Two main issues to resolve

Prolonged delays in EDs, especially when unexpected, can cause excessive suffering, low quality of care, degradation of treatment outcomes and mortality increases. Therefore, there is growing need to develop effective mechanisms of wait time forecast and announcement.

Two main factors contribute to inaccurate ED wait times. First, incorrect forecast of the remaining workload (i.e., the time until the next available physician) is made based on incomplete information. Treatment times are random and incidental and not completely foreseen before they begin. Currently, most EDs compute their anticipated wait times by multiplying the current queue length (QL, that is the number of waiting patents in the ED) by the average treatment time (ATT). Unfortunately, simply relying on QL and ATT, and ignoring further random features of treatment times is misleading and biased. Consequently, patients with more severe conditions may demand longer treatments and the actual wait time could be significantly more.

Another critical issue is that practitioners who make wait time announcements usually fail to take into account the possible scenarios during a patient’s commute time. The number of ED patients and the severity of their conditions can vary widely from minute to minute. As a result, the announcement of delay at a particular time of the day, even if accurate, may quickly become outdated. This delay announcement may be useful for a patient who lives nearby, but inaccurate for those with a longer commute to the hospital. Consider an example: at 10am, announced wait time is 20 minutes at ED A and 60 minutes at ED B. There are 20 patients who are choosing to visit one of the two EDs, and make decisions based on online wait times. All patients decide to visit ED A with the shorter wait time. Assuming a one-hour average commute time to ED A, the actual wait time of ED A at 11am suddenly can bump up to several hours due to a big group of arrivals. At the same time, ED B may become idle at 11am due to lack of arrivals. From the viewpoint of the centralized healthcare network, this issue also causes highly unbalanced workloads at different EDs, leading to system inefficiency. It is unproductive to have most ED B physicians idling with lack of patients. A more effective scenario is shorter and nearly synchronized wait times at both EDs.

Our solution, approach and preliminary results

In this project, we developed a system-level solution to the problem. Partnering with Dr. Shuangchi He, Assistant Professor of the Industrial and Systems Engineering Department at National University of Singapore, we built mathematical models for the random scenarios of ED patient flows; we took into consideration the impact of a patient’s travel time on the actual ED wait time; and we proposed effective mechanisms to forecast and announce ED delays. Countering to intuition, we discovered that the ED currently having the least number of patients or lowest workload does not necessarily offer the shortest wait time.

Our ultimate goal is to develop an accessible software for ED managers and practitioners. Based on available system information and historical data treatment time data, this software will generate effective recommendations for a patient on which ED to visit with the minimal wait time.

Developing such a tool is complex, but some preliminary results have shown beneficial progress. Using stochastic theory and queueing theory (a branch of applied mathematics that study waiting lines), we have uncovered fundamental principles that can be used as a basis for developing algorithms of ED wait time computation and announcement. To examine the effectiveness of our new policy, we apply simulation, a computer-based virtual experiment which enables us to replicate the patient population and ED dynamics. In several cases, computer simulations show we can reduce actual average wait times by nearly 50 percent. To ensure our model remains effective in practice, we next plan to feed the model using data extracted and analyzed from EDs in local hospitals.

Besides healthcare systems, this research can be applied to all industries where customers have to wait before receiving service, such as customer contact centers, restaurants and data centers. Our goal is to reduce customers’ wait times without affecting the quality of their service.

Using Stochastic Models and Systems Engineering to better forecast, Industry Today

Dr. Yunan Liu
Yunan Liu joined the Edward P. Fitts Department of Industrial and Systems Engineering at North Carolina State University as an assistant professor in 2011 after receiving his Ph.D. from Columbia University. His research focuses on queueing theory, applied probability, and stochastic modeling, with applications to service systems, especially call centers, healthcare systems, and manufacturing systems.

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