## 3 Materials and Methods
### Establishing Scheduling Policy  
In EDs, the scheduling policy is designed to allocate physicians based on the patients' condition severity, reflecting the current dynamics within the ED. The primary goal of these policies is to minimize LoS times. Severity assessment is conducted using the Korean Triage and Acuity Scale (KTAS), which is an adaptation of the Canadian Triage and Acuity Scale (CTAS) specifically tailored to fit the healthcare context in Korea. KTAS categorizes patients into five levels based on their symptoms, where a higher severity score indicates a need for longer treatment times and prioritizes patients with more severe conditions.  
* Resource Scheduling Policy Scheduling in EDs is structured around six scenarios, differentiated by three scheduling methods that distinguish between general physicians and senior physicians [31]. These scenarios are designed to ensure that physicians are matched with patients according to the severity of the medical cases they are best equipped to handle. Treatment durations are adjusted based on the capacity and specialty of the physicians. The main scheduling strategies include:  
1. First In First Out (FIFO): Patients are attended to on a first-come, first-served basis.
2. Shortest Remaining Processing Time (SRPT): Prioritizes patients based on the estimated time remaining for their treatment. This strategy aims to reduce waiting times by managing treatment flows more efficiently.
3. Critical Ratio (CR): This approach prioritizes patients based on the criticality of their conditions.
* Detailed Scheduling Policy The resource scheduling policies in our EDs are designed to optimize the allocation of physicians and manage patient flows efficiently. These strategies are implemented through a structured approach that considers both the severity of the patient's condition and the specific expertise of our medical staff. Here is a detailed breakdown of the six scenarios under our three main scheduling strategies:  
1. FIFO (Random): Under this strategy, patients are seen as they arrive, regardless of their condition severity. This scenario uses a random assignment where any available doctor, whether general or senior, may attend to the patient. This method is simple and ensures that everyone is treated without unnecessary delay.
2. FIFO (Centroid): This variation refines the FIFO approach by assigning patients based on the severity of their conditions. General physicians handle less severe cases, optimizing their quicker treatment times, while senior physicians take on more severe cases, leveraging their advanced expertise.
3. SRPT (General First): This strategy focuses on reducing overall waiting times by assigning general physicians to patients whose treatments can be completed quickly, thus clearing cases efficiently.
4. SRPT (Senior First): Similarly, senior physicians are assigned to less severe cases that can be quickly resolved, ensuring that their skills are used effectively to minimize the impact on the ED's flow.
5. CR (General First): General physicians are prioritized to treat the most severe cases they are qualified to handle, ensuring that critical patients receive immediate care.
6. CR (Senior First): The most critical patients are reserved for senior physicians, who are most capable of addressing complex and urgent medical needs quickly.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Type** & **Entity** & **Script** \\ \hline \multirow{3}{*}{Agent (Actor)} & Patient & Patients using the ED \\  & Nurse & Registration, triage, and guiding the patient to the bed \\  & General and Senior & Treating the patient. Treatment time varies depending on \\  & Doctor & the doctor’s experience. \\ \hline \hline \end{tabular}
\end{table}
Table 2: _Cont._To better illustrate how each of these strategies is applied within our ED, Table 3 provides a clear, structured overview of the process and priorities assigned to each scheduling method: