基于元胞自动机和模糊控制的交通流模型研究
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摘要
随着国民经济的发展,人们对各类交通的需求也不断增加,交通问题现在己经成为世界各国最为关注的重要问题之一。交通流理论研究的目标就是要建立能够描述实际交通一般特性的交通流模型,以揭示交通流运动的基本规律,从而预防和缓解交通堵塞,为社会的和谐发展提供基本的保障。开展交通流理论的研究,不仅具有深远的科学意义,而且还具有重要的工程应用价值。
基于元胞自动机的交通流模型作为一种新兴的交通流微观模型,在保留了复杂交通系统的非线性特征的同时,还具备计算机模拟速度快、规则灵活多变等诸多优点,已经被交通科学家广泛采用。
本文在元胞自动机理论的基础上,对元胞自动机交通流模型的建模、仿真以及研究方向等方面进行了研究,主要包括以下内容：
首先,在NS模型的基础上提出了一个改进的元胞自动机模型来模拟周期性边界条件下单车道上的交通流。考虑到不同速度应该有不同的安全车问距、反应时间和减速距离,根据车辆的速度以及车辆与前方跟驰车辆之间的间距来确定该车的运动,这样就可以间接地反映出前方跟驰车辆对当前车辆的影响。通过引入不同的安全间距就可以描述以不同速度运动的车辆接近前方车辆时的减速行为。
由于不同的安全间距的引入,并且考虑到速度的差异,因而可以较好地描述交通流中的不同现象,可以对车辆微观运动进行更合理地描述。
另一方面,为了使基于元胞自动机的交通流模型更加贴近实际,本文探索建立了一种基于模糊控制的元胞自动机模型。考虑到实际交通条件下司机对于速度、距离等信息的感知是模糊的,可以将模糊推理机制引入到车辆的随机慢化过程中。在模糊控制规则中,将当前车辆的车间距和车辆的速度以及驾驶员的反应时间列为模糊控制器的输入元素。经过一系列的模糊推理,最终推算出当前车辆本时刻的随机慢化概率。
通过计算机的仿真,可以发现：与NS模型相比,车辆的随机慢化概率不再是固定不变的,而是根据车辆的间距、车辆的行驶速度以及驾驶员的反应时间所决定的,因此可以更好地体现实际交通环境对司机的驾驶行为的影响。
With the development of national economy, the people's demand of transportation becomes increasingly expanding, traffic problems have became one of the most important issues that concerned by countries all over the world. The aim of traffic flow research is to build traffic flow model which can describe the general properties of the real traffic and to disclose the basic laws of traffic flow. In this way, traffic congestions can be prevented and alleviated, and basic traffic support can be provided to the harmonious development of the society. Thus, researching on traffic flow theory is not only profound scientifically significant, but also valuable for engineering application.
As a kind of emerging traffic flow microscopic models, cellular automaton models based on cellular automaton not only can retain the non-linear characteristics of complex traffic systems, but also are suitable for rapid computer simulations and have flexible rules. Consequently, cellular automaton models have been widely adopted by the traffic scientists.
Based on cellular automaton, this paper has a research on the model building, simulation and direction of the traffic flow model of cellular automaton. The main results achieved in this paper can be summed up as follows.
Firstly, an improved CA model was proposed to describe the traffic flow with a single lane road under the periodic boundary conditions on the basis of NS model. Considering the different speed with the different safety distance, reaction time and deceleration distance, this model claims that the motion of a vehicle at one time step depends on both its headway and the speed of the vehicle, thus including indirectly the influence of its neighboring vehicle. In addition, the different safety distance was introduced to descript the deceleration behavior of vehicles with different speeds.
Since the different safety distance was introduced into this model and differences of speeds were taken into account, this model gives a better description of the phenomena observed in the traffic flow and gives a reasonable depiction of the motion of a single vehicle.
On the other hand, a new cellular automaton model based on fuzzy control is presented in order that the traffic flow based on cellular automaton can be more consistent with true traffic phenomena. Considering that the reactions of drivers to their velocity and distance are fuzzy, fuzzy illation mechanism can be introduced into the randomization process of a single vehicle. In the fuzzy control rules, the distance of the vehicle, the velocity of the vehicle and the time of the diver's reaction are the input. After a succession of fuzzy illation, the randomization deceleration probability of the vehicle at this time can be obtained.
Through computer simulations, compared with the other NS model, we can find that the randomization deceleration probability of the vehicle is not changeless any more, is decided by the distance of the vehicle, the velocity of the vehicle and the time of the diver's reaction. For this reason, the new model based on fuzzy control can reflect the influence of the true traffic environment on the driver.
基于元胞自动机的交通流模型作为一种新兴的交通流微观模型,在保留了复杂交通系统的非线性特征的同时,还具备计算机模拟速度快、规则灵活多变等诸多优点,已经被交通科学家广泛采用。
本文在元胞自动机理论的基础上,对元胞自动机交通流模型的建模、仿真以及研究方向等方面进行了研究,主要包括以下内容：
首先,在NS模型的基础上提出了一个改进的元胞自动机模型来模拟周期性边界条件下单车道上的交通流。考虑到不同速度应该有不同的安全车问距、反应时间和减速距离,根据车辆的速度以及车辆与前方跟驰车辆之间的间距来确定该车的运动,这样就可以间接地反映出前方跟驰车辆对当前车辆的影响。通过引入不同的安全间距就可以描述以不同速度运动的车辆接近前方车辆时的减速行为。
由于不同的安全间距的引入,并且考虑到速度的差异,因而可以较好地描述交通流中的不同现象,可以对车辆微观运动进行更合理地描述。
另一方面,为了使基于元胞自动机的交通流模型更加贴近实际,本文探索建立了一种基于模糊控制的元胞自动机模型。考虑到实际交通条件下司机对于速度、距离等信息的感知是模糊的,可以将模糊推理机制引入到车辆的随机慢化过程中。在模糊控制规则中,将当前车辆的车间距和车辆的速度以及驾驶员的反应时间列为模糊控制器的输入元素。经过一系列的模糊推理,最终推算出当前车辆本时刻的随机慢化概率。
通过计算机的仿真,可以发现：与NS模型相比,车辆的随机慢化概率不再是固定不变的,而是根据车辆的间距、车辆的行驶速度以及驾驶员的反应时间所决定的,因此可以更好地体现实际交通环境对司机的驾驶行为的影响。
With the development of national economy, the people's demand of transportation becomes increasingly expanding, traffic problems have became one of the most important issues that concerned by countries all over the world. The aim of traffic flow research is to build traffic flow model which can describe the general properties of the real traffic and to disclose the basic laws of traffic flow. In this way, traffic congestions can be prevented and alleviated, and basic traffic support can be provided to the harmonious development of the society. Thus, researching on traffic flow theory is not only profound scientifically significant, but also valuable for engineering application.
As a kind of emerging traffic flow microscopic models, cellular automaton models based on cellular automaton not only can retain the non-linear characteristics of complex traffic systems, but also are suitable for rapid computer simulations and have flexible rules. Consequently, cellular automaton models have been widely adopted by the traffic scientists.
Based on cellular automaton, this paper has a research on the model building, simulation and direction of the traffic flow model of cellular automaton. The main results achieved in this paper can be summed up as follows.
Firstly, an improved CA model was proposed to describe the traffic flow with a single lane road under the periodic boundary conditions on the basis of NS model. Considering the different speed with the different safety distance, reaction time and deceleration distance, this model claims that the motion of a vehicle at one time step depends on both its headway and the speed of the vehicle, thus including indirectly the influence of its neighboring vehicle. In addition, the different safety distance was introduced to descript the deceleration behavior of vehicles with different speeds.
Since the different safety distance was introduced into this model and differences of speeds were taken into account, this model gives a better description of the phenomena observed in the traffic flow and gives a reasonable depiction of the motion of a single vehicle.
On the other hand, a new cellular automaton model based on fuzzy control is presented in order that the traffic flow based on cellular automaton can be more consistent with true traffic phenomena. Considering that the reactions of drivers to their velocity and distance are fuzzy, fuzzy illation mechanism can be introduced into the randomization process of a single vehicle. In the fuzzy control rules, the distance of the vehicle, the velocity of the vehicle and the time of the diver's reaction are the input. After a succession of fuzzy illation, the randomization deceleration probability of the vehicle at this time can be obtained.
Through computer simulations, compared with the other NS model, we can find that the randomization deceleration probability of the vehicle is not changeless any more, is decided by the distance of the vehicle, the velocity of the vehicle and the time of the diver's reaction. For this reason, the new model based on fuzzy control can reflect the influence of the true traffic environment on the driver.
引文
[1]张起森,张亚平.道路通行能力分析[M].北京：人民交通出版社,2002：40-48
[2]高自友,任华玲.城市动态交通流分配模型及算法[M].北京：人民交通出版社,2005：70-83
[3]吴清松,蒋锐,李晓白.微宏观方法相结合推进交通流理论新发展[J].交通运输系统工程与信息,2005,5(3)：108-126
[4]Chowdhury D., Santen L., Sehadschneider A. Statistical physics of vehicular traffic and some related systems[J]. Phys. ReP.,2000,329:199-329
[5]姜锐.交通流复杂动态特性的微观和宏观模式研究[D].合肥：中国科学技术大学,2002
[6]翟忠民.道路交通组织优化[M].北京：人民交通出版社,2004：124-140
[7]戴世强,冯苏苇,顾国庆.交通流动力学：它的内容、方法和意义[J].自然杂志,1997,11：196-201
[8]Kerner B. S. Three phase traffic theory and highway capacity[J]. Physica A,2004,333:379-440
[9]Schadschneider A. Traffic flow:a statistical physics point of view[J]. Physica A,2002,313:153-187
[10]贾斌,高自友,李克平,等.基于元胞自动机的交通系统建模与模拟[M].北京：科学出版社,2007：10-130
[11]Wolfram S. Theory and applications of cellular automata[M]. Singapore:World Scientific,1986: 120-145
[12]Wolfram S. Statistical mechanics of cellular automata[J]. Rev. Mod. Phys,1983,55:601-644
[13]Cremer M., Ludwig J. A fast simulation model for traffic flow on the basis of Boolean operations[J]. Mathematics and Computers in Simulation,1986,28:297-303
[14]Nagel K., Schreckenberg M. A cellular automaton model for freeway traffic[J]. Journal of Physics I(France),1992,2:2221-2229
[15]Biham O., Middleton A. A., Levine D. A. Self-organization and a dynamical transition in traffic flow models[J]. Physical Review A,1992,46:6124-6127
[16]Treiterer J. Investigation of traffic dynamics by aerial photogrammetry techniques[J]. Tech. Rep. No. PB 246,094, Ohio State University,1975
[17]Li K. P., Gao Z. Y. Noise-induced phase transition in traffic flow[J]. Commun. Theor. Phys.,2004,42: 369-372
[18]Helbing D. Traffic and related self-driven many particle systems[J]. Rev. Mod. Phys.,2001,73: 1067-1141
[19]Burks A.W. Von Neumann's self-reproducing automata//Burks A.W. Essays on Cellular Automata[J]. University of Illinois Press,1970:3-64
[20]Gardner M. The fantastic combination of John Conway's new solitaire game life[J]. Scientific American,1970,220(4):120-123
[21]Wofram S. A New Kind of Science[M]. Champaign Illinois:Wolfram Media,2002:163-175
[22]LI X. B., WU Q. S., Jiang R. Cellular automaton model considering the velocity effect of a car on the successive car [J]. Physics Review E,2001,64:066128
[23]Barlovic R., Santen L., Schreckenburg A. Metastable states in cellular automata for traffic flow[J]. Eur. Phys. J. B,1998,5:793～800
[24]丹尼尔L.鸠洛夫,马休J.休伯.交通流理论-美国运输科学研究所专题报告165号[M].北京：人民交通出版社,1983：130-153
[25]董力耘,薛郁,戴世强.基于跟车思想的一维元胞自动机交通流模型[J].应用数学和力学,2002,23(4)：331-337
[26]DONG Liyun, XUE Yu, DAI Shiqiang. One-dimension cellular automaton model of traffic flow based on car-following idea[J]. Applied Mathematics and Mechanics,2002,23(4):331-337
[27]葛红霞,戴世强.改进的元胞自动机交通流模型[J].太原理工大学学报,2005,36(6)：721-724
[28]牟勇飚,钟诚文.基于安全驾驶的元胞自动机交通流模型[J].物理学报,2005,54(12)：5597-5560
[29]Lotfi Asker Zadeh. Fuzzy Sets[J]. Information and control,1965,8:338-353
[30]王耀南.智能控制系统(第二版)[M].湖南：湖南大学出版社,2006：15-20
[31]龚永罡,陈涛.基于模糊控制规则的元胞自动机模型[J].计算机应用,2008,28(9)：2366-2368
[32]陈涛.基于元胞自动机的三相交通流理论建模与模拟[D].北京：北京交通大学,2008
[33]赵磊,唐慧佳.基于元胞自动机和模糊控制的交通仿真研究[J].信息技术,2010,11：135-138
[34]赵磊.基于元胞自动机和模糊控制的微观交通仿真研究[D].成都：西南交通大学,2010
[35]周德俭,吴斌.智能控制[M].重庆：重庆大学出版社,2005：5l-55
[36]刘少军.现代控制方法及其计算机辅助设计[M].湖南：中南大学出版社,2003：67-98
[37]刘智勇.智能交通控制理论及其应用[M].北京：科学出版社,2003：127-143
[2]高自友,任华玲.城市动态交通流分配模型及算法[M].北京：人民交通出版社,2005：70-83
[3]吴清松,蒋锐,李晓白.微宏观方法相结合推进交通流理论新发展[J].交通运输系统工程与信息,2005,5(3)：108-126
[4]Chowdhury D., Santen L., Sehadschneider A. Statistical physics of vehicular traffic and some related systems[J]. Phys. ReP.,2000,329:199-329
[5]姜锐.交通流复杂动态特性的微观和宏观模式研究[D].合肥：中国科学技术大学,2002
[6]翟忠民.道路交通组织优化[M].北京：人民交通出版社,2004：124-140
[7]戴世强,冯苏苇,顾国庆.交通流动力学：它的内容、方法和意义[J].自然杂志,1997,11：196-201
[8]Kerner B. S. Three phase traffic theory and highway capacity[J]. Physica A,2004,333:379-440
[9]Schadschneider A. Traffic flow:a statistical physics point of view[J]. Physica A,2002,313:153-187
[10]贾斌,高自友,李克平,等.基于元胞自动机的交通系统建模与模拟[M].北京：科学出版社,2007：10-130
[11]Wolfram S. Theory and applications of cellular automata[M]. Singapore:World Scientific,1986: 120-145
[12]Wolfram S. Statistical mechanics of cellular automata[J]. Rev. Mod. Phys,1983,55:601-644
[13]Cremer M., Ludwig J. A fast simulation model for traffic flow on the basis of Boolean operations[J]. Mathematics and Computers in Simulation,1986,28:297-303
[14]Nagel K., Schreckenberg M. A cellular automaton model for freeway traffic[J]. Journal of Physics I(France),1992,2:2221-2229
[15]Biham O., Middleton A. A., Levine D. A. Self-organization and a dynamical transition in traffic flow models[J]. Physical Review A,1992,46:6124-6127
[16]Treiterer J. Investigation of traffic dynamics by aerial photogrammetry techniques[J]. Tech. Rep. No. PB 246,094, Ohio State University,1975
[17]Li K. P., Gao Z. Y. Noise-induced phase transition in traffic flow[J]. Commun. Theor. Phys.,2004,42: 369-372
[18]Helbing D. Traffic and related self-driven many particle systems[J]. Rev. Mod. Phys.,2001,73: 1067-1141
[19]Burks A.W. Von Neumann's self-reproducing automata//Burks A.W. Essays on Cellular Automata[J]. University of Illinois Press,1970:3-64
[20]Gardner M. The fantastic combination of John Conway's new solitaire game life[J]. Scientific American,1970,220(4):120-123
[21]Wofram S. A New Kind of Science[M]. Champaign Illinois:Wolfram Media,2002:163-175
[22]LI X. B., WU Q. S., Jiang R. Cellular automaton model considering the velocity effect of a car on the successive car [J]. Physics Review E,2001,64:066128
[23]Barlovic R., Santen L., Schreckenburg A. Metastable states in cellular automata for traffic flow[J]. Eur. Phys. J. B,1998,5:793～800
[24]丹尼尔L.鸠洛夫,马休J.休伯.交通流理论-美国运输科学研究所专题报告165号[M].北京：人民交通出版社,1983：130-153
[25]董力耘,薛郁,戴世强.基于跟车思想的一维元胞自动机交通流模型[J].应用数学和力学,2002,23(4)：331-337
[26]DONG Liyun, XUE Yu, DAI Shiqiang. One-dimension cellular automaton model of traffic flow based on car-following idea[J]. Applied Mathematics and Mechanics,2002,23(4):331-337
[27]葛红霞,戴世强.改进的元胞自动机交通流模型[J].太原理工大学学报,2005,36(6)：721-724
[28]牟勇飚,钟诚文.基于安全驾驶的元胞自动机交通流模型[J].物理学报,2005,54(12)：5597-5560
[29]Lotfi Asker Zadeh. Fuzzy Sets[J]. Information and control,1965,8:338-353
[30]王耀南.智能控制系统(第二版)[M].湖南：湖南大学出版社,2006：15-20
[31]龚永罡,陈涛.基于模糊控制规则的元胞自动机模型[J].计算机应用,2008,28(9)：2366-2368
[32]陈涛.基于元胞自动机的三相交通流理论建模与模拟[D].北京：北京交通大学,2008
[33]赵磊,唐慧佳.基于元胞自动机和模糊控制的交通仿真研究[J].信息技术,2010,11：135-138
[34]赵磊.基于元胞自动机和模糊控制的微观交通仿真研究[D].成都：西南交通大学,2010
[35]周德俭,吴斌.智能控制[M].重庆：重庆大学出版社,2005：5l-55
[36]刘少军.现代控制方法及其计算机辅助设计[M].湖南：中南大学出版社,2003：67-98
[37]刘智勇.智能交通控制理论及其应用[M].北京：科学出版社,2003：127-143