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Complexity analysis of traffic flow based on multi-scale entropy

Xiang Zheng-Tao Chen Yu-Feng Li Yu-Jin Xiong Li

Complexity analysis of traffic flow based on multi-scale entropy

Xiang Zheng-Tao, Chen Yu-Feng, Li Yu-Jin, Xiong Li
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  • Research on the complexity of traffic flow evolution is helpful to deeply understand the evolution rule of traffic flow system, which can provide the theoretical foundation for forecasting and controlling traffic flow. Multi-scale entropy (MSE) method is widely used in the analyses of time series of physiology and traffic of computer networks. Considering the similarity between the vehicle arrival in traffic flow system and the packet arrival in computer network, the complexity of the time headway in braking light model is analyzed to show the complexity of traffic flow evolution by using the MSE method. The analysis results show that the complexity of the time headway decreases with the increase of the time scale, which reflects that it is difficulty to predict the traffic flow in a shorttime. In addition, the difference in the complexity of the time headway between the phases of the free flow and synchronized flow is small when the time scale is small. However, with the increase of the time scale, the MSE of the time headway decreases rapidly for free flow, but rather slowly for synchronized flow. Such a difference can be used as a very important reference to distinguish the synchronized flow and the free flow. Research results in this paper can provide new ideas and methods for investigating the complexity of traffic flow evolution.
    • Funds: Project supported by the National High Technology Research and Development Program of China (Grant No.2012AA101701), the Key Program of the Natural Science Foundation of Hubei Province, China(Grant No. 2013CFA054), and the Shanghai Planning Project of Philosophy and Social Science (Grant No. 2011BTQ001).
    [1]

    Nagel K, Wagner P, Woesler R 2003 Operations Research 51 681

    [2]

    He G G, Ma S T, Feng W G 2002 China Journal of Highway and Transport 15 82 (in Chinese) [贺国光, 马寿峰, 冯蔚东 2002 中国公路学报 15 82]

    [3]

    Pei W L, Li H P 2006 Journal of Highway and Transportation Research and Development 23 115 (in Chinese) [裴玉龙, 李洪萍2006 公路交通科技 23 115]

    [4]

    Meng Q, Khoo H L 2009 Journal of Transportation Engineering-ASCE 135 864

    [5]

    Nair A S, Liu J C, Rilett L, Gupta S 2001 Proceeding of International IEEE Intelligent Transportation Systems Oakland, CA, United states, August 25–29, 2001 p25

    [6]

    Li K P, Gao Z Y 2004 Modern Physics Letters B 18 1395

    [7]

    Lan L W, Sheu J B, Huang Y S 2008 Transportation Research C 16 116

    [8]

    Krese B, Govekar E 2013 Transportation Research C 36 27

    [9]

    Karmakar K, Majumder S K 2008 Applied Mathematics and Computation 195 61

    [10]

    Zhang Y, Guang W 2009 Journal of Traffic and T ransport ation Engineering 9 89 (in Chinese) [张勇, 关伟 2009 交通运输工程学报 9 89]

    [11]

    Yu D, Yin X M, Xie J X 2009 Proceeding of International Conference on Measuring Technology and Mechatronics Automation Zhangjiajie, Hunan, China, April 11–12, 2009 p617

    [12]

    Liao G L, Shang P J 2012 Fractals 20 233

    [13]

    Costa M, Goldberger A L, Peng C K 2002 Physical Review Letters 89 068102

    [14]

    Costa M, Goldberger A L, Peng C K 2005 Physical Review E 71 021906

    [15]

    Petkov V, Rajagopal R, Obraczka K 2013 ACM Transactions on Modeling and Computer Simulation 23 14

    [16]

    Riihijarvi J, Mahonen P, Wellens M 2008 Proceeding of International Conference on Telecommunications St. Petersburg, Russia, June 16–19, 2008 p1

    [17]

    Riihijarvi J, Wellens M, Mahonen P 2009 Proceeding of IEEE International Conference on Computer Communications Rio de Janeiro, Brazil, 2009 April 19-25 p1107

    [18]

    Wang J, Shang P J, Zhao X J, Xia J N 2013 International Journal of Modern Physics C 24 1350006

    [19]

    Pincus S M 1991 Proceedings of the National Academy of Sciences of the United States of America 88 297

    [20]

    Richman J S, Moorman J R 2000 American Journal of Physiology-Heart and Circulatory Physiology 278 2039

    [21]

    Jiang R, Wu Q S 2005 Physical Review E 72 067103

    [22]

    Jiang R, Wu Q S 2005 European Physical Journal B 46 581

    [23]

    Gao K, Jiang R, Hu S X, Wang B H, Wu Q S 2007 Physical Review E 76 026105

    [24]

    Jiang R, Hu M B, Jia B, Wang R L, Wu Q S 2007 Physics Letters A 365 6

    [25]

    Chen S D, Zhu L H, Kong L J, Liu M R 2007 Acta Physica Sinica 56 2517 (in Chinese) [陈时东, 朱留华, 孔令江, 刘慕仁 2007 物理学报 56 2517]

    [26]

    Zhao B H, Hu M B, Jiang R, Wu Q S 2009 Chinese Physics Letters 26 118902

    [27]

    Sheng P, Zhao S L, Wang J F, Tang P, Gao L 2009 Chinese Physics B 18 3347

    [28]

    Ning H X, Xue Y 2012 Chinese Physics B 21 040506

    [29]

    Knospe W, Santen L, Schadschneider A, Schreckenberg M 2000 Journal of Physics A 33 L477

    [30]

    Jiang R, Wu Q S 2003 Journal of Physics A 36 381

    [31]

    Tian J F, Jia B, Li X G, Jiang R, Zhao X M, Gao Z Y 2009 Physica A 388 4827

    [32]

    Xiang Z T, Li Y J, Chen Y F, Xiong L 2013 Physica A 392 5399

    [33]

    Kerner B S 2004 The Physics of Traffic, Springer

    [34]

    Kerner B S 2009 Introduction to Modern Traffic Flow Theory and Control, Springer

  • [1]

    Nagel K, Wagner P, Woesler R 2003 Operations Research 51 681

    [2]

    He G G, Ma S T, Feng W G 2002 China Journal of Highway and Transport 15 82 (in Chinese) [贺国光, 马寿峰, 冯蔚东 2002 中国公路学报 15 82]

    [3]

    Pei W L, Li H P 2006 Journal of Highway and Transportation Research and Development 23 115 (in Chinese) [裴玉龙, 李洪萍2006 公路交通科技 23 115]

    [4]

    Meng Q, Khoo H L 2009 Journal of Transportation Engineering-ASCE 135 864

    [5]

    Nair A S, Liu J C, Rilett L, Gupta S 2001 Proceeding of International IEEE Intelligent Transportation Systems Oakland, CA, United states, August 25–29, 2001 p25

    [6]

    Li K P, Gao Z Y 2004 Modern Physics Letters B 18 1395

    [7]

    Lan L W, Sheu J B, Huang Y S 2008 Transportation Research C 16 116

    [8]

    Krese B, Govekar E 2013 Transportation Research C 36 27

    [9]

    Karmakar K, Majumder S K 2008 Applied Mathematics and Computation 195 61

    [10]

    Zhang Y, Guang W 2009 Journal of Traffic and T ransport ation Engineering 9 89 (in Chinese) [张勇, 关伟 2009 交通运输工程学报 9 89]

    [11]

    Yu D, Yin X M, Xie J X 2009 Proceeding of International Conference on Measuring Technology and Mechatronics Automation Zhangjiajie, Hunan, China, April 11–12, 2009 p617

    [12]

    Liao G L, Shang P J 2012 Fractals 20 233

    [13]

    Costa M, Goldberger A L, Peng C K 2002 Physical Review Letters 89 068102

    [14]

    Costa M, Goldberger A L, Peng C K 2005 Physical Review E 71 021906

    [15]

    Petkov V, Rajagopal R, Obraczka K 2013 ACM Transactions on Modeling and Computer Simulation 23 14

    [16]

    Riihijarvi J, Mahonen P, Wellens M 2008 Proceeding of International Conference on Telecommunications St. Petersburg, Russia, June 16–19, 2008 p1

    [17]

    Riihijarvi J, Wellens M, Mahonen P 2009 Proceeding of IEEE International Conference on Computer Communications Rio de Janeiro, Brazil, 2009 April 19-25 p1107

    [18]

    Wang J, Shang P J, Zhao X J, Xia J N 2013 International Journal of Modern Physics C 24 1350006

    [19]

    Pincus S M 1991 Proceedings of the National Academy of Sciences of the United States of America 88 297

    [20]

    Richman J S, Moorman J R 2000 American Journal of Physiology-Heart and Circulatory Physiology 278 2039

    [21]

    Jiang R, Wu Q S 2005 Physical Review E 72 067103

    [22]

    Jiang R, Wu Q S 2005 European Physical Journal B 46 581

    [23]

    Gao K, Jiang R, Hu S X, Wang B H, Wu Q S 2007 Physical Review E 76 026105

    [24]

    Jiang R, Hu M B, Jia B, Wang R L, Wu Q S 2007 Physics Letters A 365 6

    [25]

    Chen S D, Zhu L H, Kong L J, Liu M R 2007 Acta Physica Sinica 56 2517 (in Chinese) [陈时东, 朱留华, 孔令江, 刘慕仁 2007 物理学报 56 2517]

    [26]

    Zhao B H, Hu M B, Jiang R, Wu Q S 2009 Chinese Physics Letters 26 118902

    [27]

    Sheng P, Zhao S L, Wang J F, Tang P, Gao L 2009 Chinese Physics B 18 3347

    [28]

    Ning H X, Xue Y 2012 Chinese Physics B 21 040506

    [29]

    Knospe W, Santen L, Schadschneider A, Schreckenberg M 2000 Journal of Physics A 33 L477

    [30]

    Jiang R, Wu Q S 2003 Journal of Physics A 36 381

    [31]

    Tian J F, Jia B, Li X G, Jiang R, Zhao X M, Gao Z Y 2009 Physica A 388 4827

    [32]

    Xiang Z T, Li Y J, Chen Y F, Xiong L 2013 Physica A 392 5399

    [33]

    Kerner B S 2004 The Physics of Traffic, Springer

    [34]

    Kerner B S 2009 Introduction to Modern Traffic Flow Theory and Control, Springer

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  • Received Date:  14 October 2013
  • Accepted Date:  10 November 2013
  • Published Online:  05 February 2014

Complexity analysis of traffic flow based on multi-scale entropy

  • 1. School of Electrical and Information Engineering, Hubei University of Automotive Technology, Shiyan 442002, China;
  • 2. School of Management, Shanghai University, Shanghai 200444, China
Fund Project:  Project supported by the National High Technology Research and Development Program of China (Grant No.2012AA101701), the Key Program of the Natural Science Foundation of Hubei Province, China(Grant No. 2013CFA054), and the Shanghai Planning Project of Philosophy and Social Science (Grant No. 2011BTQ001).

Abstract: Research on the complexity of traffic flow evolution is helpful to deeply understand the evolution rule of traffic flow system, which can provide the theoretical foundation for forecasting and controlling traffic flow. Multi-scale entropy (MSE) method is widely used in the analyses of time series of physiology and traffic of computer networks. Considering the similarity between the vehicle arrival in traffic flow system and the packet arrival in computer network, the complexity of the time headway in braking light model is analyzed to show the complexity of traffic flow evolution by using the MSE method. The analysis results show that the complexity of the time headway decreases with the increase of the time scale, which reflects that it is difficulty to predict the traffic flow in a shorttime. In addition, the difference in the complexity of the time headway between the phases of the free flow and synchronized flow is small when the time scale is small. However, with the increase of the time scale, the MSE of the time headway decreases rapidly for free flow, but rather slowly for synchronized flow. Such a difference can be used as a very important reference to distinguish the synchronized flow and the free flow. Research results in this paper can provide new ideas and methods for investigating the complexity of traffic flow evolution.

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