## 5 Conclusions  
In this study, the level of service was analysed based on a multidimensional approach taking the metro system in Valparaiso, Chile, as a case study. This multidimensional approach included a model composed of five dimensions: passenger behaviour, train design, passenger characteristics, train operation, and platform built environment. Inside the train, it can be observed that seats are occupied most of the time (occupation of 83%). The corridors had a lower number of passengers detected compared to the central hall, which could be related to the type of service in Valparaiso Metro. For instance, \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Independent** & **Coefficient** & **Coefficient** & **Coefficient** \\
**Variables** & **(7:00 a.m.–7:20 a.m.)** & **(7:20 a.m.–7:40 a.m.)** & **(7:40 a.m.–8:00 a.m.)** \\ \hline Platform features & \(-0.170051\)*** & \(0.020419\)*** & \(-0.351792\)*** \\ Type of passenger & \(0.186987\)*** & \(-0.109071\)*** & \(0.400202\)*** \\ Detected passengers & \(0.046950\)*** & \(0.009448\)*** & \(0.018714\)*** \\ Dispersion & \(0.136052\)*** & \(0.003626\)* & \(-0.232739\)*** \\ Constant & \(-0.034553\) & \(0.117472\)*** & \(0.755561\)*** \\ R-squared & \(0.477861\) & \(0.097675\) & \(0.09881\) \\ \hline \hline \end{tabular}  
* Prob.: **
* \(<0.001\); *
* \(<\) or \(=0.010\).  
\end{table} 
Table 2: Results of the least square regression model. Figure 13: Level of service based on a multidimensional approach. passengers in urban services prefer to stay closer to the train doors rather than stay along the length of the train (e.g., corridors). With respect to the platform, it was found that the speed of passengers is a relevant variable that varies according to the moment of time observed, reaching a value on average between 0.47 and 1.12 m/s. This variable is affected by other variables according to other dimensions presented in the model such as the height of passengers, the number of passengers around (e.g., crowding level), and features around the platform, among others. From the model, some important results are obtained. Passengers are affected by other passengers around them. In addition, adult passengers have a higher speed compared to children (defined as passengers with a height of less than 1.2 m). An interesting variable is the dispersion of passengers, which is related to the speed of passengers. For instance, if the standard deviation of the distance between passengers increases (i.e., higher dispersion is obtained), then the speed of passengers is increased at the platform; however, when the number of passengers detected on the platform increases, the dispersion negatively affects the speed of passengers. The new model may allow practitioners and researchers to expand the level of service reported in the literature [6; 7], which is mainly based on the speed, density, and flow of passengers. This study opens the opportunity to analyse the level of service from different dimensions, including different views and perspectives in a multidimensional approach, which could be then used for railway management. Although this approach is focused on urban services, this study could be expanded to other railway systems such as interurban services or rural services. In addition, other stations and times of day could be considered in further studies to compare the level of service in different conditions (e.g., underground vs. overground stations or peak hour vs. off-peak hour). With respect to the area of analysis, this pilot study considered one carriage, six seats, and one hall plus a corridor. This area will be then expanded in further studies to consider other conditions inside the train. Conceptualization, V.A., T.F. and S.S.; methodology, G.G., V.A., T.F. and S.S.; software, V.A. and A.L. ; validation, V.A., S.S. and G.G. ; formal analysis, S.S.; investigation, V.A., S.S. and G.G. ; resources, S.S.; data curation, S.S.; writing--original draft preparation, S.S.; writing--review and editing, V.A. and G.G. ; visualization, V.A., S.S. and G.G.