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Based on the optimal velocity model, with the consideration of the effect of drivers heterogeneity of the disturbance risk appetite, an extended model is proposed. The linear stable judging condition is obtained for the extended model by its stability analysis, which shows the smaller the ratio of the coefficient of the disturbance risk appetite for the former car driver to that for the following-car driver, the larger the stability area of the extended model is. The kink-antikink density wave is attained in an unstable area of the model by nonlinear analysis. Simulation results also show that the smaller the ratio of the coefficient of the disturbance risk appetite for the former car driver to that for the following-car driver, the better it is for the initial traffic flow to inhibit the disturbance propagation, hinder the formation of traffic jams and restore homeostasis. This paper provides a viable idea to reduce traffic congestion, for example, by forming convoys traveling in order from small to big according to the relative size of drivers coefficients of the disturbance risk appetite.
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Keywords:
- traffic congestion /
- the car-following model /
- driversheterogeneity /
- the disturbance risk appetite
[1] Newell G F 1961 Oper. Res. 9 209
[2] Bando M, Hasebe K, Nakyaama A, Shibata A, Sugiyama Y 1995 Phys. Rev. E 51 1035
[3] Nagatani T 1999 Phys. Rev. E 60 6395
[4] Helbing D, Tilch B 1998 Phys. Rev. E 58 133
[5] Jiang R, Wu Q S, Zhu Z J 2001 Phys. Rev. E 64 017101
[6] Jiang R, Wu Q S, Zhu Z J 2000 Chin. Sci. Bull. 45 1895 (in Chineses) [姜锐, 吴清松, 朱祚金 2000 科学通报 45 1895]
[7] Xue Y 2003 Acta Phys. Sin. 52 2750 (in Chinese) [薛郁 2003 物理学报 52 2750]
[8] Xue Y, Dong L Y, Yuan Y W, Dai S Q 2002 Acta Phys. Sin. 51 492 (in Chinese) [薛郁, 董力耘, 袁以武, 戴世强 2002 物理学报 51 492]
[9] Xue Y 2002 Chin. Phys. B 11 1128
[10] Peng G H, Sun D H, He H P 2008 Acta Phys. Sin. 57 7541 (in Chinese) [彭光含, 孙棣华, 何恒攀 2008 物理学报 57 7541]
[11] Peng G H 2011 J. Syst. Engineer. Theory & Practice 31 569 (in Chinese) [彭光含 2011 系统工程理论与实践 31 569]
[12] Peng G H 2010 Chin. Phys. B 19 056401
[13] Peng G H, Sun D H 2009 Chin. Phys. B 18 5420
[14] Wang T, Gao Z Y, Zhao X M 2006 Acta Phys. Sin. 55 634 (in Chinese) [王涛, 高自友, 赵小梅 2006 物理学报 55 634]
[15] Yuan N, Hua C C 2012 Acta Phys. Sin. 61 160509 (in Chinese) [袁娜, 化存才 2012 物理学报 61 160509]
[16] Sun D H, Tian C 2011 Acta Phys. Sin. 60 068901 (in Chinese) [孙棣华, 田川 2011 物理学报 60 068901]
[17] Zhong Y P, Zhang C B, Shi Y H 2010 J. Traffic Information Security 28 17 (in Chinese) [钟益萍, 张存保, 石永辉 2010 交通信息与安全 28 17]
[18] Zhang L D, Jia L, Zhu W X 2012 Acta Phys. Sin. 61 074501 (in Chinese) [张立东, 贾磊, 朱文兴 2012 物理学报 61 074501]
[19] He Z C, Su W B 2013 Acta Phys. Sin. 62 108901 (in Chinese) [何兆成, 孙文博 2013 物理学报 62 108901]
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[1] Newell G F 1961 Oper. Res. 9 209
[2] Bando M, Hasebe K, Nakyaama A, Shibata A, Sugiyama Y 1995 Phys. Rev. E 51 1035
[3] Nagatani T 1999 Phys. Rev. E 60 6395
[4] Helbing D, Tilch B 1998 Phys. Rev. E 58 133
[5] Jiang R, Wu Q S, Zhu Z J 2001 Phys. Rev. E 64 017101
[6] Jiang R, Wu Q S, Zhu Z J 2000 Chin. Sci. Bull. 45 1895 (in Chineses) [姜锐, 吴清松, 朱祚金 2000 科学通报 45 1895]
[7] Xue Y 2003 Acta Phys. Sin. 52 2750 (in Chinese) [薛郁 2003 物理学报 52 2750]
[8] Xue Y, Dong L Y, Yuan Y W, Dai S Q 2002 Acta Phys. Sin. 51 492 (in Chinese) [薛郁, 董力耘, 袁以武, 戴世强 2002 物理学报 51 492]
[9] Xue Y 2002 Chin. Phys. B 11 1128
[10] Peng G H, Sun D H, He H P 2008 Acta Phys. Sin. 57 7541 (in Chinese) [彭光含, 孙棣华, 何恒攀 2008 物理学报 57 7541]
[11] Peng G H 2011 J. Syst. Engineer. Theory & Practice 31 569 (in Chinese) [彭光含 2011 系统工程理论与实践 31 569]
[12] Peng G H 2010 Chin. Phys. B 19 056401
[13] Peng G H, Sun D H 2009 Chin. Phys. B 18 5420
[14] Wang T, Gao Z Y, Zhao X M 2006 Acta Phys. Sin. 55 634 (in Chinese) [王涛, 高自友, 赵小梅 2006 物理学报 55 634]
[15] Yuan N, Hua C C 2012 Acta Phys. Sin. 61 160509 (in Chinese) [袁娜, 化存才 2012 物理学报 61 160509]
[16] Sun D H, Tian C 2011 Acta Phys. Sin. 60 068901 (in Chinese) [孙棣华, 田川 2011 物理学报 60 068901]
[17] Zhong Y P, Zhang C B, Shi Y H 2010 J. Traffic Information Security 28 17 (in Chinese) [钟益萍, 张存保, 石永辉 2010 交通信息与安全 28 17]
[18] Zhang L D, Jia L, Zhu W X 2012 Acta Phys. Sin. 61 074501 (in Chinese) [张立东, 贾磊, 朱文兴 2012 物理学报 61 074501]
[19] He Z C, Su W B 2013 Acta Phys. Sin. 62 108901 (in Chinese) [何兆成, 孙文博 2013 物理学报 62 108901]
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