基于超统计理论的高速铁路跨线列车晚点分布模型研究
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摘要
精确描述高速铁路跨线列车晚点时长分布是准确计算跨线列车晚点引起的后效晚点的基础,也是精细化管理能力紧张的高速铁路的依据,具有重要的理论和实践意义。通过对高速铁路跨线列车晚点实绩数据的分析,运用超统计理论对列车晚点机理进行研究,构建跨线列车晚点时长q-指数分布模型。以2018年9月京沪高速铁路跨线列车晚点数据为样本,通过非线性回归拟合和Kolmogorov-Smirnov检验比较常见的正偏态厚尾分布模型及用于建模普速铁路列车晚点的指数分布模型对跨线列车晚点时长分布曲线的拟合效果。结果表明:q-指数分布模型相比于常见的正偏态厚尾分布模型,有更优的拟合效果,能更精确地描述高速铁路跨线列车晚点时长分布。
Accurate description of the delay distribution of high-speed railway off-line trains, as the basis for precisely calculating the train daughter delay time caused by the off-line trains, as well as the basis for the delicacy management of high-speed railways with limited capacity, has important theoretical and practical significance. Based on the analysis of operational data of high-speed railway off-line trains, this paper studied the train delay mechanism by using the theory of the superstatistics, and established the q-exponential distribution model of off-line train delay. The nonlinear regression fitting and Kolmogorov-Smirnov test were used for the comparison of the fitness of curves between the common positive skewness and fat-tailed distribution models and the exponential distribution model used to model the normal-speed railway trains delay based on the delay data of Beijing-Shanghai high-speed railway off-line trains in September 2018. The results confirm that the q-exponential distribution model has better fitting effect and can describe the delay distribution of high-speed railway off-line trains more accurately than the common positive skewness and fat-tailed distribution model.
Accurate description of the delay distribution of high-speed railway off-line trains, as the basis for precisely calculating the train daughter delay time caused by the off-line trains, as well as the basis for the delicacy management of high-speed railways with limited capacity, has important theoretical and practical significance. Based on the analysis of operational data of high-speed railway off-line trains, this paper studied the train delay mechanism by using the theory of the superstatistics, and established the q-exponential distribution model of off-line train delay. The nonlinear regression fitting and Kolmogorov-Smirnov test were used for the comparison of the fitness of curves between the common positive skewness and fat-tailed distribution models and the exponential distribution model used to model the normal-speed railway trains delay based on the delay data of Beijing-Shanghai high-speed railway off-line trains in September 2018. The results confirm that the q-exponential distribution model has better fitting effect and can describe the delay distribution of high-speed railway off-line trains more accurately than the common positive skewness and fat-tailed distribution model.
引文
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[22] 雷强,黄登笑.人民币/美元汇率收益率的统计特性和非线性特征研究[J].科学技术与工程,2009,9(10):2698-2702.LEI Qiang,HUANG Dengxiao.Statistic and Nonlinear Research of RMB/USD Exchange Rate Returns[J].Science Technology and Engineering,2009,9(10):2698-2702.
[23] 皮天雷,李未无.对资产收益率“尖峰厚尾”现象的探讨[J].统计与决策,2004(4):10-11.PI Tianlei,LI Weiwu.Discussion on the Phenomenon of “Peak and Thick Tail” of Return on Assets[J].Statistics and Decision,2004(4):10-11.
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[2] 张星臣,杨浩,胡思继,等.京沪高速铁路高中速列车共线混行模式下中速列车晚点影响的仿真分析[J].铁道学报,1998,20(5):1-9.ZHANG Xingchen,YANG Hao,HU Siji,et al.A Simulation Analysis of Mid-speed Train Delay Influence under the Operating Mode with High and Middle Speed Train in Jinghu High-speed Railway[J].Journal of the China Railway Society,1998,20(5):1-9.
[3] 陈霞.高速铁路跨线列车运行方案优化研究[D].成都:西南交通大学,2017:1-6.
[4] SCHWANH?U?ER W.Die Bemessung der Pufferzeiten im Fahrplangefüge der Eisenbahn[D].Aachen:Rheinisch-Westf?lischen Technischen Hochschule,1974.
[5] GOVERDE R M P,HOOGHIEMSTRA G,et al.Statistical Analysis of Train Traffic:The Eindhoven Case[M].Delft:Delft University Press,2001.
[6] 孙焰,刘胤宏,李致中,等.列车运行图的晚点概率分析[J].长沙铁道学院学报,1998,16(4):83-89.SUN Yan,LIU Yinhong,LI Zhizhong,et al.The Analysis of Delaying Time Probability for the Travelling Graph of Trains[J].Journal of Changsha Railway University,1998,16(4):83-89.
[7] 刘岩,郭竞文,罗常津,等.列车运行实绩大数据分析及应用前景展望[J].中国铁路,2015(6):70-73.LIU Yan,GUO Jingwen,LUO Changjin,et al.Train Operation Big Data Analysis and Its Application Prospect[J].China Railway,2015(6):70-73.
[8] XU P,CORMAN F,PENG Q.Analyzing Railway Disruptions and Their Impact on Delayed Traffic in Chinese High-speed Railway[J].IFAC PapersOnLine,2016,49(3):84-89.
[9] BRIGGS K,BECK C.Modelling Train Delays with Q-exponential Functions[J].Physica A:Statistical Mechanics and Its Applications,2007,378(2):498-504.
[10] 庄河,文超,李忠灿,等.基于高速列车运行实绩的致因-初始晚点时长分布模型[J].铁道学报,2017,39(9):25-31.ZHUANG He,WEN Chao,LI Zhongcan,et al.Cause Based Primary Delay Distribution Models of High-speed Trains on Account of Operation Records[J].Journal of the China Railway Society,2017,39(9):25-31.
[11] 杨越.基于超统计理论的网络流量异常检测方法研究[D].武汉:华中科技大学,2010:26-36.
[12] BECK C,COHEN E.Superstatistics[J].Physica A:Statistical Mechanics and Its Applications,2003,322(1-4):267-275.
[13] Wikipedia Contributors.Superstatistics[EB/OL].Wikipedia,The Free Encyclopedia.https://en.wikipedia.org/w/index.php?title=Superstatistics&oldid=819536603,2019-02-24/2019-01-09.
[14] BECK C.Generalized Statistical Mechanics of Cosmic Rays[J].Physica A:Statistical Mechanics and Its Applications,2004,331(1-2):173-181
[15] CHEN L L,BECK C.A Superstatistical Model of Metastasis and Cancer Survival[J].Physica A:Statistical Mechanics and Its Applications,2008,387(13):3162-3172.
[16] KOSUN C,OZDEMIR S.A Superstatistical Model of Vehicular Traffic Flow[J].Physica A:Statistical Mechanics and Its Applications,2016,444:466-475.
[17] 胡思继,孙全欣,胡锦云,等.区段内列车晚点传播理论的研究[J].中国铁道科学,1994,15(2):41-54.HU Siji,SUN Quanxin,HU Jinyun,et al.Research on the Train Delay Propagation Theory in the Section[J].China Railway Science,1994,15(2):41-54.
[18] 陈东,彭其渊,李永辉.列车到达晚点对技术站车流接续影响仿真分析[J].西南交通大学学报,2014,49(6):1108-1115.CHEN Dong,PENG Qiyuan,LI Yonghui.Simulation of Effect of Train Arrival Delay on Wagon Flow Connection at Technical Stations[J].Journal of Southwest Jiaotong University,2014,49(6):1108-1115.
[19] TSALLIS C.What Are the Numbers that Experiments Provide?[J].Quimica Nova,1994,17(6):468-471.
[20] WILK G,WLODARCZYK Z.Interpretation of the Nonextensivity Parameter Q in Some Applications of Tsallis Statistics and Levy Distributions[J].Physical Review Letters,2000,84(13):2770-2773.
[21] 陆阳,庄新田.跨期决策中动态不一致性程度研究[J].东北大学学报(自然科学版),2015,36(5):753-756.LU Yang,ZHUANG Xintian.Research on the Degree of Dynamic Inconsistency in Intertemporal Decision Making[J].Journal of Northeastern University (Natural Science),2015,36(5):753-756.
[22] 雷强,黄登笑.人民币/美元汇率收益率的统计特性和非线性特征研究[J].科学技术与工程,2009,9(10):2698-2702.LEI Qiang,HUANG Dengxiao.Statistic and Nonlinear Research of RMB/USD Exchange Rate Returns[J].Science Technology and Engineering,2009,9(10):2698-2702.
[23] 皮天雷,李未无.对资产收益率“尖峰厚尾”现象的探讨[J].统计与决策,2004(4):10-11.PI Tianlei,LI Weiwu.Discussion on the Phenomenon of “Peak and Thick Tail” of Return on Assets[J].Statistics and Decision,2004(4):10-11.
[24] 陈希孺.概率论与数理统计[M].合肥:中国科学技术大学出版社,1992.