路口瓶颈处交通状态的相图及元胞自动机模型研究
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摘要
如今,交通拥堵已经成为城市公害,它增加能源消耗,导致环境污染,成为制约我国大中城市可持续发展的主要瓶颈,严重影响经济建设。解决交通拥堵的根本出路在于发展交通科学技术,开展交通流理论研究。交通流理论研究的目标是建立能描述实际交通一般特性的交通流模型,寻找交通流的基本规律,以揭示交通拥堵产生的机理。只有这样,才有可能实现从”治标”到”治本”的转化,为现代城市的可持续快速发展提供基本保障。因此,很有必要开展交通流理论的研究。
元胞自动机是一种空间、时间和变量均离散的数学模型,具有算法简单、物理图像清晰、并行程度高等优越的特点。元胞自动机方法和相关的建模技术是描述、认识和模拟复杂系统行为的强有力的方法。如今,它已被广泛用于交通系统的研究,各种元胞自动机交通流模型也已陆续地被提出。由于在该模型中便于考虑各种实际交通因素,因此正被广泛用于研究交通流的各种复杂现象。
基于交通动力学研究的复杂性和丰富性的特征,并在对国内外交通流理论的研究动态充分调研的基础上,本论文选取了若干受到广泛关注的动力学问题进行研究。研究内容包括一维、二维交通流的建模与模拟,路口瓶颈处交通流的数值模拟及理论分析研究。
首先,一维元胞自动机交通流模型的研究：
1、经典的Nagel-Schreckenberg模型中的随机慢化规则可以捕捉由于人的行为、各种外界条件等因素导致的固有的速度涨落,是产生自发的阻塞现象的关键,同时也引入了驾驶员因随机刹车导致的过度反应。本论文对其随机慢化规则进行了改进：当车辆的期望速度小于它本身的车头距时,以及车辆以速度等于1行驶时且等于车头距情况下,车辆也无需随机慢化；由于在单车道模型中不允许超车,只有当某个车辆的期望速度等于它车头距时,考虑到行车安全,车辆需要以一定的概率进行慢化。计算机模拟表明,本文改进模型的基本图敏感地依赖于延迟概率。与Nagel-Schreckenberg模型相比,本文模型中系统的最大流量值更接近实际道路测量结果,速度分布更为合理。因而,本文模型更适合模拟实际道路交通。
2、本论文研究一维混合交通流的车间距的分布特性。计算机模拟表明,对于给定混合比例的系统,在低密度及中间密度情况下,其车间距分布情况因随机慢化概率不同而不同。对于给定随机慢化概率的系统,在低密度的情况下,混合比例系数对其车间距的分布有很大的影响。
其次,构建路口瓶颈处交通状态的相图：
1、本论文研究了由两条相互垂直的单车道构成的十字路口交通流模型的相图,此两车道均采用周期边界条件且并行更新。车辆的更新采用Fukui-Ishibashi确定性模型的演化规则且在十字路口处车辆不允许转向。其中,如果在十字路口上游的两条道上各有一辆车要占据或经过十字路口,需要遵循收益动力学的减速规则。依据构建相图的原则,本论文绘制了各种最大速度情况下的流量相图,通过比较发现它们均具有不同的拓扑结构,其结构与最大速度有关。并采用理论分析的方法推导了相图中各个区域的流量公式,这些结果也被计算机模拟所证实。
2、类似于上面的研究,只不过模型中车辆的更新采用Nagel-Schreckenberg确定性模型的演化规则。本部分也绘制了各种最大速度情况下的流量相图,也采用理论的方法推导了相图中各个区域的流量公式。本论文中采用的理论分析方法不仅简单,而且可能被广泛地应用于其它交通瓶颈问题的研究。
最后,提出了车辆可以换道的二维Bihan-Middleton-Levine元胞自动机交通流模型：
本论文在经典的Biham-Middleton-Levine模型基础上,建立了较符合实际交通情况的车辆可以换道的二维城市交通模型。通过对正方形及长方形网格的交通系统进行计算机模拟,结果均发现新的自由流位形图,以及一些新的中间态,且中间态能维持在较大的密度范围内。
Traffic congestion has become a national urban public nuisance. It has resulted in the increase of energy consumption, environmental pollution and has become a ma-jor bottleneck restricting the sustainable development of large and medium-sized cities in China. Consequently, it has a great impact on economic development. The fun-damental way to solve the traffic congestion problem is to develop the transportation science and technology and carry out the study of traffic flow theory. The objective of the study of traffic flow theory is to establish traffic flow model which can describe general characteristics of actual traffic, find the basic law of traffic flow and then reveal mechanism of traffic congestion. Only in this way, we can achieve the transformation from "symptoms" to "disease" and provide basic protection for sustainable and rapid development of modern city. Therefore, it is necessary to study traffic flow theory.
Cellular automata is a mathematical model which is discrete in space, time and variables. It has many great characteristics, such as simple algorithm, clear physi-cal pictures and high degree of parallelism. Cellular automata methods and relevant modeling techniques are powerful way to describe, perceive and simulate behaviors of complex system. Nowadays, cellular automata have been widely used in research of the transport system and a variety of cellular automata traffic flow models have also been proposed. Due to the fact that it is easy to consider various actual traffic factors in the model, it is widely used to study the various complex phenomena of traffic flow.
Based on the complexity and richness of the traffic dynamics research, we first survey domestic and overseas relevant research developments of traffic flow theory, and then study a number of popular dynamics issues. The research contents include modeling and simulations of one-dimensional, two-dimensional traffic flow; computer simulations and theoretical analysis of traffic flow in the intersection bottlenecks.
First of all, this dissertation has studied a one-dimensional cellular automata traffic flow model:
1. In the evolutionary rules of the classical Nagel-Schreckenberg model, the ran-domization rule captures natural speed fluctuations due to human behavior or varying external conditions. This rule introduces overreactions of drivers when braking, pro-viding the key to the formation of spontaneously emerging jams. In this dissertation, the randomization rule is improved as follows:compared with the case that velocities are equal to or greater than2, it is notable that vehicles moving at their lower velocity1are relatively safe and the randomization rule may be neglected (not be considered). Here, none of vehicles is permitted to overtake in one lane, so the vehicle velocities must be less or equal to their corresponding gaps. That is to say, vehicle needs to slow down when their velocities equal their corresponding gaps and are no less than2. Ac-cording to simulation results, it has been found that the structure of the fundamental diagram of the new model is sensitively dependent on the values of the delay probabil-ity.In comparison with the Nagel-Schreckenberg model, one notes that the maximum flow value of the fundamental diagram in our model is more consistent with the results measured in the real traffic,and the velocity distributions of our model are relatively reasonable. Thus, our model is more fit for simulating actual traffic.
2. Using the cellular automaton traffic flow model, we have studied the vehicle gap distribution of the mixed traffic flow. By computer simulations, one notes that the vehicle gap distribution varies with the delay probability in the case of low and intermediate vehicle density for the system with given mixing rate. Furthermore, one notes that the mixing rate has great effect on the vehicle gap distribution in the case of low vehicle density for system with given delay probability.
Secondly, this dissertation has mapped out phase diagrams of traffic states in the intersection bottlenecks:
1. This dissertation has studied phase diagrams of traffic flow at an unsignalized intersection consisting of two perpendicular one-lane roads where periodic boundary conditions are adopted and parallel update rules are employed. One simulates the mo-tion of vehicles by using deterministic Fukui-Ishibashi cellular automata traffic model. Vehicles are not allowed to turn at the intersection. At the intersection, if conflict hap-pens, the yielding dynamics will be implemented. Based on the principles for making phase diagrams, we have presented the phase diagrams for the cases of various maxi-mum vehicle velocities, and it is noted that the phase diagrams have several different topology structures which are shaped by maximum velocities. The flow formulas in all regions in the phase diagram have been derived. The results of theoretical analysis are in good agreement with simulation ones.
2. Similar to the studies above, the following study allows vehicles to adopt the evolutionary rules of the deterministic Nagel-Schreckenberg cellular automata traffic model. We have also presented the phase diagrams for the cases of various maximum vehicle velocities. The flow formula in all regions in phase diagrams have also been deduced by the same way of the theoretical method. The theoretical analysis approach used in this dissertation is not only simple but also may be widely used in the study of other bottlenecks.
Last but not least, this dissertation has put forward a two-dimensional cellular automata traffic flow model where vehicles can change lanes:
Based on the classical Biham-Middleton-Levine model, this dissertation has es-tablished a two-dimensional urban traffic flow model where vehicles can change lanes. Comparatively speaking, this model can simulate actual traffic better. By using numer-ical simulations on the square and rectangular grid traffic systems, some new config-uration graphs have been found in free flow regime. In addition, some intermediate stable phases, where jams and freely flowing traffic coexist, have been discovered and stay within larger density range.
元胞自动机是一种空间、时间和变量均离散的数学模型,具有算法简单、物理图像清晰、并行程度高等优越的特点。元胞自动机方法和相关的建模技术是描述、认识和模拟复杂系统行为的强有力的方法。如今,它已被广泛用于交通系统的研究,各种元胞自动机交通流模型也已陆续地被提出。由于在该模型中便于考虑各种实际交通因素,因此正被广泛用于研究交通流的各种复杂现象。
基于交通动力学研究的复杂性和丰富性的特征,并在对国内外交通流理论的研究动态充分调研的基础上,本论文选取了若干受到广泛关注的动力学问题进行研究。研究内容包括一维、二维交通流的建模与模拟,路口瓶颈处交通流的数值模拟及理论分析研究。
首先,一维元胞自动机交通流模型的研究：
1、经典的Nagel-Schreckenberg模型中的随机慢化规则可以捕捉由于人的行为、各种外界条件等因素导致的固有的速度涨落,是产生自发的阻塞现象的关键,同时也引入了驾驶员因随机刹车导致的过度反应。本论文对其随机慢化规则进行了改进：当车辆的期望速度小于它本身的车头距时,以及车辆以速度等于1行驶时且等于车头距情况下,车辆也无需随机慢化；由于在单车道模型中不允许超车,只有当某个车辆的期望速度等于它车头距时,考虑到行车安全,车辆需要以一定的概率进行慢化。计算机模拟表明,本文改进模型的基本图敏感地依赖于延迟概率。与Nagel-Schreckenberg模型相比,本文模型中系统的最大流量值更接近实际道路测量结果,速度分布更为合理。因而,本文模型更适合模拟实际道路交通。
2、本论文研究一维混合交通流的车间距的分布特性。计算机模拟表明,对于给定混合比例的系统,在低密度及中间密度情况下,其车间距分布情况因随机慢化概率不同而不同。对于给定随机慢化概率的系统,在低密度的情况下,混合比例系数对其车间距的分布有很大的影响。
其次,构建路口瓶颈处交通状态的相图：
1、本论文研究了由两条相互垂直的单车道构成的十字路口交通流模型的相图,此两车道均采用周期边界条件且并行更新。车辆的更新采用Fukui-Ishibashi确定性模型的演化规则且在十字路口处车辆不允许转向。其中,如果在十字路口上游的两条道上各有一辆车要占据或经过十字路口,需要遵循收益动力学的减速规则。依据构建相图的原则,本论文绘制了各种最大速度情况下的流量相图,通过比较发现它们均具有不同的拓扑结构,其结构与最大速度有关。并采用理论分析的方法推导了相图中各个区域的流量公式,这些结果也被计算机模拟所证实。
2、类似于上面的研究,只不过模型中车辆的更新采用Nagel-Schreckenberg确定性模型的演化规则。本部分也绘制了各种最大速度情况下的流量相图,也采用理论的方法推导了相图中各个区域的流量公式。本论文中采用的理论分析方法不仅简单,而且可能被广泛地应用于其它交通瓶颈问题的研究。
最后,提出了车辆可以换道的二维Bihan-Middleton-Levine元胞自动机交通流模型：
本论文在经典的Biham-Middleton-Levine模型基础上,建立了较符合实际交通情况的车辆可以换道的二维城市交通模型。通过对正方形及长方形网格的交通系统进行计算机模拟,结果均发现新的自由流位形图,以及一些新的中间态,且中间态能维持在较大的密度范围内。
Traffic congestion has become a national urban public nuisance. It has resulted in the increase of energy consumption, environmental pollution and has become a ma-jor bottleneck restricting the sustainable development of large and medium-sized cities in China. Consequently, it has a great impact on economic development. The fun-damental way to solve the traffic congestion problem is to develop the transportation science and technology and carry out the study of traffic flow theory. The objective of the study of traffic flow theory is to establish traffic flow model which can describe general characteristics of actual traffic, find the basic law of traffic flow and then reveal mechanism of traffic congestion. Only in this way, we can achieve the transformation from "symptoms" to "disease" and provide basic protection for sustainable and rapid development of modern city. Therefore, it is necessary to study traffic flow theory.
Cellular automata is a mathematical model which is discrete in space, time and variables. It has many great characteristics, such as simple algorithm, clear physi-cal pictures and high degree of parallelism. Cellular automata methods and relevant modeling techniques are powerful way to describe, perceive and simulate behaviors of complex system. Nowadays, cellular automata have been widely used in research of the transport system and a variety of cellular automata traffic flow models have also been proposed. Due to the fact that it is easy to consider various actual traffic factors in the model, it is widely used to study the various complex phenomena of traffic flow.
Based on the complexity and richness of the traffic dynamics research, we first survey domestic and overseas relevant research developments of traffic flow theory, and then study a number of popular dynamics issues. The research contents include modeling and simulations of one-dimensional, two-dimensional traffic flow; computer simulations and theoretical analysis of traffic flow in the intersection bottlenecks.
First of all, this dissertation has studied a one-dimensional cellular automata traffic flow model:
1. In the evolutionary rules of the classical Nagel-Schreckenberg model, the ran-domization rule captures natural speed fluctuations due to human behavior or varying external conditions. This rule introduces overreactions of drivers when braking, pro-viding the key to the formation of spontaneously emerging jams. In this dissertation, the randomization rule is improved as follows:compared with the case that velocities are equal to or greater than2, it is notable that vehicles moving at their lower velocity1are relatively safe and the randomization rule may be neglected (not be considered). Here, none of vehicles is permitted to overtake in one lane, so the vehicle velocities must be less or equal to their corresponding gaps. That is to say, vehicle needs to slow down when their velocities equal their corresponding gaps and are no less than2. Ac-cording to simulation results, it has been found that the structure of the fundamental diagram of the new model is sensitively dependent on the values of the delay probabil-ity.In comparison with the Nagel-Schreckenberg model, one notes that the maximum flow value of the fundamental diagram in our model is more consistent with the results measured in the real traffic,and the velocity distributions of our model are relatively reasonable. Thus, our model is more fit for simulating actual traffic.
2. Using the cellular automaton traffic flow model, we have studied the vehicle gap distribution of the mixed traffic flow. By computer simulations, one notes that the vehicle gap distribution varies with the delay probability in the case of low and intermediate vehicle density for the system with given mixing rate. Furthermore, one notes that the mixing rate has great effect on the vehicle gap distribution in the case of low vehicle density for system with given delay probability.
Secondly, this dissertation has mapped out phase diagrams of traffic states in the intersection bottlenecks:
1. This dissertation has studied phase diagrams of traffic flow at an unsignalized intersection consisting of two perpendicular one-lane roads where periodic boundary conditions are adopted and parallel update rules are employed. One simulates the mo-tion of vehicles by using deterministic Fukui-Ishibashi cellular automata traffic model. Vehicles are not allowed to turn at the intersection. At the intersection, if conflict hap-pens, the yielding dynamics will be implemented. Based on the principles for making phase diagrams, we have presented the phase diagrams for the cases of various maxi-mum vehicle velocities, and it is noted that the phase diagrams have several different topology structures which are shaped by maximum velocities. The flow formulas in all regions in the phase diagram have been derived. The results of theoretical analysis are in good agreement with simulation ones.
2. Similar to the studies above, the following study allows vehicles to adopt the evolutionary rules of the deterministic Nagel-Schreckenberg cellular automata traffic model. We have also presented the phase diagrams for the cases of various maximum vehicle velocities. The flow formula in all regions in phase diagrams have also been deduced by the same way of the theoretical method. The theoretical analysis approach used in this dissertation is not only simple but also may be widely used in the study of other bottlenecks.
Last but not least, this dissertation has put forward a two-dimensional cellular automata traffic flow model where vehicles can change lanes:
Based on the classical Biham-Middleton-Levine model, this dissertation has es-tablished a two-dimensional urban traffic flow model where vehicles can change lanes. Comparatively speaking, this model can simulate actual traffic better. By using numer-ical simulations on the square and rectangular grid traffic systems, some new config-uration graphs have been found in free flow regime. In addition, some intermediate stable phases, where jams and freely flowing traffic coexist, have been discovered and stay within larger density range.
引文
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