Patient Flow Modeling and Optimal Staffing for Emergency Departments: A Petri Net Approach

Patient flow is the movement of patients through a healthcare facility. Over the past decades, healthcare service providers have spent tremendous effort in optimizing patient flow and reducing patient waiting time (WT), aiming to provide better healthcare service and higher patient satisfaction. There are many factors causing patient congestion; understaffing is undoubtedly a critical one. However, as staffing accounts for about 75% of the cost of all emergency medicine groups, emergency department (ED) staffing must match the demand for services. In this article, we attempt to employ a systematic and formal approach to find out optimal staffing levels for EDs. For this purpose, a hierarchal modeling process of patient flow in typical EDs with stochastic timed Petri nets (STPNs) is developed. Special attention is paid to resource requirements, resource sharing, and service duration. The evaluation of average patient WT is discussed based on simulation. Two staffing options are considered, and the decision on the optimal staffing level with each option is addressed. A software tool has been developed to aid the ED performance evaluation and staffing.