搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

部分道路关闭引起的交通激波特性研究

孙晓燕 朱军芳

引用本文:
Citation:

部分道路关闭引起的交通激波特性研究

孙晓燕, 朱军芳

Study of the shock wave induced by closing partial road in traffic flow

Sun Xiao-Yan, Zhu Jun-Fang
PDF
导出引用
  • 本文根据实际交通中经常遇到的交通事故或部分道路施工等情况, 建立了部分道路关闭的交通流模型. 采用平均场理论分析和确定性NS元胞自动机规则分别对模型进行解析和数值模拟, 结果表明, 系统存在三种稳定的物理状态:低密度相、激波相和高密度相, 并找到了系统发生相变的临界密度. 理论分析和数值模拟能很好地符合.
    There often occurs traffic accident or road construction in real traffic, which leads to partial road closure. In this paper, we set up a traffic model for the partial road closure. According to the Nagel-Schreckenberg (NS) cellular automata update rules, the road can be separated into cells with the same length of 7.5 m. L = 4000 (corresponding to 30 km) is set to the road length in the simulations. For a larger system size, our simulations show that the results are the same with those presented in the following. In our model, vmax rtial road is closed (for convenience, we define the road length as L1), vmax 2= 2 (corresponding to 54 km/h) in the section of normal road (we define the road length as L2). In our simulations, let L1= L2 = 2000. We would like to mention that changing these parameter values does not have a qualitative influence on the simulation results. The simulation results demonstrate that three stationary phases exist, that is, low density (LD), high density (HD) and shock wave (SW). Two critical average densities are found:the critical point ρcr 1= 3/8 separates the LD phase from the SW phase, and ρcr 2= 1/2 separates the SW phase from the HD phase. We also analyze the relationship between the average flux J and average density ρ. In the LD phase J = 4/3ρ, in the HD phase J= 1 -ρ and J is 0.5 in the SW phase. We investigate the dependence of J on ρ. It is shown that with the increase of ρ, J first increases, at this stage J corresponds to the LD phase. Then J remains to be a constant 0.5 when the critical average density ρcr 1 is reached, and J corresponds to the SW phase (this time,J reaches the maximum value 0.5). One goal of traffic-management strategies is to maximize the flow. We find that the optimal choice of the average density is 3/8 ρρcr 2 is reached, J decreases with the increase of average density, which corresponds to the HD phase. We also obtain the relationship between the shock wave position and the average density by theoretical calculations, i.e. Si = i+4-8ρ, which is in agreement with simulations.
    • 基金项目: 国家自然科学基金(批准号:71461002,11402058,11202175)、广西壮族自治区自然科学基金(批准号:2014GXNSFAA118012)和广西高等学校优秀中青年骨干教师培养工程(第一期)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 71461002, 11402058, 11202175), the Natural Science Foundation of Guangxi Province, China (Grant No. 2014GXNSFAA118012), and the project of outstanding young teachers’ training in higher education institutions of Guangxi.
    [1]

    Chowdhury D 2000 Phys. Rep. 329 199

    [2]

    Gao H W, Gao Z Y, Xie D F 2011 Acta Phys. Sin. 60 058902 (in Chinese) [郭宏伟, 高自友, 谢东繁 2011 物理学报 60 058902]

    [3]

    He H D, Lu W Z, Dong L Y 2011 Chin. Phys. B 20 040514

    [4]

    Lakouari N, Ez-Zahraouy H, Benyoussef A 2014 Phys. Lett. A 378 3169

    [5]

    Nagatani T 2014 Physica A 413 352

    [6]

    Tang T Q, Huang H J, Shang H Y 2010 Chin. Phys. B 19 050517

    [7]

    Jia B, Jiang R, Wu Q S 2003 Int. J Mod. Phys. C 14 1295

    [8]

    Zhang L, Du W 2012 J. Wuhan Univ. Tech. 36 886 (in Chinese) [张邻, 杜文 2012 武汉理工大学学报 36 886]

    [9]

    Zhang Ao M H, Gao Z Y 2012 J. Trans. Sys. Engin. Inf. Tech. 12 46 (in Chinese) [张敖木翰, 高自友 2012 交通运输系统工程与信息 12 46]

    [10]

    Qian Y S, Zeng J W, Du J W, Liu Y F, Wang M, Wei J 2011 Acta Phys. Sin. 60 060505 (in Chinese) [钱勇生, 曾俊伟, 杜加, 刘宇斐, 王敏, 魏军 2011 物理学报 60 060505]

    [11]

    Kanai M Phys. Rev. E 2005 72 035102(R)

    [12]

    Yamauchi A, Tanimoto J, Hagishima A, Sagara H 2009 Phys. Rev. E 79 036104

    [13]

    Nakata M, Yamauchi A, Tanimoto J, Hagishima A 2010 , Physica A 389 5353

    [14]

    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) (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)]

    [15]

    Li L, Jiang R, Jia B, Zhao X M 2011 T heory and Application of Modern Traffic flow(Vol. 1)-freeway traffic flow (Beijing:Tsinghua University Press) [李力, 姜锐, 贾斌, 赵小梅 2011 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)]

    [16]

    Sun D 2011 Ph. D. Dissertation (Hefei:University of Science and Technology of Chian) (in Chinese) [孙舵 2011 博士学位论文 (合肥:中国科学技术大学)]

    [17]

    Nagel K, Schreckenberg M 1992 J. Phys. I (France) 2 2221

    [18]

    Sun X Y, Xie Y B, He Z W, Wang B H 2011 Phys. Lett. A 375 2699

    [19]

    Derrida B, Evans M R, Hakim V 1993 J. Phys. A:Math. Gen. 26 1493

  • [1]

    Chowdhury D 2000 Phys. Rep. 329 199

    [2]

    Gao H W, Gao Z Y, Xie D F 2011 Acta Phys. Sin. 60 058902 (in Chinese) [郭宏伟, 高自友, 谢东繁 2011 物理学报 60 058902]

    [3]

    He H D, Lu W Z, Dong L Y 2011 Chin. Phys. B 20 040514

    [4]

    Lakouari N, Ez-Zahraouy H, Benyoussef A 2014 Phys. Lett. A 378 3169

    [5]

    Nagatani T 2014 Physica A 413 352

    [6]

    Tang T Q, Huang H J, Shang H Y 2010 Chin. Phys. B 19 050517

    [7]

    Jia B, Jiang R, Wu Q S 2003 Int. J Mod. Phys. C 14 1295

    [8]

    Zhang L, Du W 2012 J. Wuhan Univ. Tech. 36 886 (in Chinese) [张邻, 杜文 2012 武汉理工大学学报 36 886]

    [9]

    Zhang Ao M H, Gao Z Y 2012 J. Trans. Sys. Engin. Inf. Tech. 12 46 (in Chinese) [张敖木翰, 高自友 2012 交通运输系统工程与信息 12 46]

    [10]

    Qian Y S, Zeng J W, Du J W, Liu Y F, Wang M, Wei J 2011 Acta Phys. Sin. 60 060505 (in Chinese) [钱勇生, 曾俊伟, 杜加, 刘宇斐, 王敏, 魏军 2011 物理学报 60 060505]

    [11]

    Kanai M Phys. Rev. E 2005 72 035102(R)

    [12]

    Yamauchi A, Tanimoto J, Hagishima A, Sagara H 2009 Phys. Rev. E 79 036104

    [13]

    Nakata M, Yamauchi A, Tanimoto J, Hagishima A 2010 , Physica A 389 5353

    [14]

    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) (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)]

    [15]

    Li L, Jiang R, Jia B, Zhao X M 2011 T heory and Application of Modern Traffic flow(Vol. 1)-freeway traffic flow (Beijing:Tsinghua University Press) [李力, 姜锐, 贾斌, 赵小梅 2011 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)]

    [16]

    Sun D 2011 Ph. D. Dissertation (Hefei:University of Science and Technology of Chian) (in Chinese) [孙舵 2011 博士学位论文 (合肥:中国科学技术大学)]

    [17]

    Nagel K, Schreckenberg M 1992 J. Phys. I (France) 2 2221

    [18]

    Sun X Y, Xie Y B, He Z W, Wang B H 2011 Phys. Lett. A 375 2699

    [19]

    Derrida B, Evans M R, Hakim V 1993 J. Phys. A:Math. Gen. 26 1493

  • [1] 张升博, 张焕好, 张军, 毛勇建, 陈志华, 石启陈, 郑纯. 激波与轻质气柱作用过程的磁场抑制特性研究. 物理学报, 2024, 0(0): 0-0. doi: 10.7498/aps.73.20231916
    [2] 贾雷明, 王智环, 王澍霏, 钟巍, 田宙. 二维平面激波折射的理论计算方法. 物理学报, 2023, 72(6): 064701. doi: 10.7498/aps.72.20222042
    [3] 彭旭, 李斌, 王顺尧, 饶国宁, 陈网桦. 激波冲击作用下液膜破碎的气液两相流. 物理学报, 2020, 69(24): 244702. doi: 10.7498/aps.69.20201051
    [4] 易仕和, 陈植. 隔离段激波串流场特征的试验研究进展. 物理学报, 2015, 64(19): 199401. doi: 10.7498/aps.64.199401
    [5] 康瑞, 杨凯. 敏感换道对下匝道系统交通流的影响. 物理学报, 2013, 62(23): 238901. doi: 10.7498/aps.62.238901
    [6] 梁家源, 滕维中, 薛郁. 宏观交通流模型的能耗研究. 物理学报, 2013, 62(2): 024706. doi: 10.7498/aps.62.024706
    [7] 郭宏伟, 高自友, 谢东繁. 城市道路U形转向交通流特性模拟分析. 物理学报, 2011, 60(5): 058902. doi: 10.7498/aps.60.058902
    [8] 梁玉娟, 薛郁. 道路弯道对交通流影响的研究. 物理学报, 2010, 59(8): 5325-5331. doi: 10.7498/aps.59.5325
    [9] 郑容森, 吕集尔, 朱留华, 陈时东, 庞寿全. 主干道交通流的路口效应. 物理学报, 2009, 58(8): 5244-5250. doi: 10.7498/aps.58.5244
    [10] 王健, 李应红, 程邦勤, 苏长兵, 宋慧敏, 吴云. 等离子体气动激励控制激波的机理研究. 物理学报, 2009, 58(8): 5513-5519. doi: 10.7498/aps.58.5513
    [11] 陈时东, 朱留华, 孔令江, 刘慕仁. 优先随机慢化及预测间距对交通流的影响. 物理学报, 2007, 56(5): 2517-2522. doi: 10.7498/aps.56.2517
    [12] 吴钦宽. 一类非线性方程激波解的Sinc-Galerkin方法. 物理学报, 2006, 55(4): 1561-1564. doi: 10.7498/aps.55.1561
    [13] 郭四玲, 韦艳芳, 薛 郁. 元胞自动机交通流模型的相变特性研究. 物理学报, 2006, 55(7): 3336-3342. doi: 10.7498/aps.55.3336
    [14] 黄乒花, 谭惠丽, 孔令江, 刘慕仁. 开放边界条件下二维可转向主干道交通流模型的研究. 物理学报, 2005, 54(7): 3044-3050. doi: 10.7498/aps.54.3044
    [15] 陈燕红, 薛 郁. 随机延迟概率对交通流的影响. 物理学报, 2004, 53(12): 4145-4150. doi: 10.7498/aps.53.4145
    [16] 薛郁. 优化车流的交通流格子模型. 物理学报, 2004, 53(1): 25-30. doi: 10.7498/aps.53.25
    [17] 何枫, 杨京龙, 沈孟育. 激波和剪切层相互作用下的超音速射流. 物理学报, 2002, 51(9): 1918-1922. doi: 10.7498/aps.51.1918
    [18] 谭惠丽, 刘慕仁, 孔令江. 开放边界条件下改进的Nagel-Schreckenberg交通流模型的研究. 物理学报, 2002, 51(12): 2713-2718. doi: 10.7498/aps.51.2713
    [19] 张树东, 张为俊. 激光烧蚀Al靶产生的等离子体中辐射粒子的速度及激波. 物理学报, 2001, 50(8): 1512-1516. doi: 10.7498/aps.50.1512
    [20] 吕晓阳, 孔令江, 刘慕仁. 一维元胞自动机随机交通流模型的宏观方程分析. 物理学报, 2001, 50(7): 1255-1259. doi: 10.7498/aps.50.1255
计量
  • 文章访问数:  4985
  • PDF下载量:  223
  • 被引次数: 0
出版历程
  • 收稿日期:  2014-09-09
  • 修回日期:  2014-11-25
  • 刊出日期:  2015-06-05

/

返回文章
返回