基于换道时间分布的交通流随机微分方程

doi:10.3785/j.issn.1008-973X.2023.08.015

浙江大学学报(工学版)

2023, Vol. 57

Issue (8): 1629-1635 DOI: 10.3785/j.issn.1008-973X.2023.08.015

土木工程、交通工程

基于换道时间分布的交通流随机微分方程

吴中(

),梁明琰,杨海飞*(

)

河海大学土木与交通学院，江苏南京 210098

Stochastic differential equation of traffic flow model based on distribution of lane-changing duration

Zhong WU(

),Ming-yan LIANG,Hai-fei YANG*(

)

College of Civil and Transportation Engineering, Hohai University, Nanjing 210098, China

全文: PDF(986 KB) HTML

摘要：

在总结随机交通流理论发展的基础上，提出考虑换道时间随机性的随机交通流动力学方程，给出包括换道行为的交通流方程数值解法. 解法结合换道时间的密度分解和偏微分方程的差分求解，对快速路交织区车流速度在时空上的演变概率进行求解，得到交通流速度演变趋势的随机可能性，并表达为速度变化的概率密度. 求解结果表明，交通流动力学随机微分方程及其数值解法能够描述复杂交通流的随机特性，速度概率密度函数弥补了其他交通流方程难以表达的车流速度随机特征，为深入研究拥堵工况的交通流演变规律提供了新研究手段，也为交通设施和交通控制设计提供了通行能力之类的参量在可靠性上的理论分析方法.

关键词： 换道时间; 交织区; 交通流; 概率分布; 随机微分方程

Abstract:

A mechanical equation of stochastic traffic flow considering the randomness of lane change time was proposed, on the basis of summarizing the development of stochastic traffic flow theory. The numerical method of traffic flow equation including lane change behavior was given. The method combined the density decomposition of lane change time and the difference solution of partial differential equation. The evolution probability of traffic velocity of expressway weaving area in the spatial-temporal domain was solved. The random probability of the evolving trend of traffic flow velocity was obtained and expressed as the probability density of the velocity change. Results show that the stochastic differential equations of traffic flow mechanics and their numerical solutions can describe the stochastic characteristics of complex traffic flows. Velocity probability density function makes up the random characteristics of traffic flow velocity which is difficult to be expressed by other traffic flow equations. It provides a new research method for the in-depth study of traffic flow evolution law of traffic facilities under congestion conditions. It provides a new research method for an in-depth study of the evolution of traffic flow under congested conditions, and provides a theoretical analysis method for the reliability of capacity and other parameters in the design of traffic facilities and traffic control.

Key words: lane-changing duration weaving area traffic flow distribution of probability stochastic differential equation

收稿日期: 2022-09-22 出版日期: 2023-08-31

CLC:

TU 491

基金资助: 国家自然科学基金资助项目（71801080）

通讯作者: 杨海飞 E-mail: wuhohai@126.com;yanghaifei@hhu.edu.cn

作者简介: 吴中（1964—），男，教授，博士，从事交通运输规划与管理、流体动力学研究. orcid.org/0000-0002-2956-5641. E-mail: wuhohai@126.com

	服务
	把本文推荐给朋友
	加入引用管理器
	E-mail Alert
	作者相关文章
	吴中
	梁明琰
	杨海飞

引用本文:

吴中,梁明琰,杨海飞. 基于换道时间分布的交通流随机微分方程[J]. 浙江大学学报(工学版), 2023, 57(8): 1629-1635.

Zhong WU,Ming-yan LIANG,Hai-fei YANG. Stochastic differential equation of traffic flow model based on distribution of lane-changing duration. Journal of ZheJiang University (Engineering Science), 2023, 57(8): 1629-1635.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2023.08.015 或 https://www.zjujournals.com/eng/CN/Y2023/V57/I8/1629

图 1 高峰时段换道时间分布频次直方图及其拟合曲线

图 2 某快速路交织区网格剖分图

表 1 高峰期交织区小时OD矩阵

图 3 车道1网格单元3第30 s分段速度概率分布

图 4 车道1网格单元3第30 s速度概率密度

图 5 车道1网格单元3在0~60 s历时下每2 s时间点的速度概率密度

图 6 交织区车道2网格单元8时均车流速度概率密度

1	ZHENG Z, AHN S, MONSERE C M Impact of traffic oscillations on freeway crash occurrences[J]. Accident Analysis and Prevention, 2010, 42 (2): 626- 636 doi: 10.1016/j.aap.2009.10.009
2	STORM P J, MANDJES M, van AREM B Efficient evaluation of stochastic traffic flow models using Gaussian process approximation[J]. Transportation Research Part B: Methodological, 2022, 164: 126- 144 doi: 10.1016/j.trb.2022.08.003
3	BOUADI M, JIA B, JIANG R, et al Stochastic factors and string stability of traffic flow: analytical investigation and numerical study based on car-following models[J]. Transportation Research Part B: Methodological, 2022, 165: 96- 122 doi: 10.1016/j.trb.2022.09.007
4	龚鲁光. 随机微分方程引论: 第2版[M]. 北京: 北京大学出版社, 1995.
5	OKSENDAL B. Stochastic differential equations [M]. 6th ed. New York: Springer-Verlag Heidelberg, 2012.
6	SINGH S K, ACHARYA S K A Bayesian inference to estimate change point for traffic intensity in M/M/1 Queueing Model[J]. Opsearch, 2021, 59 (4): 166- 206
7	LIGHTHILL M J, WHITHAM G B On kinematic waves. II. a theory of traffic flow on long crowded roads.[J]. Proceedings of the Royal Society of London Series A: Mathematical and Physical Sciences, 1955, 229 (1178): 317- 345
8	RICHARDS P I Shock waves on the highway[J]. Operations Research, 1956, 4 (1): 42- 51 doi: 10.1287/opre.4.1.42
9	王昊, 杨万波速度梯度模型的高速公路交通流状态估计方法[J]. 哈尔滨工业大学学报, 2015, 47 (9): 84- 89 WANG Hao, YANG Wan-bo Freeway traffic state estimation by using speed gradient model[J]. Journal of Harbin Institute of Technology, 2015, 47 (9): 84- 89
10	TSCHARAKTSCHIEW S Why are highway speed limits really justified? An equilibrium speed choice analysis[J]. Transportation Research Part B: Methodological, 2020, 138 (3): 317- 351
11	周文海, 李舒健, 董力耘非均匀路段交通流的元胞自动机模拟[J]. 上海大学学报: 自然科学版, 2022, 28 (4): 594- 607 ZHOU Wen-hai, LI Shu-jian, DONG Li-yun Simulation of traffic flow on non-uniform road sections with cellular automaton model[J]. Journal of Shanghai University: Natural Science Edition, 2022, 28 (4): 594- 607
12	帅斌, 秦梦瑶, 许旻昊基于元胞自动机的高速铁路列车运行仿真研究[J]. 计算机仿真, 2022, 39 (8): 153- 159 SHUAI Bin, QIN Meng-yao, XU Min-hao Simulation study of high-speed railroad train operation based on cellular automata[J]. Computer Simulation, 2022, 39 (8): 153- 159
13	HASSANIN O, WANG X, WU X, et al Efficiency performance and safety evaluation of the responsibility-sensitive safety in freeway car-following scenarios using automated longitudinal controls[J]. Accident Analysis and Prevention, 2022, 177: 106799 doi: 10.1016/j.aap.2022.106799
14	潘义勇, 管星宇基于分位数回归的随机优化速度跟驰模型[J]. 浙江大学学报: 工学版, 2022, 56 (8): 1553- 1559 PAN Yi-yong, GUAN Xing-yu Stochastic optimal velocity car-following model based on quantile regression[J]. Journal of Zhejiang University: Engineering Science, 2022, 56 (8): 1553- 1559
15	TAJALLI M, NIROUMAND R, HAJBABAIE A Distributed cooperative trajectory and lane changing optimization of connected automated vehicles: freeway segments with lane drop[J]. Transportation Research Part C: Emerging Technologies, 2022, 143: 103761 doi: 10.1016/j.trc.2022.103761
16	程晓明, 李文权元胞自动机交通流模型的随机规则[J]. 交通运输工程与信息学报, 2007, (3): 96- 99 CHENG Xiao-ming, LI Wen-quan Randomization rules of 1D cellular automaton traffic flow model[J]. Journal of Transportation Engineering and Information, 2007, (3): 96- 99 doi: 10.3969/j.issn.1672-4747.2007.03.018
17	刘立英, 李新刚, 贾斌基于元胞自动机模型的交织区通行能力特性分析[J]. 交通信息与安全, 2013, 31 (3): 28- 32 LIU Li-ying, LI Xin-gang, JIA Bin Analysis of capacity of weaving section based on cellular automata model[J]. Journal of Transport Information and Safety, 2013, 31 (3): 28- 32
18	LI X, GAO Z, JIA B. Capacity analysis of type-A weaving section by using cellular automata model [C]// Transportation Research Board. Kunming: 7th International Conference on Traffic and Transportation Studies, 2010: 1010-1018.
19	JIA B, GAOU J Y Traffic behavior around the weaving section in cellular automata model[J]. International Journal of Modern Physics C, 2010, 21 (3): 409- 422 doi: 10.1142/S012918311001518X
20	HELBING K D Three-phase traffic theory and two-phase models with a fundamental diagram in the light of empirical stylized facts[J]. Transportation Research Part B: Methodological, 2010, 44 (8): 983- 1000
21	BAËR N, BOUCHERIE R J, van OMMEREN J C W Threshold queueing to describe the fundamental diagram of uninterrupted traffic[J]. Transportation Science, 2019, 53 (2): 585- 596 doi: 10.1287/trsc.2018.0850
22	WANG Y, LI X, TIAN J, et al Stability analysis of stochastic linear car-following models[J]. Transportation Science, 2020, 54 (1): 274- 297 doi: 10.1287/trsc.2019.0932
23	姚佼, 张凯敏, 徐洁琼基于离散多项Logit模型的多时段控制过渡方案选择[J]. 公路交通科技, 2018, 35 (10): 104- 110 YAO Jiao, ZHANG Kai-min, XU Jie-qiong Multinomial logit model based time-of-day control transition scheme selection[J]. Journal of Highway and Transportation Research and Development, 2018, 35 (10): 104- 110
24	NEWELL G F Memoirs on highway traffic flow theory in the 1950s[J]. Operations Research, 2002, 50 (1): 173- 178 doi: 10.1287/opre.50.1.173.17802
25	GAZIS D C The origins of traffic theory[J]. Operations Research, 2002, 50 (1): 69- 77 doi: 10.1287/opre.50.1.69.17776
26	马庆禄, 傅宝宇, 曾皓威智能网联环境下异质交通流基本图和稳定性分析[J]. 交通信息与安全, 2021, 39 (5): 76- 84 MA Qing-lu, FU Bao-yu, CENG Hao-wei Fundamental diagram and stability analysis of heterogeneous traffic flow in a connected and autonomous environment[J]. Journal of Transport Information and Safety, 2021, 39 (5): 76- 84 doi: 10.3963/j.jssn.1674-4861.2021.05.010
27	KWON J, BARKLEY T, HRANAC R, et al Decomposition of travel time reliability into various sources: incidents, weather, work zones, special events, and base capacity[J]. Transportation Research Record, 2011, 2229 (1): 28- 33 doi: 10.3141/2229-04
28	沈琪梦. 基于时变特性的城市交通出行路径可靠性研究[D]. 北京: 北京交通大学, 2020. SHEN Qi-meng. Study on the reliability of urban traffic path based on time-varying characteristics[D]. Beijing: Beijing Jiaotong University, 2020.
29	李小静, 刘林忠, 牟海波基于四阶矩的路网总行程时间可靠性评价[J]. 交通运输系统工程与信息, 2019, 19 (1): 145- 150 LI Xiao-jing, LIU Lin-zhong, MOU Hai-bo Evaluation of road network total travel time reliability based on fourth-moment[J]. Journal of Transportation Systems Engineering and Information Technology, 2019, 19 (1): 145- 150
30	徐红利, 刘煜昊, 徐薇, 等考虑决策惯性的随机网络路径选择与交通流分配模型[J]. 系统工程理论与实践, 2021, 41 (4): 1010- 1017 XU Hong-li, LIU Yu-hao, XU Wei, et al Route choice model in stochastic network and its application in traffic assignment with consideration to travelers' decision inertia[J]. Systems Engineering: Theory and Practice, 2021, 41 (4): 1010- 1017
31	何胜学基于有效路径集逐步生成的网络交通流分配方法[J]. 武汉理工大学学报: 交通科学与工程版, 2021, 45 (5): 817- 821 HE Sheng-xue Network traffic assignment method based on gradually extending the set of effective paths[J]. Journal of Wuhan University of Technology: Transportation Science and Engineering, 2021, 45 (5): 817- 821
32	LAVAL J A, DAGANZO C F Lane-changing in traffic streams[J]. Transportation Research Part B: Methodological, 2006, 40 (3): 251- 264 doi: 10.1016/j.trb.2005.04.003
33	吴中, 熊天成, 杨海飞考虑换道过程影响的城市交通流动力学方程[J]. 华东交通大学学报, 2020, 37 (6): 68- 74 WU Zhong, XIONG Tian-cheng, YANG Hai-fei Dynamic equation of urban traffic flow considering the influence of lane-changing process enhanced publishing[J]. Journal of East China Jiaotong University, 2020, 37 (6): 68- 74
34	JIANG R, WU Q, ZHU Z A new dynamics model for traffic flow[J]. Chinese Science Bulletin, 2001, 46 (4): 345- 348 doi: 10.1007/BF03187201

[1]	孟闯,王慧. 多信息融合的时空图卷积交通流量预测模型[J]. 浙江大学学报(工学版), 2023, 57(8): 1541-1550.
[2]	王殿海,谢瑞,蔡正义. 基于最优汇集时间间隔的城市间断交通流预测[J]. 浙江大学学报(工学版), 2023, 57(8): 1607-1617.
[3]	卢凯,尹帅帅,江书妍,周志洁,李青. 考虑交织路段掉头车流的邻近交叉口信号协调控制[J]. 浙江大学学报(工学版), 2023, 57(8): 1618-1628.
[4]	潘义勇,管星宇. 基于分位数回归的随机优化速度跟驰模型[J]. 浙江大学学报(工学版), 2022, 56(8): 1553-1559.
[5]	侯越,韩成艳,郑鑫,邓志远. 基于时空融合图卷积的交通流数据修复方法[J]. 浙江大学学报(工学版), 2022, 56(7): 1394-1403.
[6]	李根,翟伟,邬岚. 基于梯度提升决策树的汇合交互作用研究[J]. 浙江大学学报(工学版), 2022, 56(4): 649-655.
[7]	谭佳丽,方圣恩. 基于力学贝叶斯网络的钢桁架安全评估[J]. 浙江大学学报(工学版), 2021, 55(11): 2170-2177.
[8]	黄靖,钟书远,文元桥,罗坤. 用于交通流预测的自适应图生成跳跃网络[J]. 浙江大学学报(工学版), 2021, 55(10): 1825-1833.
[9]	闫旭,范晓亮,郑传潘,臧彧,王程,程明,陈龙彪. 基于图卷积神经网络的城市交通态势预测算法[J]. 浙江大学学报(工学版), 2020, 54(6): 1147-1155.
[10]	金南国,何家豪,付传清,金贤玉. 钢筋加速非均匀锈蚀试验方法和锈蚀形态研究[J]. 浙江大学学报(工学版), 2020, 54(3): 483-490.
[11]	赵俭斌,席义博,王振宇. 海上风机单桩基础疲劳损伤计算方法[J]. 浙江大学学报(工学版), 2019, 53(9): 1711-1719.
[12]	黄铭枫, 李强, 涂志斌, 楼文娟. 基于Copula函数的杭州地区多风向极值风速估计[J]. 浙江大学学报(工学版), 2018, 52(5): 828-835.
[13]	龚越, 罗小芹, 王殿海, 杨少辉. 基于梯度提升回归树的城市道路行程时间预测[J]. 浙江大学学报(工学版), 2018, 52(3): 453-460.
[14]	王薇, 程泽阳, 刘梦依, 杨兆升. 基于时空相关性的交通流故障数据修复方法[J]. 浙江大学学报(工学版), 2017, 51(9): 1727-1734.
[15]	周旦, 马晓龙, 金盛, 王殿海. 混合非机动车交通流超车次率影响因素模型[J]. 浙江大学学报(工学版), 2015, 49(9): 1672-1678.

Viewed

Full text

Abstract

Cited

Shared

Discussed