As more people move back into densely populated cities, bike sharing is emerging as an important mode of urban mobility. In a typical bike-sharing system (BSS), riders arrive at a station and take a bike if it is available. After retrieving a bike, they ride it for a while, then return it to a station near their final destinations. Since space is limited in cities, each station has a finite capacity of docks, which cannot hold more bikes than its capacity. In this paper, we study BSSs with stations having a finite capacity. By an appropriate scaling of our stochastic model, we prove a mean-field limit and a central limit theorem for an empirical process of the number of stations with k bikes. The mean-field limit and the central limit theorem provide insight on the mean, variance, and sample path dynamics of large-scale BSSs. We also leverage our results to estimate confidence intervals for various performance measures such as the proportion of empty stations, the proportion of full stations, and the number of bikes in circulation. These performance measures have the potential to inform the operations and design of future BSSs.

中文翻译：

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共享单车系统的随机分析

随着越来越多的人搬回人口稠密的城市，共享单车正在成为一种重要的城市出行方式。在典型的自行车共享系统 (BSS) 中，骑手到达车站并在有自行车的情况下使用自行车。取回一辆自行车后，他们骑了一会儿，然后将其返回到最终目的地附近的车站。由于城市空间有限，每个车站的码头容量有限，不能容纳超过其容量的自行车。在本文中，我们研究了具有有限容量的站点的 BSS。通过对我们的随机模型进行适当的缩放，我们证明了一个平均场极限和中心极限定理，用于站点数量的经验过程ķ自行车。平均场极限和中心极限定理提供了对大规模 BSS 的均值、方差和样本路径动态的洞察。我们还利用我们的结果来估计各种性能指标的置信区间，例如空站的比例、满站的比例和流通中的自行车数量。这些性能指标有可能为未来 BSS 的操作和设计提供信息。