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| 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 |
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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.
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Received: 22 September 2022
Published: 31 August 2023
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| Fund: 国家自然科学基金资助项目（71801080） |
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Corresponding Authors:
Hai-fei YANG
E-mail: wuhohai@126.com;yanghaifei@hhu.edu.cn
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基于换道时间分布的交通流随机微分方程
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
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