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The detrended fluctuation analysis method is applied to analyse the complexity of traffic flow time series and the scale index is obtained, which is a parameter to depict the long term evolutionary behaviour of the mixed traffic flow time series. According to the changes of the scale index, it is shown that the traffic flow time series has long-range correlation characteristics or short-range correlation characteristics. It is found that the traffic flow series shows long-range correlation when the density ρ12; and when ρ1 or ρ>ρ2, the time series displays short-range correlation. That is to say, the vehicle density plays an important role in the changes of the scale index. Additionally, we also found that the ratio of slow vehicles have influence on the changes of the scale index.
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Keywords:
- mixed traffic flow /
- detrended fluctuation analysis /
- time series /
- long-range correlation
[1] Fu Y P, Gao Z Y, Li K P 2007 Acta Phys. Sin. 56 5165 (in Chinese)[付印平、高自友、李克平 2007 物理学报 56 5165]
[2] Guo S L, Wei Y F, Xue Y 2006 Acta Phys. Sin. 55 3336 (in Chinese) [郭四玲、韦艳芳、薛 郁 2006 物理学报 55 3336]
[3] Lei L, Xue Y, Dai S Q 2003 Acta Phys. Sin. 52 2121 (in Chinese) [雷 丽、薛 郁、戴世强 2003 物理学报 52 2121]
[4] Chowdhury D, Santen L, Schadschneider A 2000 Phys.Rep. 329 199
[5] Helbing D 2001 Rev. Mod. Phys. 73 1067
[6] Kerner B S 2004 The Physics of Traffic(New York: Springer)
[7] van Zuylen H J, van Geenhuizen M S, Nijkampvan P 1999 Transportation Research Record 1685 21
[8] Qian Y S, Wang H L, Wang C L 2008 Acta Phys. Sin.57 2115 (in Chinese) [钱勇生、王海龙、王春雷 2008 物理学报 57 2115]
[9] Musha T, Higuchi H 1976 J.Appl.Phys. 15 1271
[10] Sheng P, Zhao S L, Wang J F, Tang P, Gao L 2009 Chin. Phys. B 18 3347
[11] Wang W H, Yu C X, Wen Y Z, Xu Y H, Ling B L, Gong X Z, Liu B H, Wan B N 2001 Chin. Phys. 10 139
[12] Peng C,Buldyrev S, Havlin S 1994 Phys.Rev. E 49 1685
[13] Lubeck S, Schreckenberg M, Usadel K.D 1998 Phys.Rev.E 57 1171
[14] Takayasu M, Takayasu H 1993 Fractals 1 860
[15] Zhang X, Hu G 1995 Phys.Rev.E 52 4664
[16] Tadaki S, Kikuchi M, Sugiyama Y, Sugiyama S 1999 J.Phys.Soc.Jpn. 68 3110
[17] Neubert L, Santen L, Schadschneider A, Schreckenberg M 1999 Phys. Rev. E 60 6480
[18] Vojak Robert 1995 Conference on Vehicle Navigation and Information Systems (VNIS)
[19] Trk J, Kertész J 1996 Physica A 231 515
[20] Kantelhardt J W 2002 Physica A 316 87
[21] Wu J J, Sun H J, Gao Z Y 2008 Phys. Rev.E 78 036103
[22] Yang P, Ho W, Feng G L 2008 Acta Phys. Sin. 57 5333 (in Chinese) [杨 萍、侯 威、封国林 2008 物理学报 57 5333]
[23] He W P, Wu Q, Zhang W, Wang Q G, Zhang Y 2009 Acta Phys. Sin. 58 2862 (in Chinese) [何文平、吴 琼、张 文、王启光、张 勇 2009 物理学报 58 2862]
[24] Kantelhardt J W, Bunde E K, Rego H A, Havlin S, Bunde A 2001 Physica A 441
[25] Wu K F, Kong L J, Liu M R 2006 Acta Phys. Sin. 55 6275 (in Chinese) [吴可非、孔令江、刘慕仁 2006 物理学报 55 6275]
[26] Wang B H, Wang L, Xu B M, Hu B B 2000 Acta Phys. Sin. 49 1926 (in Chinese) [汪秉宏、王雷、许伯铭、胡斑比 2000 物理学报 49 1926]
[27] Guo S L, Wei Y F, Xue Y 2006 Acta Phys. Sin. 55 3336 (in Chinese) [郭四玲、韦艳芳、薛郁 2006 物理学报 55 3336]
[28] Nagel K, Schreckenberg M 1992 J. Phys. I 2 2221
[29] Nagatani T 1994 Physica A 202 449
[30] Rickert M, Nagel K, Schreckenberg M, Latour A 1996 Physica A 231 534
[31] Wagner P, Nagel K, Wolf D E 1997 Physica A 234 687
[32] Nagel K, Wolf D E, Wagner P, Simon P 1998 Phys. Rev. E 58 1425
[33] Chowdhury D, Wolf D.E, Schreckenberg M 1997 Physica A 235 417
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[1] Fu Y P, Gao Z Y, Li K P 2007 Acta Phys. Sin. 56 5165 (in Chinese)[付印平、高自友、李克平 2007 物理学报 56 5165]
[2] Guo S L, Wei Y F, Xue Y 2006 Acta Phys. Sin. 55 3336 (in Chinese) [郭四玲、韦艳芳、薛 郁 2006 物理学报 55 3336]
[3] Lei L, Xue Y, Dai S Q 2003 Acta Phys. Sin. 52 2121 (in Chinese) [雷 丽、薛 郁、戴世强 2003 物理学报 52 2121]
[4] Chowdhury D, Santen L, Schadschneider A 2000 Phys.Rep. 329 199
[5] Helbing D 2001 Rev. Mod. Phys. 73 1067
[6] Kerner B S 2004 The Physics of Traffic(New York: Springer)
[7] van Zuylen H J, van Geenhuizen M S, Nijkampvan P 1999 Transportation Research Record 1685 21
[8] Qian Y S, Wang H L, Wang C L 2008 Acta Phys. Sin.57 2115 (in Chinese) [钱勇生、王海龙、王春雷 2008 物理学报 57 2115]
[9] Musha T, Higuchi H 1976 J.Appl.Phys. 15 1271
[10] Sheng P, Zhao S L, Wang J F, Tang P, Gao L 2009 Chin. Phys. B 18 3347
[11] Wang W H, Yu C X, Wen Y Z, Xu Y H, Ling B L, Gong X Z, Liu B H, Wan B N 2001 Chin. Phys. 10 139
[12] Peng C,Buldyrev S, Havlin S 1994 Phys.Rev. E 49 1685
[13] Lubeck S, Schreckenberg M, Usadel K.D 1998 Phys.Rev.E 57 1171
[14] Takayasu M, Takayasu H 1993 Fractals 1 860
[15] Zhang X, Hu G 1995 Phys.Rev.E 52 4664
[16] Tadaki S, Kikuchi M, Sugiyama Y, Sugiyama S 1999 J.Phys.Soc.Jpn. 68 3110
[17] Neubert L, Santen L, Schadschneider A, Schreckenberg M 1999 Phys. Rev. E 60 6480
[18] Vojak Robert 1995 Conference on Vehicle Navigation and Information Systems (VNIS)
[19] Trk J, Kertész J 1996 Physica A 231 515
[20] Kantelhardt J W 2002 Physica A 316 87
[21] Wu J J, Sun H J, Gao Z Y 2008 Phys. Rev.E 78 036103
[22] Yang P, Ho W, Feng G L 2008 Acta Phys. Sin. 57 5333 (in Chinese) [杨 萍、侯 威、封国林 2008 物理学报 57 5333]
[23] He W P, Wu Q, Zhang W, Wang Q G, Zhang Y 2009 Acta Phys. Sin. 58 2862 (in Chinese) [何文平、吴 琼、张 文、王启光、张 勇 2009 物理学报 58 2862]
[24] Kantelhardt J W, Bunde E K, Rego H A, Havlin S, Bunde A 2001 Physica A 441
[25] Wu K F, Kong L J, Liu M R 2006 Acta Phys. Sin. 55 6275 (in Chinese) [吴可非、孔令江、刘慕仁 2006 物理学报 55 6275]
[26] Wang B H, Wang L, Xu B M, Hu B B 2000 Acta Phys. Sin. 49 1926 (in Chinese) [汪秉宏、王雷、许伯铭、胡斑比 2000 物理学报 49 1926]
[27] Guo S L, Wei Y F, Xue Y 2006 Acta Phys. Sin. 55 3336 (in Chinese) [郭四玲、韦艳芳、薛郁 2006 物理学报 55 3336]
[28] Nagel K, Schreckenberg M 1992 J. Phys. I 2 2221
[29] Nagatani T 1994 Physica A 202 449
[30] Rickert M, Nagel K, Schreckenberg M, Latour A 1996 Physica A 231 534
[31] Wagner P, Nagel K, Wolf D E 1997 Physica A 234 687
[32] Nagel K, Wolf D E, Wagner P, Simon P 1998 Phys. Rev. E 58 1425
[33] Chowdhury D, Wolf D.E, Schreckenberg M 1997 Physica A 235 417
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