Predicting Station-Level Peak Hour Ridership of Metro Considering the Peak Deviation Coefficient

Predicting Station-Level Peak Hour Ridership of Metro Considering the Peak Deviation Coefficient

1. Introduction

In recent years, the urban rail transit system has been aggressively constructed because of its large volume and environmental protection [1]. By the end of 2022, 545 cities had a rail transit system in operation, with 41,386.12 km worldwide. In transportation spatial networks, traffic demand and design basis are typically observed by predicting origin–destination (OD) patterns or analyzing the characteristics of hot spots [2,3]. Due to the ridership varying by the time [4], the ridership during peak hours is usually taken as the design basis of the urban rail transit system. Thus, accurate station-level peak hour ridership (SPR) estimation is the basis for station planning, facility design, and operational decisions [5]. Currently, traditional methods generally estimate the SPR based on a unified peak hour factor (PHF) that is extracted from the line level, which relies on the assumption that the station-level ridership peak hours and PHF are roughly equal to those at the line level [6,7]. Although this greatly simplifies the estimation process, erroneous estimation results may be produced due to its assumption that the station peak and the metro line peak simultaneously occurred.
However, the peak hour of stations may not completely align with that of the attributed line [8]. This phenomenon has been increasingly revealed in numerous cities worldwide in recent years, such as Osaka, Japan (an approximate half-hour peak deviation for most stations); Shanghai, China (30.36% of stations) [9]; and Chongqing, China (69.44%–70.83% of stations) [10]. In addition to the aforementioned cities, it has also been observed in regions such as London in the UK, Los Angeles in the US, Ontario Province in Canada, and Seoul in South Korea that the time distribution of ridership in stations has different forms [11,12,13,14]. The ignorance of peak deviation may induce underestimated SPR values, which can result in an insufficient capacity design at station service facilities and consequently lead to traffic congestion. A new specification, namely the Code for Prediction of Urban Rail Transit Ridership in China, supplements the requirement for estimating station ridership within station peak hours. This specification is aimed at stations whose peak time does not completely coincide with that of the line.
To calibrate the SPR, Chen et al. developed an index called the peak deviation coefficient (PDC) to measure the magnitude of the station ridership deviation between two peaks [8]. Subsequently, several methods have been proposed to determine the PDC and can be generally divided into three categories: statistical techniques, local models, and global models. For instance, Yu et al. utilized a statistical analysis technique to explore the associations between the PDC and the land-use type of the land surrounding the station [10] and applied a local model, namely a geographically weighted regression (GWR), to investigate the determinants of the PDC [15]. However, the application of these methods is limited to the ridership analysis of existing stations rather than the ridership estimation of planned stations due to the lack of a quantitative relationship model or the local suitability of the model parameters. Aiming at a PDC estimation, local models [16] have been employed to construct PDC relationship models. Nevertheless, these methods tend to assume that the PDC estimation is independent across stations. They ignore the fact that the subway system is a network in which the stations exhibit strong spatial correlations, which means that the ridership characteristic of a station might also be influenced by the attributes of its neighbors. The omission of the spatial dependency of station ridership in these models might produce erroneous estimations and interpretations for a PDC estimation.
Moreover, in practice, station PHF values vary widely with their station attribute characteristics and geographical location rather than having a unified value. Two types of station PHFs may be distinguished in existing research depending on whether the consistent peak assumption is adopted. Under the assumption of a consistent peak, Liu et al. found that the PHF value of subway stations in Guangzhou, China, changed in a wide range of 0.036 to 0.322 [17]. Considering the peak deviation phenomena, Zhao et al. revealed that the actual PHF values of stations in Nanjing, China, varied between 0.125 and 0.433 [18]. Similar research was carried out by Feng et al. [19] and Jin [20]. The method of assigning a unified PHF value to all types of stations is obviously coarse and flawed, regardless of whether research is carried out under the assumption of a consistent peak or considering the peak deviation phenomenon, which may further induce biased SPR estimation results.

To fill these research gaps, this study proposes a more comprehensive and refined estimation approach framework for SPR. The PDC is introduced to embrace the context of the station peak for methodological extensions, and a global spatial model, namely the spatial Durbin model (SDM), is employed to construct the quantitative relationship models of two key parameters (i.e., the PDC and PHF) for methodological improvement. In the proposed framework, the network-based distance is utilized instead of the Euclidean-based distance to characterize the spatial correlation feature of the station adapted to the context of subway networks. Moreover, a feature selection technique, namely the least absolute shrinkage and selection operator (LASSO), is adopted to eliminate the multi-collinearity and select significant variables before model input. Compared to the conventional approach, the main contributions of the present study concern the following aspects:

  • The subway station-level PHR estimation approach is fine-tuned with PDC values using a spatial regression-based methodology framework. The case study results reveal that the proposed framework boosts the stability and accuracy of the station-level PHR forecasting results.

  • The underlying causes of the peak deviation phenomenon and the temporal distribution patterns of asymmetric ridership are interpreted from a reliable and comprehensive perspective, with both direct and indirect effects of individual variables across different peak periods. This offers crucial insights for planners aiming to balance travel demand between peak and off-peak hours by more efficiently allocating land-use resources and thereby enhancing subway line performance.

4. Discussion and Conclusions

This study proposed a comprehensive and refined framework for SPR estimation that can simultaneously accommodate the scenarios of stations with peak consistency and peak deviation. The proposed framework introduces the PDC to calibrate the SPR estimation results of peak deviation stations and employs a spatial regression model, namely the SDM, to model and determine the two key parameters in the SPR estimation process (i.e., the PHF and PDC). The empirical results demonstrate the wider applicability and higher estimation accuracy of the proposed approach.

The construction of the subway might increase the inequity of the city [32], forcing the government to make more residents enjoy subway travel by increasing feeder buses or raising land-use construction around stations. This presents a challenge for planning authorities, namely how to achieve the optimal allocation of land-use attributes along subway lines. The land generating commuter flow makes the peak sharp, while the land generating life travel makes the peak inconsistent with the lines’ peak. The PHF and the PDC reflect the time aggregation characteristics of station-level ridership from two aspects, meaning the aggregation and deviation of peaks. The results show that land-use attributes that greatly influence the two parameters have opposite signs, revealing that the same property of the land can only cause the ridership to exhibit one of the aggregation or deviation phenomena. The better estimation results of the spatial model imply that the PHF and PDC of a station are also influenced by the attributes of its neighbors. Thus, when planning the land around stations, we need to balance different types of land, reducing the ridership peak value and preventing the peak deviation at the same time.

Regarding land use, morning boarding and evening alighting can be recognized as a group, while morning alighting and evening boarding can be considered another group. The fitting results of most factors to PHF have the same plus and minus signs in the same group, while they have different plus and minus signs in different groups. This indicates that these lands contribute to forming the commuter flow and have opposite influences on the generation or attraction in the peak hour. However, the fitting results of PDC do not have this regularity, implying the disorder of non-commuting travel. In the morning peak hour, living services, residences, and healthcare are the main sources of generation, and restaurants and finance spots are the main sources of attraction. The regression coefficients of PHF in these two groups have the opposite law of positive and negative effects, but the coefficients of PDC are negative influences. The impacts on PHF of retailers are negative both in boarding and alighting, suggesting that this land does not produce commuter traffic, and its PDCs in boarding and alighting are diverse. However, schools have little influence on PHF, this may be related to the policy of attending a designated primary school belonging to the living location issued by the Chinese government, which reduced the travel distance of attending school. Thus, planners can use these results to balance the peak and off-peak travel demands to improve the operating efficiency of subway lines.

The distance to the city center has a highly positive influence on PHF in morning alighting and evening boarding, while it has a highly negative influence on PDC in morning boarding and evening alighting and a highly positive influence in morning alighting. This finding seems to be related to the fact that the Xi’an city skeleton enlarged and the travel distance lengthened with the relocation of its government from the city center to the north, the maturity of the high-tech industrial area in the southwest, and the education area in the south.

Furthermore, the SDM enables the underlying spatial influencing mechanisms of the PHF and PDC to be revealed, which provides a theoretical reference for decision-makers to prudently deploy land-use resources while incorporating a spatial perspective, thereby balancing the travel demand between peak and off-peak periods and thus improving the line operation efficiency.

However, this study was characterized by some limitations. For instance, more related influencing factors should be considered in the PHF and PDC models if the data are available. Moreover, the spatial model performance will be further improved by constructing more complicated schemes of the spatial weight matrix [33].

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