Service-level computation in time-varying queueing system with priorities: Application to physician staffing in the emergency department

Abstract

For many service systems, waiting time is a critical performance indicator of customer experience. This study addresses service-level computation techniques in a time-varying mixed-preemptive priorities queueing system. This queueing system has two distinguishing characteristics. First, it has time-varying arrival rates and service capacities. Second, and more importantly, there are multiple classes of customers, and both preemptive and non-preemptive priorities are considered in this system. Combining these two characteristics in a queueing system makes it difficult to compute the service level for each customer class. We derive the exact computation methods for pointwise and piecewise service levels. Furthermore, we propose closed-form expressions to approximate the service levels. Lastly, we show how to apply these service-level computation techniques to a real-life physician staffing problem in the emergency department, in which the service levels of each class of patients are considered as constraints. The computational tests are performed using data generated based on real data from a large hospital. The results show that our staffing solutions are better than the hospital’s current staffing solution, guaranteeing patients’ service levels and reducing physicians’ working times.

Keywords:

• Time-varying arrival
• mixed-preemptive priorities
• service level
• physician staffing
• emergency department

Notes

1 Accessed March 21, 2023, https://hospitalhealthcare.com/latest-issue-2017/adequate-staffing-in-the-emergency-department/.

2 The data are available at https://github.com/Wangchengkai/Service_Level_Multi_Class.

Additional information

Funding

This research is supported by the National Natural Science Foundation of China [Grant 72371161, 72192822], a General Research Fund (GRF; No. 17501022), and a Collaborative Research Fund (CRF; No. C7162-20GF) from the Research Grants Council of Hong Kong.

Notes on contributors

Ran Liu

Dr. Ran Liu is an associate professor in the Department of Industrial Engineering and Management, Shanghai Jiao Tong University, Shanghai, China. His research interests include combinatorial optimization, stochastic optimization, and their applications in healthcare and manufacturing operations management. He obtained his bachelor’s and master’s degrees from Northwestern Polytechnical University, Xi’an, China, and his PhD in industrial engineering from Shanghai Jiao Tong University, Shanghai, China.

Huiyin Ouyang

Dr. Huiyin Ouyang is an assistant professor of operations management at HKU Business School. She obtained her bachelor’s and master’s degrees from Tsinghua University, and her PhD in Statistics and Operations Research from the University of North Carolina at Chapel Hill. Prior to joining HKU Business School, she held a postdoctoral fellow position at the Department of Industrial Engineering and Management Science at Northwestern University. Her research focuses on stochastic modeling and analysis of service systems, healthcare operations, simulation analytics, and data-driven decision-making.

Chengkai Wang

Chengkai Wang is currently a PhD student in the Department of Industrial Engineering and Management at Shanghai Jiao Tong University, Shanghai, China. His research interests lie in queueing theory and the optimization of time-varying service systems. He received his BS degree in Industrial Engineering from Shanghai Jiao Tong University, Shanghai, China, in 2020, and he is currently pursuing his PhD at the same institution.

Xiaolan Xie

Xiaolan Xie is a professor of industrial engineering at the Center for Biomedical and Healthcare Engineering, Ecole des Mines, Saint Etienne, France. He has also been a chair professor at Shanghai Jiao Tong University, a research director at the Institute National de Recherche en Informatique et en Automatique, and a full professor at Ecole Nationale d’Ingenieurs de Metz. He received his Ph.D degree from the University of Nancy I, Nancy, France, in 1989, and the Habilitation à Diriger des Recherches degree from the University of Metz, France, in 1995. His research interests include modeling, performance evaluation, optimization, and data analytics of healthcare and manufacturing systems. He is author/coauthor of 350+ publications including 130+ journal articles and six books. He is a fellow of IEEE. He was the founding chair of the Technical Committee on Automation in Health Care Management of the IEEE Robotics & Automation Society. He has been an Editor/associate editor for IEEE Transactions on Automation Science & Engineering, IEEE Transaction on Automatic Control, IEEE Transactions on Robotics & Automation and International Journal of Production Research. He is the general chair of IEEE conference CASE2021.