## 4 Results
### Space Used by Passengers Waiting to Board the Train  
The following results are presented in which the space occupied by a passenger with reduced mobility is compared to the case of a passenger without reduced mobility. The comparison is considered in the situation of passengers waiting to board the train on the platform. Table 1 shows that the average space occupied by the wheelchair passenger varied in a range between 1.09 m\({}^{2}\)/pass to 1.70 m\({}^{2}\)/pass, with an average of 1.42 m\({}^{2}\)/pass. The standard deviation is 0.26 m\({}^{2}\)/passenger. It is interesting to note that the front distance is smaller than the rear distance, which could be due to passengers keeping a greater distance from the wheelchair, as the user needs more space to maneuver (e.g., make turns or stop before boarding the train). This is represented by distance \(d\), that has an average value of around 70 cm. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Runs**} & **Occupied Space** & **Rear Distance** & **Lateral Right** & **Lateral Left** & **Front Distance** & **Distance** \(d\) **to the** \\  & **(m\({}^{2}\)/pass)** & **(cm)** & **Distance (cm)** & **Distance (cm)** & **(cm)** & **Passenger with** \\  & & & & & & **Reduced Mobility (cm)** \\ \hline
1 & 1.65 & 59.52 & 43.69 & 34.31 & 57.68 & 78.94 \\
2 & 1.65 & 78.02 & 48.82 & 19.01 & 55.29 & 66.97 \\
3 & 1.67 & 89.81 & 45.94 & 24.16 & 48.92 & 64.61 \\
4 & 1.47 & 62.70 & 53.61 & 15.73 & 53.33 & 75.77 \\
5 & 1.03 & 42.02 & 46.39 & 27.96 & 52.52 & 67.17 \\
6 & 1.55 & 68.14 & 37.86 & 45.18 & 43.79 & 67.59 \\
7 & 1.50 & 53.30 & 46.56 & 46.69 & 45.55 & 75.81 \\
8 & 1.70 & 84.68 & 31.89 & 23.46 & 60.54 & 77.65 \\
9 & 1.27 & 53.26 & 36.37 & 36.18 & 52.19 & 73.19 \\ \hline \end{tabular}
\end{table} 
Table 1: Average space occupied by a wheelchair passenger waiting to board the train. The space occupied by the wheelchair user (1.42 m\({}^{2}\)/pass) represents 5 times the average value using [PERSON]'s method [2] (0.30 m\({}^{2}\)/passenger, or level of service D). This average value using [PERSON]'s method is obtained as the ratio between the platform area of 6.3 m\({}^{2}\) and 21 passengers, the total number of passengers in the experiments. This result is relevant, as it shows that a wheelchair user needs more space to move on the platform compared to the rest of the users. In addition, it seems that the average value of density using [PERSON]'s method [2] is not representative of the interaction of passengers on the platform. However, using the Petrack software [38], it is possible to locate where the wheelchair user is on the platform, and how many passengers surround the wheelchair user. Therefore, it would be possible to measure which part of the platform is more congested, and therefore, if an improvement in the design of the station layout is required or desirable (e.g., to increase the platform width). In the case of the passenger with a param, the average space is presented in Table 2. It is observed that the user with a param occupied a greater space compared to the wheelchair user, with a significant difference of about 20%, according to the Mann-Whitney test, reaching an average of 1.70 m\({}^{2}\)/passenger. This is because the param needs more space to maneuver, or requires assistance from a passenger. Similarly, if the results are compared to the average values of density using [PERSON]'s Level of Service, the difference between the average space used by a passenger with a param (1.70 m\({}^{2}\)/passenger) is around 6 times the average space, using [PERSON]'s method (0.3 m\({}^{2}\)/passenger). Therefore, the space occupied is determined by the type of passengers that wait to board the train. Consequently, greater spacing is generated, and therefore, the average distance between passengers and a passenger with reduced mobility increases.