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With the consideration of the effect of driver anticipation behavior on traffic flow, a new one-dimensional lattice model is proposed. The linear stability condition of the presented model is obtained by employing the linear stability theory. The density wave near the critical stable point is investigated analytically with the nonlinear analysis method. The results show that the occurrence of traffic jamming transitions can be described by the kink-antikink solution of the modified Korteweg-de Vries (mKdV) equation. The good agreement between the simulation results and the analytical results shows that the stability of traffic flow can be enhanced when the effect of driver anticipation behavior is considered.
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Keywords:
- anticipation effect /
- traffic flow /
- lattice model /
- numerical simulation
[1] 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]
[2] Mo Y L, He H D, Xue Y, Shi W, Lu W Z 2008 Chin. Phys. B 17 4446
[3] Tang T Q, Huang H J, Wong S C, Jiang R 2009 Chin. Phys. B 18 975
[4] 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]
[5] Ding J X, Huang H J, Tang T Q 2009 Acta Phys. Sin. 58 7591 (in Chinese) [丁建勋、 黄海军、 唐铁桥 2009 物理学报 58 7591]
[6] Ge H X, Dai S Q, Dong L Y 2008 Chin. Phys. B 17 23
[7] Sun D H, Peng G H 2009 Chin. Phys. B 18 3724
[8] Ge H X, Cheng R J 2008 Physica A 387 6952
[9] Jia B, Li X G, Jiang R, Gao Z Y 2009 Acta Phys. Sin. 58 6845(in Chinese) [贾 斌、 李新刚、 姜 锐、 高自友2009 物理学报58 6845]
[10] Tang T Q, Huang H J, Gao Z Y, Wong S C 2007 Physica A 380 481
[11] Tang T Q, Huang H J, Xu G, Xue Y 2008 Acta Phys. Sin. 57 56 [唐铁桥、 黄海军、 徐 刚、 薛 郁 2008物理学报57 56]
[12] Lighthill M J,Whitham G B 1955 Proc. Roy. Soc. A 229 317
[13] Richards P I 1956 Oper. Res. 4 42
[14] Payne H J 1971 Simul. Coun. Proc. Ser. Math. Sys. 1 51
[15] Whitham G B 1974 Linear and Nonlinear Wave (New York:John Wiley) p65
[16] Nagayani T 1998 Physica A 261 599
[17] Xue Y 2004 Acta Phys. Sin. 53 25 (in Chinese) [薛 郁 2004 物理学报53 25]
[18] Li Z P, Li X L, Liu F Q 2008 Int. J. Mod. Phys. C 19 1163
[19] Peng G H 2010 Acta Phys. Sin. 59 3824 (in Chinese) [彭光含 2010 物理学报59 3824]
[20] Tang T Q, Huang H J, Xue Y 2006 Acta Phys. Sin. 55 4026 (in Chinese) [唐铁桥、 黄海军、 薛 郁 2006物理学报55 4026]
[21] Ge H X, Dai S Q, Xue Y, Dong L Y 2005 Phys. Rev. E 71 066119
[22] Tang T Q, Huang H J, Shang H Y 2010 Phys. Lett. A 374 1668
[23] Chen X Q, Xie W J, Shi J, Shi Q X 2010 Int. J. Mod. Phys.C 21 647
[24] Chen S D, Zhu L H, Kong L J, Liu M R 2007 Acta Phys. Sin. 56 2517(in Chinese)[陈时东、 朱留华、 孔令江、 刘慕仁 2007 物理学报 56 2517 ]
[25] Tang T Q, Huang H J, Wong S C, Jiang R 2008 Acta Mech. Sin. 24 399
[26] Bando M, Hasebe K, Nakayama A, Shibata A , Sugiyama Y 1995 Phys. Rev. E 51 1035
[27] Ge H X, Cheng R H, Dai S Q 2005 Physica A 357 466
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[1] 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]
[2] Mo Y L, He H D, Xue Y, Shi W, Lu W Z 2008 Chin. Phys. B 17 4446
[3] Tang T Q, Huang H J, Wong S C, Jiang R 2009 Chin. Phys. B 18 975
[4] 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]
[5] Ding J X, Huang H J, Tang T Q 2009 Acta Phys. Sin. 58 7591 (in Chinese) [丁建勋、 黄海军、 唐铁桥 2009 物理学报 58 7591]
[6] Ge H X, Dai S Q, Dong L Y 2008 Chin. Phys. B 17 23
[7] Sun D H, Peng G H 2009 Chin. Phys. B 18 3724
[8] Ge H X, Cheng R J 2008 Physica A 387 6952
[9] Jia B, Li X G, Jiang R, Gao Z Y 2009 Acta Phys. Sin. 58 6845(in Chinese) [贾 斌、 李新刚、 姜 锐、 高自友2009 物理学报58 6845]
[10] Tang T Q, Huang H J, Gao Z Y, Wong S C 2007 Physica A 380 481
[11] Tang T Q, Huang H J, Xu G, Xue Y 2008 Acta Phys. Sin. 57 56 [唐铁桥、 黄海军、 徐 刚、 薛 郁 2008物理学报57 56]
[12] Lighthill M J,Whitham G B 1955 Proc. Roy. Soc. A 229 317
[13] Richards P I 1956 Oper. Res. 4 42
[14] Payne H J 1971 Simul. Coun. Proc. Ser. Math. Sys. 1 51
[15] Whitham G B 1974 Linear and Nonlinear Wave (New York:John Wiley) p65
[16] Nagayani T 1998 Physica A 261 599
[17] Xue Y 2004 Acta Phys. Sin. 53 25 (in Chinese) [薛 郁 2004 物理学报53 25]
[18] Li Z P, Li X L, Liu F Q 2008 Int. J. Mod. Phys. C 19 1163
[19] Peng G H 2010 Acta Phys. Sin. 59 3824 (in Chinese) [彭光含 2010 物理学报59 3824]
[20] Tang T Q, Huang H J, Xue Y 2006 Acta Phys. Sin. 55 4026 (in Chinese) [唐铁桥、 黄海军、 薛 郁 2006物理学报55 4026]
[21] Ge H X, Dai S Q, Xue Y, Dong L Y 2005 Phys. Rev. E 71 066119
[22] Tang T Q, Huang H J, Shang H Y 2010 Phys. Lett. A 374 1668
[23] Chen X Q, Xie W J, Shi J, Shi Q X 2010 Int. J. Mod. Phys.C 21 647
[24] Chen S D, Zhu L H, Kong L J, Liu M R 2007 Acta Phys. Sin. 56 2517(in Chinese)[陈时东、 朱留华、 孔令江、 刘慕仁 2007 物理学报 56 2517 ]
[25] Tang T Q, Huang H J, Wong S C, Jiang R 2008 Acta Mech. Sin. 24 399
[26] Bando M, Hasebe K, Nakayama A, Shibata A , Sugiyama Y 1995 Phys. Rev. E 51 1035
[27] Ge H X, Cheng R H, Dai S Q 2005 Physica A 357 466
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