## 4 Dwell Time Estimation Model  
In this second phase of research, we utilize the results from the first phase, including the observed dwell times (which required estimations when the departure information was missing), boarding and alighting passenger counts for all trains at all stations, in order to develop dwell time estimation models. The proposed models estimate dwell times at all stations with given boarding and alighting passenger counts and onboard passenger counts on arriving trains. Boarding, alighting, and onboard passenger counts for each train at each station are set as independent variables and the dwell time as dependent variable. This is intuitive, as dwell times are mainly affected by the boarding and alighting counts, while the onboard crowdedness in trains indirectly affects them. The dependent variable, dwell time, was extracted from the observed data as described in Section 3. Support Vector Regression (SVR), Multiple Linear Regression (MLR), and Random Forest (RF) methods were used to develop 3 different estimation models, and their estimation performances were compared. Seventy percent of the data were used as a training set to develop the model, and 30% of the data were used as a validation set. To compare the performances of the different models, performances were compared for 3 different scenarios of dwell time estimation accuracy of less than 3, 5, and 10 s between the actual and estimated dwell times. Among the validation set, the SVR model shows that 53.6% of cases have less than 3 s of errors, and 67.2% have less than 5 s of errors. On the other hand, 87.5% of the estimation by the RF model in the validation set marked below 10 s of error, as shown in Table 2. It is noted that the dwell times used for training are in integer values while the estimated dwell times from the models are in real numbers, and making distinctions between the 3 scenarios separated by a few seconds may be practically insignificant in real-life metro operations. When compared from the perspective of percentage accuracy, the SVR model performed the best in the case of less than 30% errors followed by RF and MLR models as seen in Table 3. Figures 8 and 9 show the comparison of dwell time estimation results derived from each model. The orange square represents the trains operated during the morning peak hour, the blue circle represents the trains operated during the evening peak hour, and the black triangle represents the trains operated outside the two r \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Station Name** & **Station ID** & **Symbol** & **Station Name** & **Station ID** & **Symbol** \\ \hline Gwanggyo & S01 & & Jeongja & S07 & \\ Gwanggyo Jungang & S02 & & Pangyo & S08 & \\ Sanghyeon & S03 & & Cheonggyesan & S09 & \\ Seongbok & S04 & & Yangjae Citizen’s Forest & S10 & \\ Suji-gu Office & S05 & & Yangjae & S11 & \\ Dongcheon & S06 & & Gangnam & S12 & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Symbols of each station. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model Type** & **\textless{}3 s (\%)** & **\textless{}5 s (\%)** & **\textless{}10 s (\%)** \\ \hline SVR & 53.6 & 67.2 & 84.4 \\ RF & 43.7 & 62.2 & 87.5 \\ MLR & 39.0 & 54.3 & 74.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The proportion of estimated data depends on the absolute difference between actual dwell time and estimated dwell time by the model types. Figure 8: Dwell time estimation performance comparison among the **(a)** SVR, **(b)** RF, **(c)** MLR models. Figure 9: Dwell time estimation performance comparison by the time of day. (**a–c**) in the morning peak, (**d–f**) in the evening peak and (**g–i**) in the normal period. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model Type** & **<10\% (\%)** & **<20\% (\%)** & **<30\% (\%)** \\ \hline SVR & 52.8 & 71.4 & 81.6 \\ RF & 42.3 & 69.7 & 81.0 \\ MLR & 36.5 & 62.1 & 73.8 \\ \hline \hline \end{tabular}
\end{table}