our work here seems to be the first model to quantitatively analyze the control of patient flow in an emergency department from a queueing theory perspective. Problem: In emergency departments, the physicians must choose between catering to patients right after triage, who are yet to be checked, and those that are work-in-process (WIP), who are occasionally returning to be checked. The service requirements for the two kinds of patients are different: for the patients right after triage, they must see a doctor within targeted time windows (that may depend on the patients' severity and other parameters); while the WIP patients, on the other hand, impose congestion costs. The physicians in the emergency departments have to balance between triage and WIP patients so as to minimize costs, while meeting the constraints on the time-till- first-service. Model: We model this prioritization problem as a queueing system with multi-class customers, combining deadline constraints, feedback and congestion costs together. We consider two types of congestion costs: per individual visit to a server or cumulative over all visits. The former is the base-model, which paves the way for the latter (more ED-realistic) one. Method: The method we use is conventional heavy-traffic analysis in queueing theory, based on the empirical evidence that the emergency departments can be viewed as critically-loaded stationary systems between late morning till late evening. We propose and analyze scheduling policies that asymptotically minimize congestion costs while adhering to all deadline constraints. Solution: The policies have two parts: the first chooses between triage and WIP patients using a simple threshold policy; assuming triage patients are chosen, the physicians serve the one with the largest delay relative to deadline; alternatively, WIP patients are served according to some generalized c\mu policy, in which is simply modified to account for feedbacks. The policies that we propose are easy to implement and, from an implementation point of view, has the appealing property that all information required is indeed typically available in emergency departments. For the proposed policies, asymptotic optimality, as well as some congestion laws that support forecasting of waiting and sojourn times, are established. Application: Finally, via data from the complex ED reality, we use our models to quantify the value of refined individual information, for example, whether an ED patient will be admitted to the hospital as opposed to being discharged. This is an illustration on how our recommendations can improve the operational efficiency and service quality.

Author dc:creator

• HUANG JUNFEI

• Patient flow, service management, Klimov's model, feedback, modified generalized c\mu rule