# Determination of the Peak Hour Ridership of Metro Stations in Xi’an, China Using Geographically-Weighted Regression

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Data Sources and Variables

#### 3.1. Data Sources

#### 3.2. Dependent Variable

_{s}is the ridership of a metro station during its own peak hour and P

_{c}is the ridership of this metro station during the city’s peak hour, and PDC is the peak deviation coefficient. The closer the value of the PDC is to 1, the more similar the ridership at the station’s peak hour is to the ridership at the city’s peak hour.

^{b}denotes the boarding PDC, and PDC

^{a}denotes the alighting PDC; both are dependent variables. The boarding and alighting ridership in a city’s peak hour, the difference between ridership during a station’s peak hour and the city’s peak hour, and the PDC values of Xi’an metro stations in the morning are presented in Figure 5 and Figure 6. Most PDC values are near 1, indicating that these stations’ peak hours align with the city’s peak hour. However, there are also some stations with a PDC value greater than 1, and some with a PDC value even greater than 1.4. Table 1 presents the morning and evening PDC values of 52 stations of Chongqing metro lines 1, 3, and 6 [41]. It can be seen that although most PDC values are in the range of 1–1.2, 7.69% and 13.46% of stations’ morning and evening PDCs, respectively, are found to be greater than 1.2. Thus, the phenomenon of the ridership of a metro station during a city’s peak hour not always being the same as that during a station’s own peak hour is not a unique case in Xi’an. For the sake of the meticulous design and sustainable development of metro systems, it is important to study the PDC.

#### 3.3. Independent Variable Selection

#### 3.3.1. Built Environment

#### 3.3.2. Distance to the City Center

#### 3.3.3. Betweenness Centrality

_{i}is the betweenness centrality of station i, ε

_{sit}is the number of shortest paths from station s to station t via station i, and ε

_{st}is the number of shortest paths in the metro network from station s to station t.

#### 3.4. Summary of Variables

## 4. Methodology

_{i}is the PDC of metro station i, (u

_{i}, v

_{i}) denotes the location of station i, β

_{k}(u

_{i}, v

_{i}) indicates the kth regression parameter at station i, which is a function of the geographical position, and x

_{ik}is the independent variable, of which there are four used in this study (the proportion of WPR, the undeveloped land area, the distance to the city center, and BC); their definitions and formulas were introduced in the previous chapter. Additionally, ε

_{i}is the normally distributed error term of station i, and p is the total number of stations.

_{ij}is the distance between station i and station j, and b is the kernel bandwidth parameter.

## 5. Results and Discussion

#### 5.1. Spatial Autocorrelation and Local Collinearity Test

#### 5.2. Results

#### 5.2.1. Summary Statistics

^{2}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 R

^{2}value was 0.7. Thus, the adjusted R

^{2}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 PDC

^{a}, the value of proportion of WPR is less than 0, demonstrating that the variable has a negative influence on the PDC, whereas for the PDC

^{b}, the value is near 0.

#### 5.2.2. Spatial Distributions of the Coefficients

^{b}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 PDC

^{a}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.

^{a}values is slightly larger than that of the PDC

^{b}values. The spatial distributions are approximately the same, and the larger values occur in the periphery. By comparing Figure 9 and Figure 11c,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 PDC

^{b}and PDC

^{a}values, which is consistent with the fact that trips to undeveloped land occur relatively seldom.

^{b}and the PDC

^{a}. 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

^{b}, and PDC

^{a}, and the results are presented in Table 6 and Figure 12. The PDC

^{b}and PDC

^{a}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 PDC

^{a}values in the 4th kind of station are greater than 1.13, and the PDC

^{b}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 PDC

^{b}values are close to 1, but the PDC

^{a}values are the greatest among all the PDC

^{a}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.

^{b}and PDC

^{a}values are both very large; if the proportion of WPR is greater than 0.5, most PDC

^{b}and PDC

^{a}values are close to 1.

#### 5.3. Discussion—Future Station Design and Policy

^{a}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 [8,53] 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.

^{b}value is close to 1, but the PDC

^{a}value is greater among the PDC

^{a}values of all stations. Moreover, the regression coefficients of PDC

^{a}are negative, but the regression coefficients of PDC

^{b}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.

## 6. Conclusion

^{a}value. In the morning, the proportion of WPR has more influence on the alighting ridership than on the boarding ridership. 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.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 5.**The morning boarding ridership in the peak hours of the city and stations, and the PDC values of Xi’an metro stations.

**Figure 6.**The morning alighting ridership in the peak hours of the city and stations, and the PDC values of Xi’an metro stations.

**Figure 8.**Spatial distribution of the proportions of work, primary and middle schools, and residences (WPR) of Xi’an metro stations.

Range | Morning PDC | Evening PDC | ||
---|---|---|---|---|

Data | Ratio | Data | Ratio | |

(1.00, 1.10) | 37 | 71.15% | 34 | 65.38% |

(1.10, 1.20) | 11 | 21.15% | 11 | 21.15% |

(1.20, 1.30) | 3 | 5.77% | 2 | 3.85% |

(1.30, 1.40) | 0 | 0.00% | 1 | 1.92% |

(1.40, +∞) | 1 | 1.92% | 4 | 7.69% |

Variable | Explanation | Value | ||
---|---|---|---|---|

Mean | Max | Min | ||

PDC^{b} | Dimensionless continuous values | 1.134 | 3.990 | 1.000 |

PDC^{a} | Dimensionless continuous values | 1.068 | 1.693 | 1.000 |

Proportion of WPR | Dimensionless continuous values | 0.764 | 0.995 | 0.062 |

Undeveloped land | Unit: 10^{4} km^{2} | 22.778 | 76.516 | 0.000 |

Distance to the city center | Continuous values, unit: km | 7.561 | 17.800 | 0.200 |

BC | Dimensionless continuous values | 0.113 | 0.457 | 0.000 |

Eigenvalue | Condition Index | Variance ratio | |||
---|---|---|---|---|---|

Proportion of WPR | Distance to City Center | Undeveloped Land Area | BC | ||

0.03 | 11.58 | 0.17 | 0.86 | 0.23 | 0.50 |

0.10 | 5.40 | 0.29 | - | 0.41 | 0.46 |

Variable | Moran I | Expectation Index | Mean Value | Z-score | P-value |
---|---|---|---|---|---|

Proportion of WPR | 0.099 | −0.012 | −0.011 | 1.788 | 0.044 |

Undeveloped land area | 0.548 | −0.012 | −0.010 | 8.476 | 0.001 |

BC | 0.523 | −0.012 | −0.008 | 6.610 | 0.001 |

Model | Dependent Variable | Corrected Akaike Information Criterion (AICc) | Adjusted R^{2} | Proportion of WPR | Undeveloped Land Area | BC |
---|---|---|---|---|---|---|

Ordinary least square (OLS) | PDC^{b} | 700.068 | 0.522 | −0.777 | 1.433 | 14.038 |

PDC^{a} | 643.217 | 0.750 | −14.110 | 2.013 | 23.630 | |

Geographically weighted regression (GWR) | PDC^{b} | 607.986 | 0.860 | −0.611 | 0.752 | 8.955 |

PDC^{a} | 575.484 | 0.900 | −8.184 | 1.419 | 15.182 |

Variables | 1st Kind | 2nd Kind | 3rd Kind | 4th Kind | 5th Kind | |
---|---|---|---|---|---|---|

PDC^{b} | Mean | 1.171 | 1.006 | 1.010 | 3.635 | 1.036 |

Max | 1.309 | 1.008 | 1.034 | 3.990 | 1.186 | |

Min | 1.001 | 1.004 | 1.001 | 3.281 | 1.000 | |

PDC^{a} | Mean | 1.051 | 1.280 | 1.025 | 1.230 | 1.014 |

Max | 1.143 | 1.328 | 1.101 | 1.323 | 1.047 | |

Min | 1.004 | 1.232 | 1.000 | 1.137 | 1.004 | |

Proportion of WPR | Mean | 0.759 | 0.871 | 0.854 | 0.410 | 0.685 |

Max | 0.786 | 0.936 | 0.995 | 0.503 | 0.739 | |

Min | 0.721 | 0.805 | 0.777 | 0.317 | 0.575 | |

BC | Mean | 0.405 | 0.094 | 0.143 | 0.113 | 0.160 |

Max | 0.457 | 0.108 | 0.248 | 0.225 | 0.323 | |

Min | 0.367 | 0.079 | 0.000 | 0.000 | 0.045 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Yu, L.; Cong, Y.; Chen, K. Determination of the Peak Hour Ridership of Metro Stations in Xi’an, China Using Geographically-Weighted Regression. *Sustainability* **2020**, *12*, 2255.
https://doi.org/10.3390/su12062255

**AMA Style**

Yu L, Cong Y, Chen K. Determination of the Peak Hour Ridership of Metro Stations in Xi’an, China Using Geographically-Weighted Regression. *Sustainability*. 2020; 12(6):2255.
https://doi.org/10.3390/su12062255

**Chicago/Turabian Style**

Yu, Lijie, Yarong Cong, and Kuanmin Chen. 2020. "Determination of the Peak Hour Ridership of Metro Stations in Xi’an, China Using Geographically-Weighted Regression" *Sustainability* 12, no. 6: 2255.
https://doi.org/10.3390/su12062255