## 2 Existing Studies Related to the Level of Service in Metro Stations  
The level of service of pedestrians has been studied for the last 50 years. The first studies [13,14] were conducted by observations such as videos or photographs in which pedestrians were represented as fluids or particles. This type of representation is called macroscopic, in which pedestrians are analysed in a global view by three main variables: speed, density, and flow. Therefore, this representation is simple to use for standards and it culminates in a graphical representation of the results such as videos, tables, and maps. [PERSON] [6] defines 1.43 m/s (5.15 km/h) as the free-flow speed of a pedestrian when there is a unidirectional flow and 1.36 m/s (4.9 km/h) when there is a bidirectional flow. In addition, the author states that the average speed of pedestrians is directly related to the free-flow speed and the density, which is defined as the ratio between pedestrians and the total area. Since then, different studies have been conducted to analyse the walking speed of pedestrians and its relationship to density. All these studies have been compared to the well-known relation between walking speed and density proposed by [PERSON] (1993) [15], where the jam density reached a value of 5.4 passengers/m\({}^{2}\). The free-flow speed for pedestrians is defined as 1.34 m/s. However, this free-flow speed can vary among types of pedestrians. For example, shoppers have a free-flow speed of 1.04 m/s, commuters 1.45 m/s, and tourists 0.99 m/s. Another study of bidirectional corridors at Hong Kong MTR stations presented a walking speed at free flow of 1.37 m/s and 0.61 m/s at capacity [16]. The authors compared these values to bidirectional corridors in London Underground (LU) stations, in which the  
Figure 1: Platform–train interface in Valparaiso Metro: (**a**) platform; (**b**) inside the train. walking speed at capacity was 0.6 m/s. Moreover, [PERSON] et al. [17] calculated instantaneous Fundamental Diagrams, in which the instantaneous density is defined as the inverse of the spatial headway (number of passengers/m) and the instantaneous velocity is a function of the headway. The authors found that pedestrians avoid other pedestrians and they adapt their speed to the following pedestrian. As a summary, [PERSON] et al. [18] reported Fundamental Diagrams based on three main variables: speed, density, and flow. Fundamental Diagrams are important tools to evaluate if a space such as the train and the platform in metro stations are congested [19]. In relation to density and speed, [PERSON] et al. [18] reported that if the density increases, then the speed will decrease almost linearly. However, this type of linearity is not produced for the flow. This variable (flow) is defined as the ratio between the number of pedestrians and time per metre of section. For instance, if we look at [PERSON]'s curves, it can be seen that if the density increases, the flow will also increase to its capacity, which is reached at approximately 1.3 passengers/m-s. At this point, the density is almost 2.0 passengers/m\({}^{2}\). This value of density generates two new zones: zone 1 (unsaturated) and zone 2 (oversaturated). These new zones are related to the concept of saturation flow, which is defined as the flow divided by the capacity. Another example of a macroscopic method is the use of [PERSON]'s level of service or LOS, which indicates the degree of congestion and conflict in an area (flat areas, queues, or stairs) using general parameters such as speed, density, or flow. As reported by [PERSON] et al. [20], [PERSON] studied the behaviour of passengers in existing stations, in which the objective of the LOS was to obtain the capacity of a path. If the space is reduced, then the flow will reach capacity and then passengers' movement will be reduced. The author considered two different types of pedestrians: commuters and shoppers. As a result of the observations, the LOS was classified into different levels.