智能手机应用程序对自行车共享系统的影响
The Impact of Smartphone Apps on Bike Sharing Systems
摘要：
随着越来越多的人在日常通勤中采用可持续交通解决方案，自行车共享系统在世界各地的城市中呈爆炸式增长。然而，随着越来越多的人使用该系统，乘客经常遇到自行车或码头可能无法到达车站。因此，许多像CitiBike和Divvy这样的系统通过智能手机应用程序向骑手提供有关网络的信息，以便骑手可以找到有可用自行车的站点。然而，并非所有客户都采用这些智能手机应用程序来选择电台。通过结合客户选择模型和有限容量排队模型，我们探索了智能手机应用程序技术的影响，以增加吞吐量和减少阻塞的自行车共享系统。为此，我们证明了一个平均场极限和一个中心极限定理的经验过程中的站点数量与$k$自行车。我们还证明了极限定理的一个新的过程，称为比率过程，其特征在于的比例站的自行车可用率位于一个特定的分区的区间[0，1]。对于平均场极限，我们证明了平衡点的存在性和唯一性，以及经验测度的定态分布在同一平衡点收敛于狄拉克质量，从而给出了极限互换的结果（$\lim_{t\rightarrow \infty}\lim_{N\rightarrow \infty}=\lim_{N\rightarrow \infty}\lim_{t\rightarrow \infty}$）.我们的极限定理提供了对大规模自行车共享系统的均值、方差和样本路径动态的洞察。我们的研究结果表明，如果我们增加使用智能手机应用程序信息的客户比例，自行车共享网络的熵就会降低，骑车人在网络中遇到的阻塞也会减少。
英文摘要：
Bike-sharing systems are exploding in cities around the world as more people are adopting sustainable transportation solutions for their everyday commutes. However, as more people use the system, riders often encounter that bikes or docks might not be available when they arrive to a station. As a result, many systems like CitiBike and Divvy provide riders with information about the network via smartphone apps so that riders can find stations with available bikes. However, not all customers have adopted the use of these smartphone apps for their station selection. By combining customer choice modeling and finite capacity queueing models, we explore the impact of the smartphone app technology to increase throughput and reduce blocking in bike sharing systems. To this end, we prove a mean-field limit and a central limit theorem for an empirical process of the number of stations with $k$ bikes. We also prove limit theorems for a new process called the ratio process, which characterizes the proportion of stations whose bike availability ratio lies within a particular partition of the interval [0,1]. For the mean field limit, we prove that the equilibrium exists, is unique, and that the stationary distribution of the empirical measure converges to a Dirac mass at the same equilibrium, thus showing an interchange of limits result ($\lim_{t\rightarrow \infty}\lim_{N\rightarrow \infty}=\lim_{N\rightarrow \infty}\lim_{t\rightarrow \infty}$). Our limit theorems provide insight on the mean, variance, and sample path dynamics of large scale bike-sharing systems. Our results illustrate that if we increase the proportion of customers that use smartphone app information, the entropy of the bike sharing network is reduced, and riders experience less blocking in the network.
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