As a representative mode of shared mobility, bike-sharing serves not only as a convenient way to conduct short-distance trips in urban areas, but also as a feeder mode to public transit, forming the Bike and Ride (BnR) system. Conducting management for such a hybrid multi-modal system faces various challenges, including the complex interactions between bike-sharing and other modes, highly dynamic passenger demand, and the difficulty of accessing direct transfer data. To overcome such difficulties, our study proposes a framework for assessing the dependency between the two usage modes. Firstly, a Dynamic-Time-Warping-based (DTW) method is utilized to determine the catchment area (CA) between the two modes, allowing the BnR-related tendency similarity under a given time scale to be considered. Then, the patterns of probabilistic dependence between travel demand of the two modes are obtained by a copula-based approach, which separates correlations under specific usage levels from single modal demands. A case study on the multi-modal system formed by docked bike-sharing and subway in New York is conducted to validate the proposed framework. The tendency similarity is found to be most pronounced within 500 m on average under a 4-hour interval. For each formed station group (SG), the best-fitted copula type is selected, capturing the strong tail correlations present only at specific usage levels. The results show a variety of different correlation patterns within SGs, despite the close geographic locations they may share. Areas of potential transfer resistance between the two modes are identified, which is more evident in first-mile-related (FMR) activities. In contrast, the two modes display more weak connections in last-mile-related (LMR) activities. The obtained results can be utilized by bike-sharing service providers to analyze demand distributions and conduct efficient station-level rebalancing. Compared to previous methods, our proposed framework is computationally inexpensive since no direct transfer of data or complex inference network is required. It incorporates statistically significant spatial–temporal information, allowing for a more accurate determination of the bi-modal assessment range. Moreover, considering that single-mode influences are mathematically removed, the resulting correlation in principle links to the strength of the connections between the two modes. Therefore, it can be assessed as an indicator of the reliability of the multi-modal system.

中文翻译：

---

一种基于 copula 的多模式需求依赖建模方法：地铁需求与共享单车之间的时间相关性


作为共享出行的代表方式，共享单车不仅在城市地区进行短途旅行的便捷方式，也是公共交通的支线模式，形成了自行车和骑行 （BnR） 系统。对这种混合多模式系统进行管理面临各种挑战，包括共享单车和其他模式之间的复杂交互、高度动态的乘客需求以及访问直接传输数据的困难。为了克服这些困难，我们的研究提出了一个框架来评估两种使用模式之间的依赖关系。首先，采用基于动态时间翘曲 （DTW） 的方法确定两种模式之间的集水区 （CA），从而考虑给定时间尺度下与 BnR 相关的趋势相似性。然后，通过基于 copula 的方法获得两种模式的出行需求之间的概率依赖模式，该方法将特定使用水平下的相关性与单一模式需求分开。对纽约共享单车和地铁对接形成的多模式系统进行了案例研究，以验证所提出的框架。发现趋势相似性在 500 小时间隔内平均在 4 m 内最为明显。对于每个形成的站组 （SG），选择最拟合的 copula 类型，捕获仅在特定使用级别存在的强尾部相关性。结果显示 SG 中存在各种不同的相关模式，尽管它们可能具有相似的地理位置。确定了两种模式之间潜在的转移阻力区域，这在第一英里相关 （FMR） 活动中更为明显。相比之下，这两种模式在最后一英里相关 （LMR） 活动中显示出更多的弱连接。 共享单车服务提供商可以利用获得的结果来分析需求分布并进行有效的站点级再平衡。与以前的方法相比，我们提出的框架在计算上是廉价的，因为不需要直接传输数据或复杂的推理网络。它结合了具有统计意义的时空信息，从而可以更准确地确定双峰评估范围。此外，考虑到单模态影响在数学上被去除，由此产生的相关性原则上与两种模态之间连接的强度有关。因此，它可以被评估为多模态系统可靠性的指标。