## 7 Access Distance from Home Location to Station  
To evaluate the impact of access distance from the HSR, we calculate Euclidian distance between the HSR station and origin (Home), and develop density figures based on the mobile phone data, which only includes origins inside the city boundary. The density of mobile population against the Euclidian distance is calculated according to the location of each HSR station and individual location of mobile phone data observed. The density is denoted as seen in Equation (2).  
\[\mathrm{D}_{i}\left(p/\mathrm{m}^{2}\right)=\sum p/d_{i} \tag{2}\]  
where, \(\mathrm{D}_{i}\) is the density of mobile population at distance (i) from the station, \(p\) is the observed mobile population within cells of \(50\times 50\) m, and \(d_{i}=\sqrt{\left(x_{i}-x_{s}\right)^{2}+\left(y_{i}-y_{s}\right)^{2}}\), which is the Euclidian distance between the HSR station and individual origin location of the mobile user. The x-y location of each station is denoted as \(\left(x_{s},\ y_{s}\right)\), and each origin location of the p-cell \(\left(x_{i},\ y_{i}\right)\) is used to calculate the distance from the HSR station. The density distribution of the number of observed instances of mobile data with respect to distance at each HSR station is shown in Figure 4.  
Figure 4: Comparison of density of access distance before and after the opening of the HSR.  
From the figure, we can see that most of the access trips in Seoul were made within 50 km, and majority of trips ranged between 20 km and 25 km from the station. Although the density is slightly decreased within a radius of 25 km from the station, Seoul is megacity, and various transit modes are available to access an HSR station. Therefore, the HSR seems to cover a wider area in Seoul than in other cities. However, the density distribution is similar to that of the before condition, which means that HSR had little effect on the access conditions, because the station for Seoul-Busan HSR line opened in 2004, and is shared with the Honam HSR line.  
Interestingly, it is found that the access distance distribution varies depending on city size (small or medium). Iksan station shows that the access population is observed in wider area after HSR, as major access trips were generated approximately 15 km-25 km away from the station. This phenomenon can be explained by the shape of the city center and location of Iksan station. Iksan station is located at the southern section of the city boundary, so that people living in the outer side of the city center can gain access to the station (refer to Figure 4b). Another interesting point is that the density of mobile population observed approximately 20 km away from the station was the highest at before the HSR opened, and it plateaued in the after condition. Although the reason cannot be clearly explained, the expensive fare of the HSR would make people choose cheaper modes of travel, such as express buses and the existing railway.  
Jeongeup city, as a small city, also shows that the HSR attracted more people living farther from station, compared to access distance in the before condition. However, the density of access distance within 15 km was shrunk after the opening of the HSR, which would be caused by the decreased number of older people (over 60 years old).  
Mokpo, as a medium city, presents high access density close to the HSR station, mainly within 15 km. From the results, it can be seen that the distribution of access distance from the station is affected by the geographical structure of cities, socio-demographic conditions, and transport systems. We also found that as access distance increases, the density also increases. Therefore, the HSR clearly provides an opportunity for travelers to use high-quality transport services in a wider area.