具有加权顾前势的交通流模型

郑伟范; 张继业; 王明文; 唐东明

doi:10.7498/aps.63.228901

摘要

交通流随机行为的研究对于理解交通系统的内在演化规律具有重要作用. 基于元胞自动机模型和顾前势模型, 提出了一种考虑加权顾前势的交通流模型. 通过引入顾前势加权系数及对越靠近自身车辆的相互作用势赋予越大的权重, 使得建模过程更符合实际交通中司机根据前面车辆和环境情况进行随机决策的过程. 通过数值模拟, 再现了丰富的高密度交通行为. 仿真结果表明, 加权系数在高密度情况下作用明显, 更有利于在保持较高交通密度的同时, 具有较高的交通流量和道路通行能力.

关键词:

交通流 /
顾前势 /
随机模型 /
加权

Abstract

Research on the stochastic behavior of traffic flow is important to understand the intrinsic evolution rule of traffic system. On the basis of cellular automata model and traffic flow model with look-ahead potential, in this paper, a novel traffic flow model with weighted look-ahead potential is presented. By introducing the weighting coefficient into the look-ahead potential and endowing the potential of vehicle closer to itself with a greater weight, the modeling process is more suitable for the driver's random decision-making process which is based on the vehicle and enviroment situation in front of him in actual traffic. Complex high-density traffic behavior is reproduced by numerical simulations. The simulation results show that the weighting coefficient has an obvious effect on high-density traffic flux, and the weighted model is more conducive to keeping high traffic flux and road capacity while maintaining a high traffic density.

Keywords:

作者及机构信息

1.
西南交通大学, 牵引动力国家重点实验室, 成都 610031;

2.
西南交通大学数学学院, 成都 610031;

3.
西南交通大学信息化研究院, 成都 610031

基金项目: 国家自然科学基金(批准号:11172247,61100118)和四川省科技支撑计划(批准号:2013GZX0166)资助的课题.

Authors and contacts

1.
Traction Power State Key Laboratory, Southwest Jiaotong University, Chengdu 610031, China;

2.
School of Mathematics, Southwest Jiaotong University, Chengdu 610031, China;

3.
Institute of Information Research, Southwest Jiaotong University, Chengdu 610031, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11172247, 61100118), and the Science and Technology support Project of Sichuan Province (Grant No. 2013GZX0166).

参考文献

[1]	Gazis D C 2002 Operat. Res. 50 69
[2]
[3]	Greenshields B N 1934 Proceedings of the 14th Annual Meeting of the Highway Research Board Washington D.C., December 6-7, 1934 Part I. p448
[4]
[5]	Jia B, Gao Z Y, Li K P, Li X G 2007 Models and Simulations of Traffic System Based on the Theory of Cellular Automaton (Beijing: Science Press) pp289-296 (in Chinese) [贾斌, 高自友, 李克平, 李新刚 2007 基于元胞自动机的交通系统建模与模拟 (北京: 科学出版社) 第289296页]
[6]	Cremer M, Ludwig J 1986 Math. Comput. Simulat. 28 297
[7]
[8]	Nagel K, Schreckenberg M 1992 J. Phys. I 2 2221
[9]
[10]
[11]	Benjamin S C, Johnson N F, Hui P M 1996 J. Phys. A: Math. Gen. 29 3119
[12]	Li X B, Wu Q S, Jiang R 2001 Phys. Rev. E 64 066128
[13]
[14]	Barlovic R, Santen L, Schadschneider A, Schrechenberg M 1998 Eur. J. Phys. B 5 793
[15]
[16]	Knospe W, Santen L, Schadschneider A, Schrechenberg M 2000 J. Phys. A 33 L477
[17]
[18]	Knospe W, Santen L, Schadschneider A, Schrechenberg M 2002 Phys. Rev. E 65 056133
[19]
[20]	Jiang R, Wu Q S 2003 J. Phys. A: Math. Gen. 36 381
[21]
[22]
[23]	Mou Y B, Zhong C W 2005 Acta Phys. Sin. 54 5597 (in Chinese) [牟勇飚, 钟诚文 2005 54 5597]
[24]
[25]	Ding J X, Huang H J, Tang T Q 2009 Acta Phys. Sin. 58 7591 (in Chinese) [丁建勋, 黄海军, 唐铁桥 2009 58 7591]
[26]
[27]	Bentaleb K, Jetto K, Ez-Zahraouy H, Benyoussef A 2013 Chin. Phys. B 22 018902
[28]	Xiang Z T, Xiong Li 2013 Chin. Phys. B 22 028901
[29]
[30]
[31]	Sopasakis A, Katsoulakis M A 2006 SIAM J. Appl. Math. 66 92
[32]
[33]	Sopasakis A 2004 Physica A 342 741
[34]
[35]	Alperovich T, Sopasakis A 2008 J. Statist. Phys. 133 1083
[36]
[37]	Sopasakis A 2013 Procedia-Social and Behavioral Sciences 80 837
[38]
[39]	Ni D 2011 Math. Aeterna, Hilaris Ltd. 12 7
[40]
[41]	Ni D 2013 Appl. Math. Sci. 7 1929
[42]
[43]	Ni D 2013 Appl. Math. Sci. 7 1947
[44]
[45]	Ni D 2013 Appl. Math. Sci. 7 1965
[46]
[47]	Hauck C, Sun Y, Timofeyev I 2012 arXiv:1209.5802 [math. PR]
[48]
[49]	Vlachos D G, Katsoulakis M A 2000 Phys. Rev. Lett. 85 3898
[50]	Liggett T M 1985 Interact. Part. Syst. (Berlin: Springer) pp361-413
[51]
[52]
[53]	Lightill M J, Whitham G B 1995 Proc. Roy. Soc. A 229 317

施引文献

[1]	Gazis D C 2002 Operat. Res. 50 69
[2]
[3]	Greenshields B N 1934 Proceedings of the 14th Annual Meeting of the Highway Research Board Washington D.C., December 6-7, 1934 Part I. p448
[4]
[5]	Jia B, Gao Z Y, Li K P, Li X G 2007 Models and Simulations of Traffic System Based on the Theory of Cellular Automaton (Beijing: Science Press) pp289-296 (in Chinese) [贾斌, 高自友, 李克平, 李新刚 2007 基于元胞自动机的交通系统建模与模拟 (北京: 科学出版社) 第289296页]
[6]	Cremer M, Ludwig J 1986 Math. Comput. Simulat. 28 297
[7]
[8]	Nagel K, Schreckenberg M 1992 J. Phys. I 2 2221
[9]
[10]
[11]	Benjamin S C, Johnson N F, Hui P M 1996 J. Phys. A: Math. Gen. 29 3119
[12]	Li X B, Wu Q S, Jiang R 2001 Phys. Rev. E 64 066128
[13]
[14]	Barlovic R, Santen L, Schadschneider A, Schrechenberg M 1998 Eur. J. Phys. B 5 793
[15]
[16]	Knospe W, Santen L, Schadschneider A, Schrechenberg M 2000 J. Phys. A 33 L477
[17]
[18]	Knospe W, Santen L, Schadschneider A, Schrechenberg M 2002 Phys. Rev. E 65 056133
[19]
[20]	Jiang R, Wu Q S 2003 J. Phys. A: Math. Gen. 36 381
[21]
[22]
[23]	Mou Y B, Zhong C W 2005 Acta Phys. Sin. 54 5597 (in Chinese) [牟勇飚, 钟诚文 2005 54 5597]
[24]
[25]	Ding J X, Huang H J, Tang T Q 2009 Acta Phys. Sin. 58 7591 (in Chinese) [丁建勋, 黄海军, 唐铁桥 2009 58 7591]
[26]
[27]	Bentaleb K, Jetto K, Ez-Zahraouy H, Benyoussef A 2013 Chin. Phys. B 22 018902
[28]	Xiang Z T, Xiong Li 2013 Chin. Phys. B 22 028901
[29]
[30]
[31]	Sopasakis A, Katsoulakis M A 2006 SIAM J. Appl. Math. 66 92
[32]
[33]	Sopasakis A 2004 Physica A 342 741
[34]
[35]	Alperovich T, Sopasakis A 2008 J. Statist. Phys. 133 1083
[36]
[37]	Sopasakis A 2013 Procedia-Social and Behavioral Sciences 80 837
[38]
[39]	Ni D 2011 Math. Aeterna, Hilaris Ltd. 12 7
[40]
[41]	Ni D 2013 Appl. Math. Sci. 7 1929
[42]
[43]	Ni D 2013 Appl. Math. Sci. 7 1947
[44]
[45]	Ni D 2013 Appl. Math. Sci. 7 1965
[46]
[47]	Hauck C, Sun Y, Timofeyev I 2012 arXiv:1209.5802 [math. PR]
[48]
[49]	Vlachos D G, Katsoulakis M A 2000 Phys. Rev. Lett. 85 3898
[50]	Liggett T M 1985 Interact. Part. Syst. (Berlin: Springer) pp361-413
[51]
[52]
[53]	Lightill M J, Whitham G B 1995 Proc. Roy. Soc. A 229 317

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