5.2.1. Summary Statistics
The summary statistics of the local coefficients are shown in Table 5
. If the Akaike information criterion (AIC) difference between the two models is greater than 3, the goodness of fit is considered to be significantly improved [44
], and AIC is converted to corrected Akaike information criterion (AICc) in the case of a small sample. In Table 5
, the AICc of GWR are decreased by more than 67 compared with the AICc of the OLS model. The adjusted R2
values are larger for the GWR (more than 0.8 for the PDCs) than for the OLS model. Cardozo [5
] used the GWR model to forecast ridership at the metro station level. He used nine variables and the adjusted R2
value was 0.7. Thus, the adjusted R2
values in this paper are acceptable. The values of the undeveloped land area and BC are higher than 0, indicating that these variables have positive influences on the PDC
. For the PDCa
, the value of proportion of WPR is less than 0, demonstrating that the variable has a negative influence on the PDC
, whereas for the PDCb
, the value is near 0.
5.2.2. Spatial Distributions of the Coefficients
The spatial distributions of the regression coefficients are presented in Figure 11
, from which it is evident that the spatial distributions of the same coefficients exhibit differences for different PDCs.
For the proportion of WPR, the regression coefficients of PDCb have both positive and negative numbers, and the values are small, ranging from −2.5 to 1.0. This demonstrates that this variable does not have a dominant influence on the PDC. For the spatial distribution of the proportion of WPR, the coefficients are close to 0.0 in the center and the northeast of the city, the coefficients are less than 0.0 in the north, south, and east of the city, and the coefficients are greater than 0.0 in the west of the city. In the northeast of the city, the land has not been maturely developed. In the north, south, and east of the city, there are three sub-centers near the stations 2#FCWL, 2#XZ, and 1#FZC. To the northwest of Xi’an, there is another city—Xianyang. The two cities are so close that the linear distance from 1#HWZ to the city center of Xianyang is only about 10 km. The office space in this area is uncertain, and the influences of the proportions of WPR on these stations are small. The regression coefficients of PDCa are all negative, indicating that the proportion of WPR has a negative influence on the PDC. The regression coefficients are higher in the city center and lower in the periphery. Because the regression coefficients are all negative, the influence increases from the center to the periphery.
For the undeveloped land area, the range of the PDCa
values is slightly larger than that of the PDCb
values. The spatial distributions are approximately the same, and the larger values occur in the periphery. By comparing Figure 9
and Figure 11
c,d, it is clear that there are few stations in Metro Line 2 (the north–south line) that have undeveloped land, but the regression coefficients are substantially different. For the stations in the southeast and northeast of the city with large undeveloped land areas, the regression coefficients are still substantially different. This indicates that undeveloped land areas have uncertain influences on both the PDCb
values, which is consistent with the fact that trips to undeveloped land occur relatively seldom.
For the BC, the range of values is similar to those of the PDCb and the PDCa. Most values are positive, indicating that this variable has a positive influence on the PDC. The coefficients of the variables are smaller in the city center and larger in the periphery, which means that the BC has a greater influence on diverging a station’s peak hour from the city’s peak hour in suburban areas.
5.2.3. Station Classification
Because the undeveloped land area has an uncertain influence on the PDC
, the k-means method was used to classify stations with undeveloped land areas of 0. The classifying variables are the proportion of WPR, BC, PDCb
, and PDCa
, and the results are presented in Table 6
and Figure 12
. The PDCb
values in the 1st, 3rd, and 5th kinds of stations are all less than 1.17, and the proportions of WPR in these kinds of stations are all greater than 0.5, indicating that lands for work, primary and middle schools, and residences of these stations occupies the main body. However, the BC values in these kinds of stations are different. The BC values in the 1st kind of station are greater than 0.35, indicating that these stations are in important positions of the metro network; most of the BC values in the 3rd and 5th kinds of stations are less than 0.3, and fall within a wide range. The PDCa
values in the 4th kind of station are greater than 1.13, and the PDCb
values are very large. The values of the proportion of WPR in the 4th kind of station are less than 0.5, indicating that other land of these stations occupies the main body. The BC values in this kind of station are within a large range from 0 to 0.2. For the 2nd kind of station, the proportion of WPR is greater than 0.8, and the BC is about 0.1, meaning that these stations are commuting stations and not in very important areas. The PDCb
values are close to 1, but the PDCa
values are the greatest among all the PDCa
values. There are two stations of the 2nd kind, namely 1#KYM and 4#DMG. 1#KYM has a large amount of industrial land and many residential districts established by a factory manager, and these lands do not produce medium- or long-distance travel. 4#DMG is near cultural relics and historic sites, including Daming Palace National Heritage Park, but this area is not as developed as the Greater Wild Goose Pagoda Square, and the station only sees 276 people during the city’s peak hour and 340 people during the station’s peak hour.
Thus, the proportion of WPR has the greatest influence on the PDC. If the proportion of WPR is less than 0.5, the PDCb and PDCa values are both very large; if the proportion of WPR is greater than 0.5, most PDCb and PDCa values are close to 1.
5.3. Discussion—Future Station Design and Policy
The enlargement coefficient put forward in this paper, PDC, can be used as a simple way to convert the ridership during a city’s peak hour to the ridership during a station’s peak hour. The proportion of the WPR was found to have a negative influence on the PDCa
value. In other words, the larger the lands for work, primary and middle schools, and residences, the smaller the deviation of ridership between a station’s peak hour and the city’s peak hour, as the commuting trip during workdays constitutes the city’s peak hour. This result is consistent with the results of previous studies [8
] that investigated the metro ridership in Osaka, Shanghai, and Zhengzhou, and found that trips of going to work and going to school make the station’s peak hour earlier, while shopping and traveling trips delay the station’s peak hour.
If the proportion of WPR of a station is greater than 0.5, it can be considered that the ridership during the city’s peak hour is the highest ridership of the whole day; if it is less than 0.5, the highest ridership is the ridership during the city’s peak hour multiplied by the PDC. This result is consistent with the findings of Yu [41
], who examined two cities—Xi’an and Chongqing—and found that the PDC value of most metro stations is close to 1 when the proportion of WPR is greater than 0.5.
In the morning, the proportion of WPR has more influence on the alighting ridership than on the boarding ridership. For stations with proportions of WPR of greater than 0.5, if it is a special type of land, such as the 1#KYM and 4#DMG stations, the PDCb
value is close to 1, but the PDCa
value is greater among the PDCa
values of all stations. Moreover, the regression coefficients of PDCa
are negative, but the regression coefficients of PDCb
are both positive and negative numbers. This means that the proportion of WPR results in the alighting ridership occurring during a city’s peak hour, but does not have a clear effect on the boarding ridership. It indicates that the lands for work, primary and middle schools, and residences has more explanatory power regarding the peak hour deviation in the alighting during morning peak hours. The lands for work, primary and middle schools mostly attract office workers and students who need to arrive on time or ahead of schedule. Compared with their boarding behavior, their alighting behavior has a relatively clear arrival time. For different enterprises or schools, the time is almost the same, and is the same as the city’s peak hour. However, the boarding times will present large differences because of the distance between home and work. In China, the administrative land is more concentrated than residential land [54
], which will lead to the concentrated distribution of commuting–alighting passenger flow.
The local coefficient of BC is greater than 0, meaning it has an influence on the deviation of the peak hours of the station and city. For the spatial distribution, the BC is greater in suburban areas, indicating that the BC has a greater influence on diverging a station’s peak hour from the city’s peak hour in suburban areas. This is because commuters who live in suburban areas and work in the city center need to leave earlier. This finding is reasonable, as housing prices in suburban areas are lower; people are more willing to live in these areas, thus increasing their time spent on the metro and affecting the station’s peak hour. This evidence is consistent with the results of previous studies [43
], which found that more people want to live in suburban areas, resulting in the increased metro travel demands of these areas.
In China, station design must consider the extra peak hour passenger flow, which is the predicted peak hour passenger flow multiplied by the extra peak hour factor, which is between 1.1 and 1.4 [2
]. The extra peak hour factor (EPHF) is the highest fifteen-minute ridership during the city’s peak hour multiplied by 4, and then divided by the ridership during the city’s peak hour [55
]. The EPHF is the expanded threshold of the station’s capacity in the city’s peak hour. However, this study shows that some stations’ own peak hours are inconsistent with the city’s peak hour because of various land use and BC around the stations, and the peak load shifting is formed. This results in that the EPHF does not have constraints to these peak load shifting stations’ capacities. Thus, this paper put forward the PDC to depict this inconsistent phenomenon of the station’s peak hour. Although the EPHF and the PDC both reflect the temporal distribution of metro stations, they are totally different. The EPHF reflects the concentration of passenger flow in a city’s peak hour, while the PDC reflects the inconsistency between a station’s peak hour and the city’s peak hour. There is no comparability between the two coefficients. Moreover, the thinking methods about the EPHF and the PDC are completely different from each other. For example, stations with large proportions of administrative land usually have high EPHF values because of the instantaneous gathering of commuting ridership [56
]. But the greater commuting ridership results in the high consistency between the station’s peak hour and that of the city, leading to a PDC value close to 1. By contrast, stations with large proportions of commercial land usually have low EPHF values because of the randomness of the shopping flow [57
]. However, the peak hour of shopping flow lags behind the city’s peak hour, leading to the station’s peak hour being highly inconsistent with the city’s, and this increases the PDC value. Thus, there are two ridership options when designing stations, namely the extra peak hour ridership during a city’s peak hour and ridership during a station’s peak hour.
The morning boarding and alighting PDC and EPHF values of Xi’an metro stations are shown in Figure 13
and Figure 14
. The fluctuations of the PDC and the EPHF values are different. For the boarding ridership, the EPHF values change from 1.1 to 1.5, while most PDC values are about 1.0. However, five stations’ PDC values are greater than 1.8, and nine stations’ PDC values are greater than their EPHF values. For the alighting ridership, the EPHF values change from 1.0 to 1.8, while most PDC values are about 1.0, but fifteen stations’ PDC values are greater than their EPHF values. Therefore, the size relationship between the extra peak hour passenger flow during a city’s peak hour and the ridership during a station’s peak hour cannot be determined. If only one kind of coefficient is used to design the station, the scale of some of the station will be small. Thus, when a station is designed, both types of ridership (the extra peak hour ridership during a city’s peak hour and ridership during a station’s peak hour) must be calculated, and the larger of the two is used to design the station.
The land development in the center of Xi’an has been completed, and the city is now faced with land replacement and land development in urban areas. Land replacement refers to moving industrial land from the city center to urban areas and changing the land to other types of property. Non-commuting land can mitigate the traffic pressure of a city’s peak hour, because its travel peak is different from that of commuting land. However, the mixed land use ratio must be considered. More non-commuting land around metro stations will result in the deviation of their peak hours from those of the city. This will increase the difficulty of both passenger flow forecasting in the planning stage and train departure intervals and station management in the operation stage. Because there is only one train departure interval in a period of time in a section of a metro line, if a station’s peak hour is different from that of other stations, the train departure interval will be greater in this station‘s peak hour, and passengers will pile up. However, less non-commuting land around metro stations will result in a large extra peak hour passenger flow and a small off-peak hour passenger flow. Although a significant amount of money may be spent on building a large station, it may be nearly empty for most of the day. Thus, the proportion of commuting land around metro stations must be considered in land planning.