元胞自动机交通流模型中的相变现象和解析研究
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摘要
交通运输能力对一个国家经济的发展起着重要的支撑作用。较高的交通运输能力可以减少人们的旅行时间,提高工作效率,促进资源更好更快捷的流通。一个国家或城市的交通运输状况已经成为衡量该地区增长潜力的重要标志。
当前经济的迅速发展与交通建设的相对滞后,已构成非常突出的世界性难题。虽然一直以来各国政府对交通的改善投入了巨资,但是交通拥堵现象还未从根本上得以解决。此外在世界范围内,每年因交通堵塞和尾气过量排放造成的污染环境等问题,造成了巨大的经济损失。
如何充分地利用现有的交通资源,采用科学的理论来指导交通的规划、设计、管理和控制,成为急需解决的问题。交通流研究作为一门新兴的交叉性学科便由此诞生。
交通流研究除了具有上述工程价值,还具有非常重要的科学意义。因为交通系统是由大量存在相互作用的车辆(非牛顿力)组成。可以将其看做一种远离平衡态的系统。交通流研究可以帮助我们进一步认识人类社会中具有复杂相互作用的系统在远离平衡态时的演化规律。促进统计物理、非线性力学、流体力学、应用数学和交通工程等学科的交叉发展。
全文的工作和主要创新如下：
1.采用元胞自动机方法,研究了信号灯控制的单个T形交叉口的交通流。我们采用具有三个相的信号灯来解决交叉口的车辆冲突。首先,我们采用现实中经常使用的固定的信号灯切换顺序和信号灯周期策略。通过计算机数值模拟得到了系统的相图和总流量。并且与没有信号灯控制的模型的结果进行了比较。发现在某些情况下,固定的信号灯切换顺序策略在控制交叉口时效果并不好。
2.因此,我们接着又提出了一种新的信号灯控制策略：自适应的信号灯切换顺序策略。通过数值模拟,得到了新策略下系统的相图、流量和平均行驶时间。并和固定的切换顺序策略的结果进行了比较。模拟结果显示自适应信号灯策略好于固定切换顺序控制策略。
3.以往的二维元胞自动机模型中的车辆都是按照并行更新规则行驶。而我们将二维元胞自动机模型Biham-Middleton-Levine(BML)模型改为随机更新。在周期性边界条件下,系统从自由流相到堵塞相的相变为一阶相变。BML模型中的中间态由于随机更新而消失。在开放边界条件下,我们发现了自由流相和堵塞相共存的现象。共存相中的自由流区域的面积不随系统尺寸的变化。我们对自由流相进行了平均场分析。这个平均场方法成功地考虑了相关性并和模拟结果符合的很好。
4.我们基于BML模型研究了随机慢化对城市交通动力学的影响。在周期性边界条件下,从自由流相到堵塞相的相变是一阶相变。原先BML模型中的中间态由于随机慢化的引入而消失。自由流相的平均速度和临界密度随着随机慢化概率的增加而减小。尽管并行更新模型中的相关性很强,我们还是发展了一种新的解析方法。这种解析方法成功地得到了自由流相的平均速度。在开放边界条件下,系统只存在两个相,不存在最大流量相。我们同样采用平均场方法得到了自由流相的平均速度、密度、流量和入口概率之间的关系。
5.我们还基于BML模型研究了驾驶员闯红灯行为对城市交通动力学的影响。根据闯红灯者身份是否是固定的,我们分别研究了两个模型。模型Ⅰ中的驾闯红灯车辆不是固定的,在每个时间步是随机选择的。模型Ⅱ中的闯红灯车辆是在初始时刻随机选择的,并在以后的时间步中一直固定不变。虽然两个模型相似,但它们的结果却并不相同。模型Ⅰ在各种闯红灯者的比例下都会出现中间态。由于闯红灯者的出现,自由流相的平均速度增加了,但是临界密度阈值降低了。但是临界密度阈值随闯红灯者比例不是单调变化的。自由流相下车辆分布比较随机和均匀。因此可以通过忽略相关性得到自由流相平均速度的表达式。在模型Ⅱ中,只有在闯红灯者的比例为pv=1时才会出现中间态。这是由于堵塞前沿的头车一直被另外一个方向的车辆阻挡。系统的临界阈值随着pv的增加而减小。然而在pv=1时,它又突然增加。这是由于在自由流条带中出现很长的尾巴。一旦尾巴和上游的条带接触并相互作用,很有可能导致堵塞。我们在自由流相中发现了一种新的位形。新位形中条带的斜率不同于BML模型的自组织条带的斜率。我们同样对自由流相的平均速度进行了平均场解析,并和模拟结果符合的很好。
6. BML模型是建立在周期性的规则网格上,其中每个格点表示一个十字路口。而在实际的城市网络中,两个交叉口之间是由一条道路组成的。因此我们提出了一个接近真实的、类似于曼哈顿城市系统的元胞自动机交通流模型。数值模拟发现这个系统存在三个状态：自由流态,饱和态和全局堵塞态。系统从饱和态到全局堵塞态的相变区域是亚稳定的。我们采用网格粗粒化方法得到了自由态和饱和态的车辆分布。发现了一些有趣的车辆分布结构：风车形,T恤衫形和Y形。我们还研究了先进的旅行者信息系统(ATIS),交通灯周期和交通灯切换策略对系统的影响。
Traffic transport capacity plays an important role for the development of national economy. The higher transport capacity could improve efficiency, reduce the travel time and promote the circulation of materials. The transportation situation has been an important index to judge the growth potential of a country.
The inharmony between the rapid development of the social economy and the slow speed of transportation constrcution has become a serious problem all over the world. Although governments around the world have invested heavily on transportation, the traffic jam phenomena have not been solved fundamentally. The traffic congestion and environment pollution created by gas emission have caused a huge economic loss.
How to utilize the current traffic resources adequately, how to use the scientific theory to guide the traffic planning, designing, management and controlling, all of these have become urgent problems now. Thus, the traffic flow theory is emerging as an interdiscipline.
Besides the engineering application, the research of traffic flow theory also has the important scientific significance. The transportation system is composed of a huge number of interacting vehicles. The traffic system is a system which is far from equilibrium. The research of traffic flow will help us to understand the laws of complex systems which are far from quilibrium better and promote the cross of the subjects such as statistical physics, nonlinear dynamics, fluid mechanics, applied mathematics, traffic engeering.
The contents of the paper are as follows:
1. Traffic flow at a signal controlled T-shaped intersection has been investigated by the cellular automata model. The three phase traffic signal is used to control the conflicts of vehicles. Firstly, traffic signal with fixed period and signal phase order is used. The phase diagram and capacity of the system are investigated and compared with that of previous unsignalized model. Simulation results shows that fixed signal phase order strategy does not perform better in some special cases.
2. Thus, we introduced another type of signal controlling strategy, i.e., adaptive signal phase order strategy. The phase diagram, the capacity and the average travel time of the system are investigated and compared with that of fixed signal phase order strategy. The simulation results show that the traffic adaptive signal strategy is better than the fixed signal phase order strategy.
3. The state of car is updated in parallel in previous two-dimensional cellular automata models. A stochastic version of the Biham-Middleton-Levine (BML) model with random update rule is studied. It is shown that under periodic boundary condition, the system exhibits a sharp transition from moving phase to jamming phase. The intermediate stable phase observed in the original deterministic BML model disappears due to the random update rule. Under open boundary condition, the coexistence of moving phase and jamming phase can be observed. The size of the moving phase is roughly the same under different system sizes. We have presented a mean-field analysis for the moving phase, which successfully takes into account the correlation and produces good agreement with simulation results.
4. Effects of randomization on urban traffic dynamics are studied based on the BML model. It is found that the average velocity exhibits a first-order phase transition from moving phase to jamming phase under periodic boundary conditions. The intermediate stable phase identified in the original deterministic BML model disappears with the introduction of randomization. The average velocity in the moving phase and the critical car density decrease as the randomization probability increases. We have developed a mean-field theory which successfully predicts the average velocity in the moving phase. Under open boundary conditions, there are only two phases and the maximum current phase does not occur. The dependence of the average velocity, the density and the flow rate on the injection probability in the moving phase have also been obtained through the mean-field theory.
5. Effects of violating traffic light rule on urban traffic dynamics are studied based on the BML model. There are two models according to wether the violators are fixed or not. In model Ⅱ, the violators are selected randomly at each time step. In model Ⅱ, some drivers play the role of violator until the end of simulation after choosing as violator randomly at the beginning of simulation. Although the two models are similar, the results are different.
In model I, the intermediate phase could be found at any violator's ratio pv Simulation results show that the violator increases the average velocity of free flowing phase while decreases the threshold from free flowing phase to jam. However, the threshold does not decrease monotonously with pv. In the free flowing phase, the cars are distributed randomly and homogeneously. Thus the velocity of free flowing phase could be obtained by ignoring the correlation.
In model Ⅱ, the intermediate phase could only be found when pv=1. Because the leading car in the jam front is always hindered by cars of other direction. Simulation results show that the threshold decreases with the increase of pv. However, at pv=1, it suddenly increases. Because there are long tails stretching in the upstream direction of the stripes. Once the tails reach and interact with the upstream stripes, jam might be induced. A new kind of configuration with stripe slope different from that of BML model has been found in the free flowing phase. We have developed an analytical investigation which successfully predicts the average velocity in the free flowing phase.
6. The BML model is defined on the periodic regular lattice and each lattice site represents a crossing. However, there is a road between two successive crossings in the real city network. Thus a cellular automaton model of vehicular traffic in a Manhattan-like urban system is proposed.
The system exhibits three diffierent states, i.e. moving state, saturation state and global deadlock state. A metastability of the system is observed in the transition from the saturation state to the global deadlock state. With a grid coarsening method, vehicle distribution in the moving state and the saturation state has been studied. Interesting structures (e.g. windmill-like ones, T-shirt-like ones, Y-like ones) have been revealed. The effect of an advanced traveller information system (ATIS), the traffic light period and the traffic light switch strategy have also been investigated.
当前经济的迅速发展与交通建设的相对滞后,已构成非常突出的世界性难题。虽然一直以来各国政府对交通的改善投入了巨资,但是交通拥堵现象还未从根本上得以解决。此外在世界范围内,每年因交通堵塞和尾气过量排放造成的污染环境等问题,造成了巨大的经济损失。
如何充分地利用现有的交通资源,采用科学的理论来指导交通的规划、设计、管理和控制,成为急需解决的问题。交通流研究作为一门新兴的交叉性学科便由此诞生。
交通流研究除了具有上述工程价值,还具有非常重要的科学意义。因为交通系统是由大量存在相互作用的车辆(非牛顿力)组成。可以将其看做一种远离平衡态的系统。交通流研究可以帮助我们进一步认识人类社会中具有复杂相互作用的系统在远离平衡态时的演化规律。促进统计物理、非线性力学、流体力学、应用数学和交通工程等学科的交叉发展。
全文的工作和主要创新如下：
1.采用元胞自动机方法,研究了信号灯控制的单个T形交叉口的交通流。我们采用具有三个相的信号灯来解决交叉口的车辆冲突。首先,我们采用现实中经常使用的固定的信号灯切换顺序和信号灯周期策略。通过计算机数值模拟得到了系统的相图和总流量。并且与没有信号灯控制的模型的结果进行了比较。发现在某些情况下,固定的信号灯切换顺序策略在控制交叉口时效果并不好。
2.因此,我们接着又提出了一种新的信号灯控制策略：自适应的信号灯切换顺序策略。通过数值模拟,得到了新策略下系统的相图、流量和平均行驶时间。并和固定的切换顺序策略的结果进行了比较。模拟结果显示自适应信号灯策略好于固定切换顺序控制策略。
3.以往的二维元胞自动机模型中的车辆都是按照并行更新规则行驶。而我们将二维元胞自动机模型Biham-Middleton-Levine(BML)模型改为随机更新。在周期性边界条件下,系统从自由流相到堵塞相的相变为一阶相变。BML模型中的中间态由于随机更新而消失。在开放边界条件下,我们发现了自由流相和堵塞相共存的现象。共存相中的自由流区域的面积不随系统尺寸的变化。我们对自由流相进行了平均场分析。这个平均场方法成功地考虑了相关性并和模拟结果符合的很好。
4.我们基于BML模型研究了随机慢化对城市交通动力学的影响。在周期性边界条件下,从自由流相到堵塞相的相变是一阶相变。原先BML模型中的中间态由于随机慢化的引入而消失。自由流相的平均速度和临界密度随着随机慢化概率的增加而减小。尽管并行更新模型中的相关性很强,我们还是发展了一种新的解析方法。这种解析方法成功地得到了自由流相的平均速度。在开放边界条件下,系统只存在两个相,不存在最大流量相。我们同样采用平均场方法得到了自由流相的平均速度、密度、流量和入口概率之间的关系。
5.我们还基于BML模型研究了驾驶员闯红灯行为对城市交通动力学的影响。根据闯红灯者身份是否是固定的,我们分别研究了两个模型。模型Ⅰ中的驾闯红灯车辆不是固定的,在每个时间步是随机选择的。模型Ⅱ中的闯红灯车辆是在初始时刻随机选择的,并在以后的时间步中一直固定不变。虽然两个模型相似,但它们的结果却并不相同。模型Ⅰ在各种闯红灯者的比例下都会出现中间态。由于闯红灯者的出现,自由流相的平均速度增加了,但是临界密度阈值降低了。但是临界密度阈值随闯红灯者比例不是单调变化的。自由流相下车辆分布比较随机和均匀。因此可以通过忽略相关性得到自由流相平均速度的表达式。在模型Ⅱ中,只有在闯红灯者的比例为pv=1时才会出现中间态。这是由于堵塞前沿的头车一直被另外一个方向的车辆阻挡。系统的临界阈值随着pv的增加而减小。然而在pv=1时,它又突然增加。这是由于在自由流条带中出现很长的尾巴。一旦尾巴和上游的条带接触并相互作用,很有可能导致堵塞。我们在自由流相中发现了一种新的位形。新位形中条带的斜率不同于BML模型的自组织条带的斜率。我们同样对自由流相的平均速度进行了平均场解析,并和模拟结果符合的很好。
6. BML模型是建立在周期性的规则网格上,其中每个格点表示一个十字路口。而在实际的城市网络中,两个交叉口之间是由一条道路组成的。因此我们提出了一个接近真实的、类似于曼哈顿城市系统的元胞自动机交通流模型。数值模拟发现这个系统存在三个状态：自由流态,饱和态和全局堵塞态。系统从饱和态到全局堵塞态的相变区域是亚稳定的。我们采用网格粗粒化方法得到了自由态和饱和态的车辆分布。发现了一些有趣的车辆分布结构：风车形,T恤衫形和Y形。我们还研究了先进的旅行者信息系统(ATIS),交通灯周期和交通灯切换策略对系统的影响。
Traffic transport capacity plays an important role for the development of national economy. The higher transport capacity could improve efficiency, reduce the travel time and promote the circulation of materials. The transportation situation has been an important index to judge the growth potential of a country.
The inharmony between the rapid development of the social economy and the slow speed of transportation constrcution has become a serious problem all over the world. Although governments around the world have invested heavily on transportation, the traffic jam phenomena have not been solved fundamentally. The traffic congestion and environment pollution created by gas emission have caused a huge economic loss.
How to utilize the current traffic resources adequately, how to use the scientific theory to guide the traffic planning, designing, management and controlling, all of these have become urgent problems now. Thus, the traffic flow theory is emerging as an interdiscipline.
Besides the engineering application, the research of traffic flow theory also has the important scientific significance. The transportation system is composed of a huge number of interacting vehicles. The traffic system is a system which is far from equilibrium. The research of traffic flow will help us to understand the laws of complex systems which are far from quilibrium better and promote the cross of the subjects such as statistical physics, nonlinear dynamics, fluid mechanics, applied mathematics, traffic engeering.
The contents of the paper are as follows:
1. Traffic flow at a signal controlled T-shaped intersection has been investigated by the cellular automata model. The three phase traffic signal is used to control the conflicts of vehicles. Firstly, traffic signal with fixed period and signal phase order is used. The phase diagram and capacity of the system are investigated and compared with that of previous unsignalized model. Simulation results shows that fixed signal phase order strategy does not perform better in some special cases.
2. Thus, we introduced another type of signal controlling strategy, i.e., adaptive signal phase order strategy. The phase diagram, the capacity and the average travel time of the system are investigated and compared with that of fixed signal phase order strategy. The simulation results show that the traffic adaptive signal strategy is better than the fixed signal phase order strategy.
3. The state of car is updated in parallel in previous two-dimensional cellular automata models. A stochastic version of the Biham-Middleton-Levine (BML) model with random update rule is studied. It is shown that under periodic boundary condition, the system exhibits a sharp transition from moving phase to jamming phase. The intermediate stable phase observed in the original deterministic BML model disappears due to the random update rule. Under open boundary condition, the coexistence of moving phase and jamming phase can be observed. The size of the moving phase is roughly the same under different system sizes. We have presented a mean-field analysis for the moving phase, which successfully takes into account the correlation and produces good agreement with simulation results.
4. Effects of randomization on urban traffic dynamics are studied based on the BML model. It is found that the average velocity exhibits a first-order phase transition from moving phase to jamming phase under periodic boundary conditions. The intermediate stable phase identified in the original deterministic BML model disappears with the introduction of randomization. The average velocity in the moving phase and the critical car density decrease as the randomization probability increases. We have developed a mean-field theory which successfully predicts the average velocity in the moving phase. Under open boundary conditions, there are only two phases and the maximum current phase does not occur. The dependence of the average velocity, the density and the flow rate on the injection probability in the moving phase have also been obtained through the mean-field theory.
5. Effects of violating traffic light rule on urban traffic dynamics are studied based on the BML model. There are two models according to wether the violators are fixed or not. In model Ⅱ, the violators are selected randomly at each time step. In model Ⅱ, some drivers play the role of violator until the end of simulation after choosing as violator randomly at the beginning of simulation. Although the two models are similar, the results are different.
In model I, the intermediate phase could be found at any violator's ratio pv Simulation results show that the violator increases the average velocity of free flowing phase while decreases the threshold from free flowing phase to jam. However, the threshold does not decrease monotonously with pv. In the free flowing phase, the cars are distributed randomly and homogeneously. Thus the velocity of free flowing phase could be obtained by ignoring the correlation.
In model Ⅱ, the intermediate phase could only be found when pv=1. Because the leading car in the jam front is always hindered by cars of other direction. Simulation results show that the threshold decreases with the increase of pv. However, at pv=1, it suddenly increases. Because there are long tails stretching in the upstream direction of the stripes. Once the tails reach and interact with the upstream stripes, jam might be induced. A new kind of configuration with stripe slope different from that of BML model has been found in the free flowing phase. We have developed an analytical investigation which successfully predicts the average velocity in the free flowing phase.
6. The BML model is defined on the periodic regular lattice and each lattice site represents a crossing. However, there is a road between two successive crossings in the real city network. Thus a cellular automaton model of vehicular traffic in a Manhattan-like urban system is proposed.
The system exhibits three diffierent states, i.e. moving state, saturation state and global deadlock state. A metastability of the system is observed in the transition from the saturation state to the global deadlock state. With a grid coarsening method, vehicle distribution in the moving state and the saturation state has been studied. Interesting structures (e.g. windmill-like ones, T-shirt-like ones, Y-like ones) have been revealed. The effect of an advanced traveller information system (ATIS), the traffic light period and the traffic light switch strategy have also been investigated.
引文
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