时滞车辆跟驰模型及其分岔现象

徐鉴; 徐荣改

doi:10.6052/1000-0992-12-012

时滞车辆跟驰模型及其分岔现象

doi: 10.6052/1000-0992-12-012

徐鉴,
徐荣改

同济大学航空航天与力学学院, 上海200092

基金项目: 国家自然科学基金重点(11032009),中央高校基本科研业务费专项基金和上海市重点学科(B302)资助项目

详细信息

作者简介:
徐鉴, 男, 1961年12月生. 同济大学教授, 博士生导师, 同济大学航空航天与力学学院副院长, 同济大学航空航天与力学学院力学专业委员会主任, 1994年毕业于天津大学一般力学专业, 获工学博士学位.1996年在北京航空航天大学力学博士后流动站完成第一站博士后研究工作, 1998年在华中理工大学力学博士后流动站完成第二站博士后研究工作. 国家杰出青年基金获得者、上海市领军人才和上海市优秀学科带头人, 兼任中国力学学会动力学与控制专业委员会主任, 上海力学学会秘书长、Theoreticaland Applied Mechanics Letters、《力学季刊》和《动力学与控制学报》副主编.主要研究方向: 非线性动力学, 振动抑制和利用, 神经及其网络动力学

通讯作者:
徐鉴

中图分类号: O322,U491
计量
- 文章访问数: 2100
- HTML全文浏览量: 188
- PDF下载量: 1972
- 被引次数: 0
出版历程
- 收稿日期: 2012-02-19
- 修回日期: 2012-11-19
- 刊出日期: 2013-01-24

REVIEW OF TIME-DELAYED CAR FOLLOWING MODELS AND BIFURCATION PHENOMENA

XU Jian,
XU Ronggai

School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China

Funds: The project was supported by the State Key Program of National Natural Science Foundation of China(11032009),and the Fundamental Research Funds for the Central Universities and Shanghai Leading Academic Discipline Project(B302).

More Information

Corresponding author: XU Jian

摘要

摘要: 交通流车辆跟驰理论中, 由于生理因素, 造成司机在处理前方车辆变化信息和采取应对措施之间存在时间滞后. 即使是在自动巡航控制系统中, 设备在感知信息、计算所需操作并最终作动车辆这一过程中时滞也不可避免. 因此交通流跟驰理论的数学模型本质上应包含时滞. 时滞的存在对各种交通模式的出现及其相互演化产生怎样的影响? 这是值得我们关注的问题. 本文首先综述了各类时间和空间连续的时滞车辆跟驰模型.其次探究这类模型中存在的分岔现象的研究进展, 并指出目前研究中存在的不足. 最后提出作者的一些看法,运用时滞动力系统理论来深入挖掘富含参数的交通流时滞跟驰模型中隐藏的各种的非线性动力学现象, 这样既可以更好解释真实交通中的各种堵塞模式的形成及其演化机制, 又可以结合交通流参数平面内动力学行为从同步观点给出交通堵塞一种分类. 为交通管理部门的交通控制策略制定提供一定的参考依据, 减缓由于司机反应时滞等因素造成的交通堵塞的发生.
- 交通流 /
- 车辆跟驰模型 /
- 时滞 /
- 交通堵塞 /
- 分岔
Abstract: In car following theory of traffic dynamics, human drivers need a finite period of time to process stimuli of preceding vehicles and make a decision, which is attributed to human physiological factors. Since mechanical devices also need time for sensing, computing and actuating, time delay seems unavoidable even in autonomous cruise control systems. As a result time delays should be considered as an inherent factor in car following theories of traffic dynamics. One of the key problems in need of study is how time delays affect the traffic flow patterns and their evolutions. In this paper, time-delayed car following models which are continuous in both time and space are firstly surveyed. Then the progress in the dynamic behaviors based on bifurcation theory is reviewed. Defects of these models and the corresponding bifurcation research are pointed out in this summary. Finally we conclude that research on dynamic behaviors of time-delayed car following models with traffic flow parameters based on bifurcation theory are of great significance and necessity. By means of such research, the underlying mechanisms of traffic jam formation and evolution can be better understood. Traffic jam patterns can be categorized from a synchronization perspective through classifying dynamic behaviors in parameter plane, and hence, different traffic control strategies can be put forward by traffic management department based on the above jam patterns.
- traffic flow /
- car following models /
- time delay /
- traffic jams /
- bifurcation

HTML全文

参考文献(89)

1 Chowdhury D, Santen L, Schadschneider A. Statistical physics of vehicular traffic and some related systems. Physics Reports, 2000, 329: 199-329

2 Helbing D. Traffic and related self-driven many-particle systems. Reviews of Modern Physics, 2001, 73(4): 1067-1141

3 Bellomo N, Delitala M. On the mathematical theory of vehicular traffic flow I. Fluid dynamics and kinetic modeling. Mathematical Models and Methods in Applied Sciences.2002, 12 (12): 1801-1843

4 Shvetsov V I. Mathematical modeling of traffic flows. Automation and Remote Control, 2003, 64(11): 1651-1689

5 Nagatani T. The physics of traffic jams. Reports on Progress in Physics, 2002, 65: 1331-1386

6 Nagel K. Still following: Approaches to traffic flow and traffic jam modeling. Operations Research, 2003, 51(5):685-710

7 Bando M, Hasebe K, Nakanishi K, et al. Delay of vehicle motion in traffic dynamics. Japan J Indust Appl Math,2000, 17: 275-294

8 Green M. “How long does it take to stop?” methodological analysis of driver perception-brake times. Transportation Human Factors, 2000, 2 (3): 95-216

9 Mahmassani H. Transportation and Traffic Theory: Flow, Dynamics and Human Interaction. The Netherlands: Elsevier,2005. 245-266

10 Sipahi R, Niculescu S I. Analytical stability study of a deterministic car following model under multiple delay interactions. At Invited Session Traffic Dynamics under PPresence of Time Delays, IFAC Time Delay Systems Workshop, Italy, 2006

11 Sipahi R, Niculescu S I. Some remarks on the characterization of delay interactions in deterministic car following models, MTNS, Kyoto, Japan, 2006

12 Greenshields B D. Reaction time and automobile driving. Journal of Applied Psychology, 1936, 20:353358

13 Greenshields B D. Reaction time and traffic behavior. Civil Engineering, 1935, 7(6): 384386

14 Davis L C. Modifications of the optimal velocity traffic model to include delay due to driver reaction time. Physica A, 2003, 319: 557-567

15 Mehmood A, Easa S M. Modeling reaction time in carfollowing behaviour based on human factors. International Journal of Applied Science, Engineering and Technology,2009, 5(2): 93-101

16 丹尼尔L. 鸠洛夫著, 蒋璜等译. 交通流理论. 北京: 人民交通出版社, 1983

17 张生瑞, 邵春福, 周伟. 交通流理论与方法. 北京: 中国铁道出社, 2010

18 李力, 姜锐, 贾斌, 等. 现代交通流理论与应用, 卷I—高速公路交通流. 北京: 清华大学出版社, 2011

19 Rothery R E. Traffic Flow Theory, 2nd edn. Transportation Research Board Special Report 165. 1998

20 Subramanian H. Estimation of car following models. Massachusetts Institute of Technology, 1996. 1-93

21 Brackstone M, McDonald M. Car-following: A historical review. Transportation Research Part F 2, 1999, 2(4):181-196

22 Hoogendoorn S P, Bovy P H L. State-of-the-art of vehicular traffic flow modelling. Journal of Systems and Control Engineering, 2001, 25(4): 283-304

23 金春霞, 王慧. 跟车模型及其稳定性分析综述. 交通运输系统工程与信息, 2001, 11(13):220-225

24 张智勇, 荣建, 任福田. 跟车模型研究综述. 公路交通科技,2004, 21(4) :108-113

25 Tamp`ere C. Human-kinetic multiclass trafficflow theory and modelling: With application to advanced driver assistance systems in Congestion. The Netherlands: Thesis Series, 2004

26 Toledo T. Driving behaviour: Models and challenges. Transport Reviews, 2007, 27(1): 65-84

27 Yanlin W, Tiejun W. Car-following models of vehicular traffic. Journal of Zhejiang University Science,2006, 3(4):412-417

28 Baogui C, Zhaosheng Y. Car-following models study progress. In: Proceedings of the Second International Symposium on Knowledge Acquisition and Modeling,2009. 190-193

29 Atay F M. Complex Time Delay Systems. Berlin: Springer, 2010. 297-320

30 Pipes L A. An operational analysis of traffic dynamics. Journal of Applied Physics, 1953, 24(3): 274-281

31 Chandler R E, Herman R, Montroll E W. Traffic dynamics: Analysis of stability in car following.Operations Researsh,1958, 7(1): 165-184

32 Gazis D C, Herman R, Rothery R W. Non-linear follow the leader models of traffic flow. Operations Research,1961, 9: 545-567

33 Zhang X Y, David F J. Stability analysis of the classical car following model. Transpn Res. B,1997, 31(6): 441-462

34 Addison P S, Low D J. A novel nonlinear car following model. Chaos, 1998, 8(4): 791-799

35 Addison P S, Low D J. A nonlinear temporal headway model of traffic dynamics. Nonlinear Dynamics, 1998, 16:127-151

36 凌代俭,肖鹏. 一类非线性车辆跟驰模型的稳定性与分岔特性. 交通运输学报, 2009, 7(4): 6-11

37 Gazis D C, Herman R, Potts R B. Car following theory of steady state traffic flow. Operations Research, 1959.499-505

38 Edie L C. Car following and steady state theory for noncongested traffic. Operations Research, 1961, 9: 66-76

39 Aron M. Car following in an urban network: simulation and experiments. In Proceedings of Seminar D, 16th, PTRC Meeting, 1988. 27-39

40 Bando M, Hasebe K, Nakayama A. Dynamical model of traffic congestion and numerical simulation. Phys. Rev. E, 1995, 51: 1035-1042

41 Bando M, Hasebe K, Nakanishi K, et al. Analysis of optimal velocity model with explicit delay. Phys Rev E, 1998,58: 5429-5435

42 Davis L C. Comment on “Analysis of optimal velocity model with explicit delay”. Phys Rev E, 2002, 66: 038101

43 Orosz G, Wilson R E, Krauskopf B. Global bifurcation investigation of an optimal velocity traffic model with driver reaction time.Phys Rev E, 2004, 70 :026204

44 Orosz G, Wilson R E, Krauskopf B. Bifurcation and multiple trafficjams in a car-following model with reaction-time delay. Physica D, 2005, 211(3-4): 277-293

45 Orosz G, Stepan G. Hopf bifurcation calculations in delayed systems with translational symmetry. J. Nonlinear Sci, 2004, 14: 505-528

46 Orosz G, Stepan G. Subcritical Hopf bifurcations in a carfollowing model with reaction-time delay. Proceedings of the Royal Society of London A, 2006, 462(2073): 2643-2670

47 Orosz G, Krauskopf B, Wilson R E.Traffic jams dynamics in a carfollowing model with reaction-time delay and stochasticity of drivers. Sixth IFAC Workshop on TimeDelay Systems, P Pepe and A Germani eds, IFAC, 2006

48 Orosz G. Exciting traffic jams: Nonlinear phenomena behind traffic jam formation on highways. Phys Rev E, 2009,80: 046205

49 Orosz G, Moehlis J, Bullo F. Robotic reactions: Delayinduced patterns in autonomous vehicle systems. Phys. Rev. E, 2010, 81: 025204

50 Orosz G, Moehlis J, Bullo F, et al. Dynamics of delayed car-following models: human vs. robotic drivers. ENOC2011, Rome, Italy. 2011. 24-29

51 Engelborghs K, Luzyanina T, Roose D. Numerical bifurcation analysis of delay differential equations using DDEBIFTOOL. ACM Transactions on Mathematical Software,2002(2): 1-21

52 Roose D, Szalai R, In Numerical Continuation Methods for Dynamical Systems. Springer, New York, 2007. 359-399

53 Wagner P. Fluid-dynamical and microscopic description of traffic flow: A data-driven comparison. Phil Trans R Soc A, 2011(368): 4481-4495

54 Shamoto D, Tomoeda A, Nishi R, et al. Car-following model with relative-velocity effect and its experimental verification. Phys Rev E 2011, 83: 046105

55 Treiber M, Hennecke A, Helbing D. Congested traffic states in empirical observations and microscopic simulations. Phys. Rev. E, 2000, 62: 1805-1824

56 Treiber M, Kesting A, Helbing D. Delays, inaccuracies and anticipation in microscopic traffic models. Physica A, 2006, 360: 71-88

57 Kesting A, Treiber M, Helbing D. Enhanced intelligent driver model to access the impsct of driving strategies on traffic capacity. Phil Trans R Soc A, 2010(368): 4585-4605

58 Konishi K, Kokame H, Hirata K. Decentralized delayedfeedback control of an optimal velocity traffic model. The European Physical Journal B, 2000, 15: 715-722

59 Herman R, Montroll E W, Potts R B, etal. Traffic dynamics: analysis of stability in car following. Operations Research, 1959, 7 (1): 86-106

60 Lenz H, Wagner C K, Sollacher R. Multi-anticipative carfollowing model. The European Physical Journal B, 1999,7(2): 331-335

61 Sawada S. Nonlinear analysis of a differential-difference equation with next-nearest-neighbour interaction for traffic flow. Journal of Physics A: Mathematical and General,2001, 34: 11253-11259

62 Ge H X, Dai S Q, Dong L Y, et al. Stabilization effect of traffic flow in an extended car-following model based on an intelligent transportation system application. Phys. Rev. E, 2004, 70: 066134

63 Wilson R E, Berg P, Hooper S, et al. Many-neighbour interaction and nonlocality in traffic models. The European Physical Journal B, 2004 39(3): 397-408

64 Lei Y, Zhongke S. Nonlinear analysis of an extended traffic flow model in ITS. Chaos, Solitons and Fractals, 2008,36: 550-558

65 Newell G F. Nonlinear effects in the dynamics of car following. Operations Research, 1961. 207-229

66 Tomer E, Safonov L, Havlin S. Presence of many stable non-homogeneous states in an inertial car following model. Phys. Rev. Lett., 2000, 84: 382-385

67 Safonov L A, Tomer E. Multifractal chaotic attractors in a system of delay differential equations modeling road traffic. Chaos, 2002, 12(4): 1006-1014

68 刘力军, 王春玉, 贺国光. 交通流模型中分岔现象研究综述.系统工程, 2006, 24(8): 23-26

69 Orosz G, Wilson R E, Stepan G. Traffic jams: dynamics and control. Phil Trans R Soc A, 2010, (368): 4455-4479

70 Hermann M, Kerner B S. Local cluster effect in different traffic flow models. Physica A, 1998, 255: 163-188

71 Igarashi Y, Itoh K, Nakanishi K. Bifurcation phenomena in the optimal velocity model for traffic flow, Phys Rev E,2001, 64:047102

72 Gasser I,Sirito G,Werner B. Bifurcation analysis of a class of “car following” traffic models. Physica D, 2004, 197:222-241

73 Gasser I, Sirito G, Werner B. Car following traffic models II: Variable reaction times and aggressive drivers. Bulletin of the Institute of Mathematics Academia Sinica (New Series),2007, 2(2): 587-607

74 Gasser I, Werner B. Dynamical phenomena induced by bottleneck. Phil Trans R soc A, 2010, 368: 4543-4562

75 Sipahi R, Niculescu S I. Slow time-varying delay effects robust stability characterization of deterministic car following models. In: Proceedings of the 2006 IEEE, International Conference on Control Applications, Munich, Germany, 2006

76 Sasoh A. Impact of unsteady disturbance on multi-lane traffic flow. J. Phys. Soc. Jpn., 2002, 71: 989-996

77 Jamison S, McCartney M. A vehicle overtaking model of traffic dynamics. Chaos, 2007, 17: 033116

78 Wilson R E. Mechanisms for spatio-temporal pattern formation in highway traffic models. Phil TransR Soc A,2008, 366: 2017-2032

79 Zhou J, Peng H. Range policy of adaptive cruise control vehicles for improved flow stability and string stability. IEEE Trans Intell Transpor Syst, 2005(6): 229-237

80 Batista M, Twedy E. Optimal velocity functions for carfollowing models. J Zhejiang Univ-Sci A (Appl Phys & Eng), 2010, (7): 520-529

81 Faria T. Normal forms for retarded functional differential equations with parameters and applications to Hopf bifurcation, Journal of Differential Equations, 1995, 122:181-200

82 Das S L, Chatterjee A. Multiple scales without center manifold reductions for delay differential equations near Hopf bifurcations, Nonlinear Dynamics, 2002, 30: 323-335

83 Nayfeh A, Order reduction of retarded nonlinear systemsthe method of multiple scales versus center-manifold reduction. Nonlinear Dynamics, 2008, 51: 483-500

84 Xu J, Chung K W, Chan C L. A perturbation-incremental scheme for studying hopf bifurcation in delay differential systems, Science in China Series E: Technological Sciences,2009, 3: 698-708

85 Schonhof M, Helbing D. Criticism of three-phase traffic theory. Transportation Research Part B, 2009, 43: 784-797

86 Kerner B S. Three-phase traffic theory and highway capacity. Physica A, 2004, 333:379-440

87 Kerner B S. Introduction to Modern Traffic Flow Theory and Control: The Long Road to Three-phase traffic theory. Springer, 2009

88 Boccalettia S, Kurthsc J, Osipovd G, etal. The synchronization of chaotic systems. Physics Reports, 2002, 366:1-101

89 赵艳影, 徐鉴. 利用时滞反馈控制自参数振动系统的振动. 力学学报, 2011, 43(5): 894-904

施引文献

资源附件(0)

访问统计

点击查看大图

计量

文章访问数: 2100
HTML全文浏览量: 188
PDF下载量: 1972
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

留言板

时滞车辆跟驰模型及其分岔现象

doi: 10.6052/1000-0992-12-012

通讯作者:
徐鉴

计量

REVIEW OF TIME-DELAYED CAR FOLLOWING MODELS AND BIFURCATION PHENOMENA

Corresponding author: XU Jian

计量

目录

留言板

时滞车辆跟驰模型及其分岔现象

doi: 10.6052/1000-0992-12-012

通讯作者: 徐鉴

计量

出版历程

REVIEW OF TIME-DELAYED CAR FOLLOWING MODELS AND BIFURCATION PHENOMENA

Corresponding author: XU Jian

计量

出版历程

目录

通讯作者:
徐鉴