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

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.