地铁刷卡数据的动态统计模型  

A Dynamic Statistical Model for Metro Smart Card Data

作　　者：牟唯嫣 代铁林 熊世峰[2] MU Wei-yan;DAI Tie-lin;XIONG Shi-feng(School of Science,Beijing University of Civil Engineering and Architecture,Beijing 102616,China;Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China)

机构地区：[1]北京建筑大学理学院,北京102616 [2]中国科学院数学与系统科学研究院,北京100190

出　　处：《数理统计与管理》2024年第6期985-994,共10页Journal of Applied Statistics and Management

基　　金：科技部重点研发计划(2021YFA1000300,2021YFA1000301);国家自然科学基金(12171462)。

摘　　要：本文针对地铁客流分析问题,建立了乘客进出站刷卡时间数据的动态统计模型。该模型不需要已知列车时刻。我们提出了一个EM算法来求解模型中未知参数的极大似然估计。应用所提模型,可以基于乘客进出站刷卡时间数据推断高峰与非高峰时段的列车时刻、乘客乘各趟车的概率、乘客出站走行时间分布、乘客旅行时间分布等描述地铁系统的指标。模拟实验表明本文的EM算法能较准确地估计动态统计模型中的未知参数。通过所提模型分析了北京地铁6号线的实际数据,给出了高峰与非高峰时段客流特征的若干量化指标刻画。分析结果表明乘车时段对乘车概率和出站走行时间分布有显著影响。基于所提模型构造了乘客出站刷卡时间的动态预测区间。在测试集上的计算结果表明区间的实际覆盖率与名义覆盖率相吻合,这也显示了所提模型的有效性。This paper studies the analysis issue of metro passenger flows.We constructs a dynamic statistical model for passengers'tap-in and tap-out times.This model does not requrietrain schedules.An EM algorithm is proposed to solve the maximum likelihood estimates of unknown parameters in our model.With passengers'tap-in and tap-out times,the proposed model can be applied to infer several indices of metro systems,such as train schedules,passengers'boarding probabilities,distributions of egress times,and distributions of travel times.This point indicates that we provide a solution to the inferential problem of passenger flows in peak hours,which is not extensively discussed in the literature.Simulation results show that the proposed EM algorithm can yield accurate estimates of unknown parameters in the model.Furthermore,we apply our model to analyze a real data set from Line 6 in Beijing metro.Several quantities that describe passenger flow features in both peak and off-peak hours are presented.It is concluded that the time is a significant factor to the boarding probability and distribution of egress time.Based on the proposed model,we construct dynamic prediction intervals for passengers'tap-out times.The results on a test set indicate that the actual coverage rate is consistent with the nominal level,which also show the effectiveness of the proposed model.

关 键 词：城市交通 LOGISTIC模型 极大似然估计 地铁客流 EM算法 

分 类 号：O212[理学—概率论与数理统计] U293.5[理学—数学]