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Curved road traffic flow car-following model and stability analysis

Zhang Li-Dong Jia Lei Zhu Wen-Xing

Curved road traffic flow car-following model and stability analysis

Zhang Li-Dong, Jia Lei, Zhu Wen-Xing
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  • To find the characteristics of curved road traffic flow, we propose a new car-following model based on the typical full velocity difference model, and analyze the model stability condition with system state space method and control system stability criteria. With numerical simulation, the stability and feasibility of the model are proved. Under the condition of same initialization traffic flow density, with the increase of road curve, traffic flow stability decreases. Our study is greatly helpful for traffic control and management at road curve site.
      Corresponding author: , zhanglidong1102@126.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No.61174175), and the Natural Science Foundation of Shandong Province, China (Grant No.Y2008G34), the Postdoctoral Science Foundation of China (Grant No.20100481265), and the Special Foundation for Postdoctoral Innovation Program of Shandong Province (Grant No.201102025).
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    Lighthill M J,Whitham G B 1955 Proc.R.Soc.A 229 317

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    Serge P H,Piet H L 2000 Tran.Res.B 34 123

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    Antoniou I,Ivanova V V,Yu L 2002 Physica A 308 533

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    Zhao J Y,Sun X M,Jia L 2006 Acta Phys.Sin.55 2306 (in Chinese)[赵建玉,孙喜明,贾磊 2006 物理学报 55 230]

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    Newell G F 1961 Oper.Res.9 209

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    Bando M,Hasebe K,Nakayama A,Shibata A Sugiyama Y 1995a Phys.Rev.E 51 1035

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    Bando M,Hasebe K,Nakanishi K,Nakayama A,Shibata A Sugiyama Y 1995b J.Phys.I (France)5 1389

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    Nagatani T 1999 Phys.Rev.E 60 6395

    [12]

    Dirk H,Benno T 1998 Phys.Rev.E 58 133

    [13]

    Jiang R,Wu Q S Zhu Z J,2001 Phys.Rev.E 64 1

    [14]

    Zhao X M Gao Z Y 2007 Physica A 375 679

    [15]

    Zhu W X,Jia L 2008 Commun.Theor.Phys.(Beijing,China)50 505

    [16]

    Yu L,Li T,Shi Z K 2010 Physica A 389 2607

    [17]

    Lei L,Dong L Y,Song T,Dai S Q 2006 Acta Phys.Sin.55 1711 (in Chinese)[雷丽,董力耘,戴世强 2006 物理学报 55 1711]

    [18]

    Ge H X,Cheng R J,Li Z P 2011 Acta Phys.Sin.60 080508(in Chinese)[葛红霞,程荣军,李志鹏 2011 物理学报 60 080508]

    [19]

    Zhou X H,L¨u Y Z 2011 Chin.Phys.B 20 014501

    [20]

    Liang Y J Xue Y 2010 Acta Phys.Sin.59 5326 (in Chinese)[梁玉娟,薛郁 2010 物理学报 59 5326]

  • [1]

    Greenshields B D 1935 Proc.Highway Research Board 18 (Washington,DC:Highway Research Board)448

    [2]

    Lighthill M J,Whitham G B 1955 Proc.R.Soc.A 229 317

    [3]

    Prigogine I,Andrews F C 1960 Oper.Res 8 789

    [4]

    Schiavo M L 2002 Mathematical and computer modeling 35 607

    [5]

    Serge P H,Piet H L 2000 Tran.Res.B 34 123

    [6]

    Antoniou I,Ivanova V V,Yu L 2002 Physica A 308 533

    [7]

    Zhao J Y,Sun X M,Jia L 2006 Acta Phys.Sin.55 2306 (in Chinese)[赵建玉,孙喜明,贾磊 2006 物理学报 55 230]

    [8]

    Newell G F 1961 Oper.Res.9 209

    [9]

    Bando M,Hasebe K,Nakayama A,Shibata A Sugiyama Y 1995a Phys.Rev.E 51 1035

    [10]

    Bando M,Hasebe K,Nakanishi K,Nakayama A,Shibata A Sugiyama Y 1995b J.Phys.I (France)5 1389

    [11]

    Nagatani T 1999 Phys.Rev.E 60 6395

    [12]

    Dirk H,Benno T 1998 Phys.Rev.E 58 133

    [13]

    Jiang R,Wu Q S Zhu Z J,2001 Phys.Rev.E 64 1

    [14]

    Zhao X M Gao Z Y 2007 Physica A 375 679

    [15]

    Zhu W X,Jia L 2008 Commun.Theor.Phys.(Beijing,China)50 505

    [16]

    Yu L,Li T,Shi Z K 2010 Physica A 389 2607

    [17]

    Lei L,Dong L Y,Song T,Dai S Q 2006 Acta Phys.Sin.55 1711 (in Chinese)[雷丽,董力耘,戴世强 2006 物理学报 55 1711]

    [18]

    Ge H X,Cheng R J,Li Z P 2011 Acta Phys.Sin.60 080508(in Chinese)[葛红霞,程荣军,李志鹏 2011 物理学报 60 080508]

    [19]

    Zhou X H,L¨u Y Z 2011 Chin.Phys.B 20 014501

    [20]

    Liang Y J Xue Y 2010 Acta Phys.Sin.59 5326 (in Chinese)[梁玉娟,薛郁 2010 物理学报 59 5326]

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Publishing process
  • Received Date:  30 September 2011
  • Accepted Date:  05 April 2012
  • Published Online:  05 April 2012

Curved road traffic flow car-following model and stability analysis

    Corresponding author: zhanglidong1102@126.com
  • 1. Institute of Control Science and Engineering of Shandong University, Shandong, Jinan 250061, China;
  • 2. Shandong Computer Science Center, Shandong, Jinan 250014, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No.61174175), and the Natural Science Foundation of Shandong Province, China (Grant No.Y2008G34), the Postdoctoral Science Foundation of China (Grant No.20100481265), and the Special Foundation for Postdoctoral Innovation Program of Shandong Province (Grant No.201102025).

Abstract: To find the characteristics of curved road traffic flow, we propose a new car-following model based on the typical full velocity difference model, and analyze the model stability condition with system state space method and control system stability criteria. With numerical simulation, the stability and feasibility of the model are proved. Under the condition of same initialization traffic flow density, with the increase of road curve, traffic flow stability decreases. Our study is greatly helpful for traffic control and management at road curve site.

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