车辆排队的链式反应模型及其数值模拟
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摘要
随着社会经济的迅速发展与城市化进程的日益深化,城市人口数量及人民生活水平不断提高,城市汽车保有量持续上升。由于城市汽车保有量的增长速度远超过城市道路的建设速度,由此引起的城市交通拥堵问题日益凸显,严重影响了城市交通系统的运行效率,从而制约了城市社会经济的进一步发展。因此,交通拥堵问题已经成为各大、中城市亟待解决的关键问题之一
城市交通拥堵问题本质上是由于车辆排队过长引起的,因此研究车辆排队的内在机理对于解决交通拥堵问题显得尤为重要。本学位论文依托国家自然科学基金资助项目“城市交通中路段阻塞的链式反应机理研究”而完成。基于链式反应思想,以全新的角度描述车辆排队过程,建立了车辆排队的链式反应模型,并将该模型应用于相邻两交叉口构成的排队系统。
全文共分为六章。第一章对车辆排队问题的研究现状进行了综述。第二章介绍了链式反应的概念,并详细分析了链式反应过程与交通排队过程,发现两者具有相似性。第三章进一步将核裂变与车辆排队的链式反应过程进行对比,根据核链式反应原理,建立了基于链式反应的车辆排队形成模型、车辆排队消散模型和信号交叉口车辆排队模型。利用大连市典型路段的实测交通数据验证了车辆排队形成和消散模型,并运用MATLAB软件对不同条件的交通流进行数值模拟,分析了阻滞信号和消散信号的传播速度对于到达流量和行驶速度的灵敏度。为使模型更具有普遍性,第四章对车辆排队的链式反应模型进行了改进,建立了交通流离散模型和交通流压缩模型,并对其进行了数值模拟。此外,经过模型推导发现,车辆排队的链式反应模型中信号传播公式与交通波模型中波速传播公式形式上相同。鉴于现实的城市路网中存在大量交叉口,第五章进一步讨论车辆排队的链式反应模型在相邻两交叉口中的应用,通过数值模拟分析交通流参数及路段长度对车辆排队过程的影响。第六章对本文研究的主要内容及成果进行了总结。
本文以全新的视角描述车辆排队过程中的链式反应现象和规律,并对所建立的车辆排队链式反应模型进行了验证。结果表明,模型具有较高的精度,能够测算单车道路段上车辆排队的链式反应速度和范围,并解释车辆排队演化的内在规律。研究成果为描述交通排队现象提供了新的思路和方法,为揭示路段阻塞的链式反应规律奠定了基础,可以为解决城市交通拥堵问题提供理论依据。
With the rapid development of social economy and the increasingly deepen of urbanization process, the number of urban population and the life quality is increasing day by day. so the quantity of motor vehicles in the city is sustained growth. At the same time, the growth rate of urban car ownership is far more than the speed of the construction of urban road, which causes traffic congestion phenomenon more and more frequently. So the operating efficiency of urban transportation system is impacted seriously, and the further development of the urban socio-economic is restricted. Therefore, the problem of traffic congestion has become one of the key issues to be solved in large-and-medium-sized cities.
Essentially, the problem of traffic congestion is caused by vehicle queuing formation process, so researching the internal mechanism of vehicle queuing formation is particularly important for solving traffic congestion problem. This thesis, relying on the National Natural Science Foundation-funded project "Study on chain reaction mechanism of road link jam in urban traffic network", is mainly based on the nuclear chain reaction thought, and vehicle queuing process is described in a whole new perspective. In this thesis, a single-period and multi-period vehicle queuing models based on nuclear chain reaction are established, then using those models to describe vehicle queuing process in adjacent intersections.
This thesis is divided into six chapters. The first chapter summarizes the existing research about vehicle queuing problem. The second chapter introduces the concept of the chain reaction, and the chain reaction process of nuclear fission and traffic queuing are analyzed, and the similarity' between them is found. The third chapter compares nuclear fission to chain reaction of vehicle queuing. Then a vehicle queuing model system is presented based on nuclear chain reaction thought. In this thesis, firstly, the similarity between vehicle queuing process and nuclear fission chain reaction is described. According to the principle of nuclear chain reaction, a single-period vehicle queuing model system is established, including vehicle queuing formation model, vehicle queuing dissipation model and vehicle queuing model for signalized intersection. By using the field survey data from a typical link in Dalian city, vehicle queue formation and dissipation models were validated. Also, the numerical simulations for traffic streams under different conditions were made by applying MATLAB software. Based on the simulation results, the sensitivity of the propagation speeds of block and dissipation signals to arrival flow rates and running speeds was further analyzed. The fourth chapter, to make models much more universal, multi-period vehicle queuing model system is established, including traffic flow dissociation model and traffic flow compression model. Multi-period numerical simulation is made to exam model's stability. In addition, after the model derivation, the signal propagation of vehicle queuing chain reaction model and the wave velocity propagation of traffic wave model have consistency, although the two models point respectively from micro and macro perspective. The fifth chapter, given the reality of urban road network, there are a large number of intersections, so vehicle queuing chain reaction model used in adjacent intersections is discussed. By means of numerical simulation, the effect from traffic flow parameters and road length to vehicle queuing process is analyzed. The sixth chapter summarizes the main contents and results of this thesis.
This thesis describes chain reaction phenomenon of vehicle queuing process from a new perspective, and proves chain reaction models of vehicle queuing. The results indicate that the proposed models have a higher precision, which can be used to calculate the propagation velocity and boundary of the chain reaction of vehicle queuing, and explain the internal mechanism of vehicle queue formation and dissipation on a link with a single lane. The research achievements can offer a novel idea and method for studying traffic queue, provide a foundation for explaining the principle of the chain reaction mechanism of road link jam. and give a theoretical basis for solving urban traffic congestion and jam problems.
城市交通拥堵问题本质上是由于车辆排队过长引起的,因此研究车辆排队的内在机理对于解决交通拥堵问题显得尤为重要。本学位论文依托国家自然科学基金资助项目“城市交通中路段阻塞的链式反应机理研究”而完成。基于链式反应思想,以全新的角度描述车辆排队过程,建立了车辆排队的链式反应模型,并将该模型应用于相邻两交叉口构成的排队系统。
全文共分为六章。第一章对车辆排队问题的研究现状进行了综述。第二章介绍了链式反应的概念,并详细分析了链式反应过程与交通排队过程,发现两者具有相似性。第三章进一步将核裂变与车辆排队的链式反应过程进行对比,根据核链式反应原理,建立了基于链式反应的车辆排队形成模型、车辆排队消散模型和信号交叉口车辆排队模型。利用大连市典型路段的实测交通数据验证了车辆排队形成和消散模型,并运用MATLAB软件对不同条件的交通流进行数值模拟,分析了阻滞信号和消散信号的传播速度对于到达流量和行驶速度的灵敏度。为使模型更具有普遍性,第四章对车辆排队的链式反应模型进行了改进,建立了交通流离散模型和交通流压缩模型,并对其进行了数值模拟。此外,经过模型推导发现,车辆排队的链式反应模型中信号传播公式与交通波模型中波速传播公式形式上相同。鉴于现实的城市路网中存在大量交叉口,第五章进一步讨论车辆排队的链式反应模型在相邻两交叉口中的应用,通过数值模拟分析交通流参数及路段长度对车辆排队过程的影响。第六章对本文研究的主要内容及成果进行了总结。
本文以全新的视角描述车辆排队过程中的链式反应现象和规律,并对所建立的车辆排队链式反应模型进行了验证。结果表明,模型具有较高的精度,能够测算单车道路段上车辆排队的链式反应速度和范围,并解释车辆排队演化的内在规律。研究成果为描述交通排队现象提供了新的思路和方法,为揭示路段阻塞的链式反应规律奠定了基础,可以为解决城市交通拥堵问题提供理论依据。
With the rapid development of social economy and the increasingly deepen of urbanization process, the number of urban population and the life quality is increasing day by day. so the quantity of motor vehicles in the city is sustained growth. At the same time, the growth rate of urban car ownership is far more than the speed of the construction of urban road, which causes traffic congestion phenomenon more and more frequently. So the operating efficiency of urban transportation system is impacted seriously, and the further development of the urban socio-economic is restricted. Therefore, the problem of traffic congestion has become one of the key issues to be solved in large-and-medium-sized cities.
Essentially, the problem of traffic congestion is caused by vehicle queuing formation process, so researching the internal mechanism of vehicle queuing formation is particularly important for solving traffic congestion problem. This thesis, relying on the National Natural Science Foundation-funded project "Study on chain reaction mechanism of road link jam in urban traffic network", is mainly based on the nuclear chain reaction thought, and vehicle queuing process is described in a whole new perspective. In this thesis, a single-period and multi-period vehicle queuing models based on nuclear chain reaction are established, then using those models to describe vehicle queuing process in adjacent intersections.
This thesis is divided into six chapters. The first chapter summarizes the existing research about vehicle queuing problem. The second chapter introduces the concept of the chain reaction, and the chain reaction process of nuclear fission and traffic queuing are analyzed, and the similarity' between them is found. The third chapter compares nuclear fission to chain reaction of vehicle queuing. Then a vehicle queuing model system is presented based on nuclear chain reaction thought. In this thesis, firstly, the similarity between vehicle queuing process and nuclear fission chain reaction is described. According to the principle of nuclear chain reaction, a single-period vehicle queuing model system is established, including vehicle queuing formation model, vehicle queuing dissipation model and vehicle queuing model for signalized intersection. By using the field survey data from a typical link in Dalian city, vehicle queue formation and dissipation models were validated. Also, the numerical simulations for traffic streams under different conditions were made by applying MATLAB software. Based on the simulation results, the sensitivity of the propagation speeds of block and dissipation signals to arrival flow rates and running speeds was further analyzed. The fourth chapter, to make models much more universal, multi-period vehicle queuing model system is established, including traffic flow dissociation model and traffic flow compression model. Multi-period numerical simulation is made to exam model's stability. In addition, after the model derivation, the signal propagation of vehicle queuing chain reaction model and the wave velocity propagation of traffic wave model have consistency, although the two models point respectively from micro and macro perspective. The fifth chapter, given the reality of urban road network, there are a large number of intersections, so vehicle queuing chain reaction model used in adjacent intersections is discussed. By means of numerical simulation, the effect from traffic flow parameters and road length to vehicle queuing process is analyzed. The sixth chapter summarizes the main contents and results of this thesis.
This thesis describes chain reaction phenomenon of vehicle queuing process from a new perspective, and proves chain reaction models of vehicle queuing. The results indicate that the proposed models have a higher precision, which can be used to calculate the propagation velocity and boundary of the chain reaction of vehicle queuing, and explain the internal mechanism of vehicle queue formation and dissipation on a link with a single lane. The research achievements can offer a novel idea and method for studying traffic queue, provide a foundation for explaining the principle of the chain reaction mechanism of road link jam. and give a theoretical basis for solving urban traffic congestion and jam problems.
引文
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[3]Pipes LA. An operational analysis of traffic dynamics [J]. Journal of Applied Physics,1953,24(3): 274-281.
[4]Pipes LA. Car following models and the fundamental diagram of road traffic [J]. Transportation Research,1967.1:21-29.
[5]Chandler RE. Herman R. Montroll EW. Traffic dynamics:Studies in car following [J].Operations Research,1958,6(2):165-184.
[6]Herman R. Montroll EW. Potts RB, Rothery RW. Traffic dynamics:Analysis of stability in car following [J]. Operations Research,1959,7(1):86-106.
[7]Gazis DC, Herman R, Potts RB. Car-following theory of steady-state traffic flow [J]. Operations Research,1959,7(4):499-505.
[8]Greenberg H. An analysis of traffic flow [J]. Operations Research,1959,7(1):79-85.
[9]章三乐,肖秋生,任福田.车辆跟驰理论的实用研究[J].北京工业大学学报,1992, 9(3)：20-27
[10]王立锋,李正熙.基于车辆跟驰理论的交通流动力学模型与数值仿真[J].东南大学学报,2005.11(35)：165-]67.
[11]Lighthill MJ. Whitham GB. On kinematic waves I. Flood movement in long rivers [J].Proceedings of the Royal Society of London,1955,229A(1178):281-316.
[12]Lighthill MJ, Whitham GB. On kinematic waves Ⅱ. A theory of traffic flow on long crowded roads[J]. Proceedings of the Royal Society of London,1955,229A(1178):317-345.
[13]Richards PI. Shock waves on the highway [J]. Operations Research,1956,4(1):42-51.
[14]YI Ping. TIAN Zongzhong, ZHAO Qiang. Consistency of input-output model and shockwave analysis in queue and delay estimations [J]. Journal of Transportation Systems Engineering and Information Technology,2008,8(6):146-152.
[15]Henry X Liu. Xinkai Wu. Wenteng Ma, et al. Real-time queue length estimation for congested signalized intersections [J]. Transportation Research Part C.2009, (17):412-427.
[16]郭冠英.邹智军.道路阻塞时的车辆排队长度计算法[J].中国公路学报,1998.11(3)：92-95.
[17]陈佳,周涛.曾祥平.城市异常路段交通拥挤[J].中国水运.2007.2(7)：63-64.
[18]张亚平.李硕.信号交义口车辆集结与消散分析[J].长沙交通学院学报,1999.15(3)：57-61.
[19]隽志才,魏丽英.李江.信号交叉口排队长度宏观模拟的自适应分析法[J].中国公路学报.2000,13(1)：77-80.
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