## 5 Experimental Results  
Several experiments have been conducted over a real-life dataset to evaluate the effectiveness of the proposed method in admitting Covid-19 patients to suitable hospitals. The algorithm was programmed in Scala in a Linux environment. The real-life dataset had been provided by the King Faisal specialist hospital for Covid-19 patients [27]. The dataset contained information about demography, exposure, vaccination history, and comorbidities of the admitted patients. A set of comorbidities has been chosen from the original dataset according to [24] to assess the medical status of patients. These comorbidities have been used to identify the medical devices needed for each set of comorbidities. The admission times of hospitals and reach times of patients to hospitals have been generated randomly according to the Poisson distribution, which has been used before to mimic the random calls for emergency services in [28]. The medical devices in each hospital have been generated randomly according to normal distribution. The kidney machine has been identified to be necessary for patients that have chronic kidney disease or any serious kidney illnesses. The \(O_{2}\) Oxygen inhalation/Ventilator has been identified to be mandatory for patients that have \(O_{2}\) saturation less than 92 or have chronic pulmonary diseases. The ICU has been identified to be mandatory for patients that have chronic liver disease, comma, and Heart Failure. These criteria can be extended or changed concerning the new studies about Covid-19. The dataset was constructed of 254 patients, each had 7 comorbidities. Table 5 presents different times (minimum time, average time, maximum time) that the algorithm needs to admit each patient to the most suitable hospital, where the time is evaluated in seconds. Results in Table 5 present that the algorithm can admit patients over the different number of hospitals in real time. Even the maximum time is suitable for real-life severe cases as it does not reach a single second. Figure 3 presents a graphical comparison between the proposed algorithm using \(PO\) and the lexicographic method to vary among a different number of hospitals. The graph shows the average running time of the two methods, evaluated into seconds. The figure shows that the average running time of the lexicographic increases with the increase in the number of hospitals. However, the increase in the proposed method is very small even with the increase in the number of hospitals. This emphasizes the stability of the proposed method as it keeps a near steady performance despite the number of hospitals. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Minimum Time** & **Average Time** & **Maximum Time** \\ \hline
**Preto Optimization** & & & \\ \hline
20 Hospitals & 0 & \(3.68\times 10^{-6}\) & 0.000215 \\
30 Hospitals & 0 & \(6.59\times 10^{-6}\) & \(2.05\times 10^{-4}\) \\
40 Hospitals & 0 & \(7.53\times 10^{-6}\) & \(2.46\times 10^{-4}\) \\
50 Hospitals & 0 & \(7.71\times 10^{-6}\) & \(2.26\times 10^{-4}\) \\
60 Hospitals & 0 & \(1.23\times 10^{-5}\) & \(2.48\times 10^{-4}\) \\ \hline
**lexicographic Method** & & & \\ \hline
20 Hospitals & 0 & \(4.05\times 10^{-6}\) & 0.000226 \\
30 Hospitals & 0 & \(7.37\times 10^{-6}\) & \(2.01\times 10^{-4}\) \\
40 Hospitals & 0 & \(2.00\times 10^{-5}\) & \(4.25\times 10^{-4}\) \\
50 Hospitals & 0 & \(1.94\times 10^{-5}\) & \(3.64\times 10^{-4}\) \\
60 Hospitals & 0 & \(2.98\times 10^{-5}\) & 0.0016217 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Different times (seconds) needed to admit each patient to a hospital over a different number of hospitals. Additionally, the proposed method has been compared with the lexicographic method in terms of accuracy. The accuracy of the algorithm is computed by comparing the hospitals generated from each method to admit each patient with the correct hospital for admission identified manually.