交通流复杂动态特性的元胞自动机模型研究
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摘要
随着经济不断发展,人们对交通的需求不断增长,因此,交通问题日益成为影响人们生活、制约经济发展的一个的关键性问题。如何充分利用现有的交通设施,有计划地开发有限的交通资源；如何以科学的理论来管理、指导以及控制交通,以缓解迅速增长的交通需求,就成为现代经济社会中一个突出的问题。于是,交通流理论研究做为当今社会对经济需求的一个方面而随之产生。交通流理论研究作为二十世纪一门新兴的交叉性学科,近年来已受到许多学科研究人员的关注,例如力学、非线性科学、物理学、应用数学、系统科学、信息科学、交通工程学、统计学、计算机科学等等。交通流理论的研究目的是,利用现代科学知识正确地描述与实际相关的交通流特性,然后建立适当的数学模型,经过数值模拟和理论分析,揭示交通流现象的本质特征,为实际的交通规划以及交通管理提供可靠的科学理论依据。
本文作者在充分调查了交通流理论在国内外的发展情况以后,根据实际的交通状况,提出了更符合现实交通的模型,并通过数值模拟和理论分析,研究了交通流中出现的各种非线性现象,揭示了其物理本质。本文的主要工作如下：
提出了一个改进的双通道交通流模型。由于原来双通道交通模型存在两个明显的缺点：(1)在每一时间步,都会有一辆车到达系统的入口处；(2)当车辆不能驶入道路时,人为地将车辆剔除出去。然而,在高速道路交通中,很少存在每一秒到达一辆车的情况,并且如果车辆不能进入系统,应该停下来等待机会再次进入。鉴于这些实际情况,在本文提出的改进模型中改进了原来双通道模型的上述两个缺点：(1)假设在每一秒钟,车辆以概率λ到达双通道的入口处,其中λ是介于0到1之间的可调参数；(2)若在入口处车辆不能进入系统,则排队等候,直到能进入所选路径。
在改进模型中,我们首先假设在其中的一条道路上存在限速瓶颈(例如,行人穿马路、部分道路封闭施工等情况)。我们采用平均速度信息反馈策略对此模型进行了详细的数值模拟和数学分析。模拟结果表明系统存在四种物理状态：零态(zero state)、周期震荡态(periodic oscillation state)、交替态(alternation state)(即零态和周期震荡态交替出现)和等速度态(equal velocity state)(即系统中两条道路上车辆的平均速度近似相等)。并且,我们得到了系统处于零态时车辆到达概率与动态车比例之间的数学关系式。
紧接着上面的研究,我们进一步改进了双通道模型：组成模型的两条道路是不等长的,并且在较短路径上存在限速瓶颈,我们称这样的由两条不同道路组成的双通道系统为非对称系统。相应地,由两条完全相同的道路组成的系统称为对称系统。由于以前应用在对称双通道交通中的信息反馈策略不能直接应用于非对称双通道交通中,所以我们采用改进的平均速度反馈和改进的拥挤系数反馈研究非对称双通道系统。模拟结果表明,出行者平均出行时间与车辆到达概率λ有关,当λ较小时,采用改进的平均速度信息反馈策略能节省出行时间；当λ较大时,采用改进的拥挤系数信息反馈策略能节省出行时间。所以交通管理者要根据实际的交通情况指导交通,已达到高效的目的。
接着,针对对称双通道模型中采用行驶时间反馈策略出现的流量高幅震荡以及非对称双通道交通模型中出现的周期震荡态,我们调查了当部分动态车不遵守信息指示时的交通状态,模拟发现,对称系统及非对称系统中存在的大幅度震荡被压制了。系统的通行能力增加了,这说明,在某些情况下(例如双通道交通中进行路径选择时)司机太遵守规则反而达不到预想的效果。在这个改进模型中,我们首次研究了在何种情况下能降低双通道交通系统中道路上流量的震荡。
最后,我们提出了一种耦合演化博弈理论的一维交通流模型。考虑到实际交通流是由车辆组成的,而车辆是由具有自主意识的司机来操控的,所以组成交通流的个体之间会存在一定的冲突,这种冲突可以用进化的博弈理论来描述。因此,我们将进化博弈理论引进一维交通流模型中。首先采用周期性边界条件,研究了耦合进化博弈理论的单道交通模型。采用蒙特-卡罗方法对于单道交通模型进行模拟,结果显示,当道路上粒子密度小于临界密度时,经过短暂的暂态过程后,背叛者比例随时间呈指数衰减；当道路上粒子密度大于临界密度时,经过短暂的暂态过程后,背叛者比例不再随时间变化,而是保持为一个常数。我们将本文模型得到的临界行为与以前文献中模型的临界行为做了比较,初步解释了造成两种不同临界行为的原因可能是由于系统经历的过程不同引起的。采用平均场理论,我们分析了系统中合作者比例随时间的变化及系统中流量的变化。结果显示,由于背叛者引入,系统中粒子的流动性降低了。这一模型可以用来描述行人交通或者生物交通(例如分子马达的运动)。
做为对单道交通的扩展,同时考虑到实际的道路交通,采用开边界条件,我们进一步研究了耦合了进化博弈理论的双道交通流模型。模拟发现,当驶入道路的车辆中合作车辆所占比例增加时,系统处于较低密度的自由流区域增加了,这说明对于车辆的道路交通,车辆之间的合作与互相谦让会增加车辆的流动性,从而提高道路的通行能力。
With the continuous development of social economy, traffic demand rapidly increases. Therefore, transportation problem gradually becomes an emergent world problem, which influences human life greatly and limits economy development. How to make full use of the finite traffic resource, how to find the potential of existing infrastructure, how to guide the traffic designing, planning and management with scientific theory and how to alleviate the rapidly growing traffic supply and demand, all these become important problems to be solved. The study of traffic flow theory emerges as the times require. Recently, as a new cross subject, traffic flow theory have been paid attention by scientists on these aspects of mechanics, physics, nonlinear science, information science, traffic engineering, statistics, computer science and so on. The purpose of traffic flow theory is to describe traffic property by applying the advanced science knowledge. By founding appropriate model, carrying out computer simulation and mathematic analysis, we hope to discover the essential characteristics of traffic flow, provide reliable proof for traffic planning and managenment.
After having sufficiently investigated the development of traffic flow theory, we put forward new traffic flow models according to the practical road situation. We have found a kind of nonlinear phenomena by simulation and theory analysis and discoved the physical characteristics of traffic models. The contents of the paper are as follows:
We put forward an impoved two-route traffic flow model, in which we modified the two unreasonable aspects in previous works:(1) at every time step, a new vehicle is generated at the entrance of two routes; (2) if a new vehicle is not able to enter the desired route, it will be deleted. In our modified model, at every time step, a vehicle reaches the entrance with probabilityλand if the vehicle can not enter the selected route, it will stop and wait at the entrance. Theλis a random number between 0 and 1.
In the first modified model, assume there is a limited speed bottleneck (for example, pedestrians go throught the road and a part of road is closed for working) on a route. We discussed the model in detail under mean velocity information feedback strategy and found that there exist four different system states in our model, i.e., zero state, periodic oscillation state, alternation state and equal velocity state. Furthermore, we also obtained the relationship between dynamic vehicles and critical vehicle arriving probability in zero state.
On top of the previous work mentioned above, we have the model further developed. In the second modified two-route traffic model, the two routes are unequal and a limited speed bottleneck is sited on the shorter route, which is denoted as unsymmetrical two-toute system. Correspondin gly, the two-route system with the same routes is denoted as symmetrical two-route system. Because the previous information feedback strategies are invalid, we adopted improved mean velocity information feedback and improved congestion coefficient information feedback to study our modified model. The simulation results showed that the average cost of drivers is dependence on the vehicle arriving probabilityλ. It is able to save time under the improved mean velocity information feedback strategy when theλis small. However, it can save time under the improved congestion coefficient information feedback strategy when theλis large.
In succession, we investiged the symmetrical and unsymmetrical two-route model when some static dynamic vehicle diobey the provided information. Simulation results showed that the high amplitude of average flux appearing on two routes is suppressed and the system capacity is enhanced. This indicates that, in some case (for example, drivers choose route in two-route system), it is not the best ways for divers obeying rules.
Because the practical traffic system consists of lots of vehicles, at the same time vehicles is controlled by drivers with mind, the vehicles in traffic system can happen to compete each other. The competion is able to be described by evolutionary game. In this paper, it is the first time to introduce the evolutionary game into the one-dimensional road traffic system. Firstly, we investigated one road with periodic boundary condition. The simulation results indicated that the system is possessed of nontrivial critical behavior. There exists a critical density in our model. For large density, the fraction of cooperator maintains a nonzero constant. Contrarily, for small density, the fraction of cooperator decays exponentially. The introducing of defector decreases the mobility of vehicles. This model is able to describe pedestrian or biological traffic.
As the extension for one road traffic, we have the model further developed and introduce the evolutionary game into two road traffic. Simulation results showed that when the share of cooperator increases, the region of low density enlarges, which indicates it can increase the mobility of vehicles when the share of cooperator increases.
本文作者在充分调查了交通流理论在国内外的发展情况以后,根据实际的交通状况,提出了更符合现实交通的模型,并通过数值模拟和理论分析,研究了交通流中出现的各种非线性现象,揭示了其物理本质。本文的主要工作如下：
提出了一个改进的双通道交通流模型。由于原来双通道交通模型存在两个明显的缺点：(1)在每一时间步,都会有一辆车到达系统的入口处；(2)当车辆不能驶入道路时,人为地将车辆剔除出去。然而,在高速道路交通中,很少存在每一秒到达一辆车的情况,并且如果车辆不能进入系统,应该停下来等待机会再次进入。鉴于这些实际情况,在本文提出的改进模型中改进了原来双通道模型的上述两个缺点：(1)假设在每一秒钟,车辆以概率λ到达双通道的入口处,其中λ是介于0到1之间的可调参数；(2)若在入口处车辆不能进入系统,则排队等候,直到能进入所选路径。
在改进模型中,我们首先假设在其中的一条道路上存在限速瓶颈(例如,行人穿马路、部分道路封闭施工等情况)。我们采用平均速度信息反馈策略对此模型进行了详细的数值模拟和数学分析。模拟结果表明系统存在四种物理状态：零态(zero state)、周期震荡态(periodic oscillation state)、交替态(alternation state)(即零态和周期震荡态交替出现)和等速度态(equal velocity state)(即系统中两条道路上车辆的平均速度近似相等)。并且,我们得到了系统处于零态时车辆到达概率与动态车比例之间的数学关系式。
紧接着上面的研究,我们进一步改进了双通道模型：组成模型的两条道路是不等长的,并且在较短路径上存在限速瓶颈,我们称这样的由两条不同道路组成的双通道系统为非对称系统。相应地,由两条完全相同的道路组成的系统称为对称系统。由于以前应用在对称双通道交通中的信息反馈策略不能直接应用于非对称双通道交通中,所以我们采用改进的平均速度反馈和改进的拥挤系数反馈研究非对称双通道系统。模拟结果表明,出行者平均出行时间与车辆到达概率λ有关,当λ较小时,采用改进的平均速度信息反馈策略能节省出行时间；当λ较大时,采用改进的拥挤系数信息反馈策略能节省出行时间。所以交通管理者要根据实际的交通情况指导交通,已达到高效的目的。
接着,针对对称双通道模型中采用行驶时间反馈策略出现的流量高幅震荡以及非对称双通道交通模型中出现的周期震荡态,我们调查了当部分动态车不遵守信息指示时的交通状态,模拟发现,对称系统及非对称系统中存在的大幅度震荡被压制了。系统的通行能力增加了,这说明,在某些情况下(例如双通道交通中进行路径选择时)司机太遵守规则反而达不到预想的效果。在这个改进模型中,我们首次研究了在何种情况下能降低双通道交通系统中道路上流量的震荡。
最后,我们提出了一种耦合演化博弈理论的一维交通流模型。考虑到实际交通流是由车辆组成的,而车辆是由具有自主意识的司机来操控的,所以组成交通流的个体之间会存在一定的冲突,这种冲突可以用进化的博弈理论来描述。因此,我们将进化博弈理论引进一维交通流模型中。首先采用周期性边界条件,研究了耦合进化博弈理论的单道交通模型。采用蒙特-卡罗方法对于单道交通模型进行模拟,结果显示,当道路上粒子密度小于临界密度时,经过短暂的暂态过程后,背叛者比例随时间呈指数衰减；当道路上粒子密度大于临界密度时,经过短暂的暂态过程后,背叛者比例不再随时间变化,而是保持为一个常数。我们将本文模型得到的临界行为与以前文献中模型的临界行为做了比较,初步解释了造成两种不同临界行为的原因可能是由于系统经历的过程不同引起的。采用平均场理论,我们分析了系统中合作者比例随时间的变化及系统中流量的变化。结果显示,由于背叛者引入,系统中粒子的流动性降低了。这一模型可以用来描述行人交通或者生物交通(例如分子马达的运动)。
做为对单道交通的扩展,同时考虑到实际的道路交通,采用开边界条件,我们进一步研究了耦合了进化博弈理论的双道交通流模型。模拟发现,当驶入道路的车辆中合作车辆所占比例增加时,系统处于较低密度的自由流区域增加了,这说明对于车辆的道路交通,车辆之间的合作与互相谦让会增加车辆的流动性,从而提高道路的通行能力。
With the continuous development of social economy, traffic demand rapidly increases. Therefore, transportation problem gradually becomes an emergent world problem, which influences human life greatly and limits economy development. How to make full use of the finite traffic resource, how to find the potential of existing infrastructure, how to guide the traffic designing, planning and management with scientific theory and how to alleviate the rapidly growing traffic supply and demand, all these become important problems to be solved. The study of traffic flow theory emerges as the times require. Recently, as a new cross subject, traffic flow theory have been paid attention by scientists on these aspects of mechanics, physics, nonlinear science, information science, traffic engineering, statistics, computer science and so on. The purpose of traffic flow theory is to describe traffic property by applying the advanced science knowledge. By founding appropriate model, carrying out computer simulation and mathematic analysis, we hope to discover the essential characteristics of traffic flow, provide reliable proof for traffic planning and managenment.
After having sufficiently investigated the development of traffic flow theory, we put forward new traffic flow models according to the practical road situation. We have found a kind of nonlinear phenomena by simulation and theory analysis and discoved the physical characteristics of traffic models. The contents of the paper are as follows:
We put forward an impoved two-route traffic flow model, in which we modified the two unreasonable aspects in previous works:(1) at every time step, a new vehicle is generated at the entrance of two routes; (2) if a new vehicle is not able to enter the desired route, it will be deleted. In our modified model, at every time step, a vehicle reaches the entrance with probabilityλand if the vehicle can not enter the selected route, it will stop and wait at the entrance. Theλis a random number between 0 and 1.
In the first modified model, assume there is a limited speed bottleneck (for example, pedestrians go throught the road and a part of road is closed for working) on a route. We discussed the model in detail under mean velocity information feedback strategy and found that there exist four different system states in our model, i.e., zero state, periodic oscillation state, alternation state and equal velocity state. Furthermore, we also obtained the relationship between dynamic vehicles and critical vehicle arriving probability in zero state.
On top of the previous work mentioned above, we have the model further developed. In the second modified two-route traffic model, the two routes are unequal and a limited speed bottleneck is sited on the shorter route, which is denoted as unsymmetrical two-toute system. Correspondin gly, the two-route system with the same routes is denoted as symmetrical two-route system. Because the previous information feedback strategies are invalid, we adopted improved mean velocity information feedback and improved congestion coefficient information feedback to study our modified model. The simulation results showed that the average cost of drivers is dependence on the vehicle arriving probabilityλ. It is able to save time under the improved mean velocity information feedback strategy when theλis small. However, it can save time under the improved congestion coefficient information feedback strategy when theλis large.
In succession, we investiged the symmetrical and unsymmetrical two-route model when some static dynamic vehicle diobey the provided information. Simulation results showed that the high amplitude of average flux appearing on two routes is suppressed and the system capacity is enhanced. This indicates that, in some case (for example, drivers choose route in two-route system), it is not the best ways for divers obeying rules.
Because the practical traffic system consists of lots of vehicles, at the same time vehicles is controlled by drivers with mind, the vehicles in traffic system can happen to compete each other. The competion is able to be described by evolutionary game. In this paper, it is the first time to introduce the evolutionary game into the one-dimensional road traffic system. Firstly, we investigated one road with periodic boundary condition. The simulation results indicated that the system is possessed of nontrivial critical behavior. There exists a critical density in our model. For large density, the fraction of cooperator maintains a nonzero constant. Contrarily, for small density, the fraction of cooperator decays exponentially. The introducing of defector decreases the mobility of vehicles. This model is able to describe pedestrian or biological traffic.
As the extension for one road traffic, we have the model further developed and introduce the evolutionary game into two road traffic. Simulation results showed that when the share of cooperator increases, the region of low density enlarges, which indicates it can increase the mobility of vehicles when the share of cooperator increases.
引文
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