## 4 Results
### Evaluation of the Effectiveness of the Fast-Track Predictive Formula  
After the predictive formula was developed, the next step was to evaluate its practical application in the emergency department (ED), specifically its impact on operations when used during triage. The focus was on assessing how reserving a specific number of beds--through a Virtual Decision Room (VDR)--for patients identified at triage as having a high probability of a length of stay (LOS) greater than 4 h would affect overall ED performance. For this, a simulation was created using the PMApp application. This simulation modeled the ED process by incorporating patients flagged by the predictive formula into the VDR, assuming a fixed number of dedicated beds. The simulation replayed the patient flow, assigning those patients to the fast track if a bed was available. If no bed was available at the time of the patient's arrival, they remained in the standard queue. Admitted patients occupied a virtual bed for the same duration as in the original historical log. The analysis used a separate dataset--patients admitted between 1 January and 31 December 2022--to ensure independence from the data used to develop the formula. All patients were processed in order of arrival. The system removed those who met the predictive criteria and virtually admitted them to the fast track if space allowed. This approach allowed for the observation of the impact of removing high-LOS patients from the standard ED workflow on overall delays and occupancy levels. Two key performance indicators were measured: Delay, defined as the average LOS across all patients, compared between the original dataset and the simulated fast track scenario and Occupation, measured as the number of patients present in the ED at the same time (denoted as k), reflecting real-time system congestion. Together, these metrics provided insight into how the predictive model and VDR implementation could optimise patient flow and resource utilisation in the ED. Table 9 shows the results of the simulation. In the case of having 5 beds, these beds would be fully occupied 80.56% of the time, while if 20 beds were reserved, they would only be occupied 72.53% of the time. In the case of improving LOS, by adding 5 beds, the \begin{table}
\begin{tabular}{l c c c c} \hline
**Technic** & **Accuracy** & **Sensitivity** & **Specificity** & **Likelihood Ratio** \\ \hline Predictive formula & 0.65 & 0.5 & 0.74 & 0.67 \\ \hline Naive Bayes & 0.27 & 0.5 & 0.16 & 3.15 \\ \hline Quadratic Discriminant Analysis & 0.68 & 0.2 & 0.91 & 0.88 \\ \hline Multi-Layer Perceptron & 0.75 & 0.42 & 0.9 & 0.64 \\ \hline Ada Boost & 0.74 & 0.4 & 0.9 & 0.67 \\ \hline Random Forest & 0.33 & 0.54 & 0.23 & 2.01 \\ \hline Decision Tree & 0.67 & 0.45 & 0.77 & 0.72 \\ \hline Support Vector Machines & 0.74 & 0.43 & 0.89 & 0.64 \\ \hline \end{tabular}
\end{table} 
Table 8: Evaluation results of the classification systems used in comparison with the predictive formula. average LOS of patients would be reduced by 9%, while with 20 beds, it would be reduced by 48%. As for occupancy, with 5 beds, the average number of simultaneous patients in the ED would be reduced by 16%, while with 20 beds, it would be reduced by 84%. These reductions are especially significant for complex patients, who tend to experience the longest delays and are at higher risk of adverse outcomes. By reserving a dedicated number of beds for this population, the fast-track pathway not only reduces their LOS but also mitigates complications such as delirium and enhances their overall care experience. Graphically, Figure 16 illustrates the effects of applying the predictive formula in the simulation through a histogram. As shown, increasing the number of reserved beds leads to a smoother and lower histogram profile. This indicates a reduction in length of stay (LOS) and a noticeable leftward shift in the distribution.