## 3 Discrete Event Simulation Model
### System Description  
The ED center consists of two main circuits. First there is a short circuit whose estimated duration of care after medical contact is less than 1 h. In this circuit, pediatric, gynecological, and psychiatric patients are supported. They are mostly autonomous patients who do not need major paramedical care. Second, there is a long circuit receiving patients whose estimated duration of care after medical contact is more than 3 h. Patients arriving at the ED follow a process depicted in Figure 2. The process begins when a patient arrives at the ED entrance door and ends when a patient is discharged from the ED or transferred to the hospital inpatient units.  
Figure 2: Diagram of patient flow in ED service.  
condition of patients and (2) the pathway each patient state will go through (short or long circuit). Then, the IOA assesses the patient's clinical status and assigns a recommended maximum waiting time based on the severity of his or her condition. As denoted in [28], this step of the process plays a critical role in determining how quickly patients must be seen and how to route them to the appropriate resources throughout the process.  
Based on the patient's condition and symptoms, there are eight levels of patient acuity in the ED of the Hospital Center of Troyes. This classification [29], called EP (abbreviation of etat patient in french), helps ED staff to have a better understanding of their patient flow.  
When a patient arrives at the ED between 8 a.m. and 10 p.m., they are first registered at the reception by the receptionist; then, they are triaged by the triage nurse in a dedicated room (medical examination room) at the ED entrance. Patients who arrive between 10 p.m. and 8 a.m. will be directly examined and triaged by the triage nurse, who also does the administrative registration.  
Emergency patients follow a particular rule regarding their flow in the ED. In fact, the patient's medical condition has a direct impact on their priority of passage in the ED: a patient with a more serious state is more important than a patient with a relatively less serious pathology. Nevertheless, based on medical severity, a patient with a stable state may wait for a long time because of the permanent presence of patients with a more severe state. Therefore, the priority of passage is a compromise between the severity of the patients and their arrival time. Once an appropriate room (medical examination room) becomes free and the patient is assigned to a bed, a patient's inpatient stay starts. At that moment, the patient's waiting time will be recorded (AWT = entrance time to the room \(-\) arrival time in the ED).  
The consultation begins when the right emergency physician becomes available. The emergency physician makes a first assessment and decides if the patient needs further tests to confirm or refine his diagnosis. If not, the patient is discharged to go home. In the case where tests are requested, the patient can wait for the test results in his or her room or can be transferred, if possible, to an internal waiting room (sitting or on a stretcher) to release the room for other patients.